Nonlinear electron-magnetohydrodynamic simulations of three dimensional current shear instability
Energy Technology Data Exchange (ETDEWEB)
Jain, Neeraj [Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau (Germany); Das, Amita; Sengupta, Sudip; Kaw, Predhiman [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2012-09-15
This paper deals with detailed nonlinear electron-magnetohydrodynamic simulations of a three dimensional current shear driven instability in slab geometry. The simulations show the development of the instability in the current shear layer in the linear regime leading to the generation of electromagnetic turbulence in the nonlinear regime. The electromagnetic turbulence is first generated in the unstable shear layer and then spreads into the stable regions. The turbulence spectrum shows a new kind of anisotropy in which power transfer towards shorter scales occurs preferentially in the direction perpendicular to the electron flow. Results of the present three dimensional simulations of the current shear instability are compared with those of our earlier two dimensional simulations of sausage instability. It is found that the flattening of the mean velocity profile and thus reduction in the electron current due to generation of electromagnetic turbulence in the three dimensional case is more effective as compared to that in the two dimensional case.
Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations.
Gibbon, J D; Gupta, A; Krstulovic, G; Pandit, R; Politano, H; Ponty, Y; Pouquet, A; Sahoo, G; Stawarz, J
2016-04-01
It is shown how suitably scaled, order-m moments, D_{m}^{±}, of the Elsässer vorticity fields in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P_{M}=1. These vorticity fields are defined by ω^{±}=curlz^{±}=ω±j, where z^{±} are Elsässer variables, and where ω and j are, respectively, the fluid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes fluid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)NONLE50951-771510.1088/0951-7715/27/10/2605]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q^{±} that characterize the inertial range power-law dependencies of the z^{±} energy spectra, E^{±}(k), are then examined, and bounds are obtained. Comments are also made on (a) the generalization of our results to the case P_{M}≠1 and (b) the relation between D_{m}^{±} and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.
Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations
Gibbon, J; Krstulovic, G; Pandit, R; Politano, H; Ponty, Y; Pouquet, A; Sahoo, G; Stawarz, J
2015-01-01
We build on recent developments in the study of fluid turbulence [Gibbon \\textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\\pm}$, of $\\omega^\\pm= \\omega \\pm j$, where $\\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis, for unit magnetic Prandtl number $P_M$, how these moments can be used to identify three possible regimes for solutions of the MHD equations; these regimes are specified by inequalities for $D_m^{\\pm}$ and $D_1^{\\pm}$. We then compare our mathematical results with those from our direct numerical simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its fluid-turbulence counterpart insofar as all solutions, which we have investigated, remain in \\textit{only one of these regimes}; this regime has depleted nonlinearity. We examine the implications of our results for the exponents $q^{\\pm}$ that characterize the power-law dependences of...
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Energy Technology Data Exchange (ETDEWEB)
Jin Chen
2009-12-07
Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.
Beidler, M. T.; Cassak, P. A.; Jardin, S. C.; Ferraro, N. M.
2017-02-01
We diagnose local properties of magnetic reconnection during a sawtooth crash employing the three-dimensional toroidal, extended-magnetohydrodynamic (MHD) code M3D-C1. To do so, we sample simulation data in the plane in which reconnection occurs, the plane perpendicular to the helical (m,n)=(1,1) mode at the q = 1 surface, where m and n are the poloidal and toroidal mode numbers and q is the safety factor. We study the nonlinear evolution of a particular test equilibrium in a non-reduced field representation using both resistive-MHD and extended-MHD models. We find growth rates for the extended-MHD reconnection process exhibit a nonlinear acceleration and greatly exceed that of the resistive-MHD model, as is expected from previous experimental, theoretical, and computational work. We compare the properties of reconnection in the two simulations, revealing the reconnecting current sheets are locally different in the two models and we present the first observation of the quadrupole out-of-plane Hall magnetic field that appears during extended-MHD reconnection in a 3D toroidal simulation (but not in resistive-MHD). We also explore the dependence on toroidal angle of the properties of reconnection as viewed in the plane perpendicular to the helical magnetic field, finding qualitative and quantitative effects due to changes in the symmetry of the reconnection process. This study is potentially important for a wide range of magnetically confined fusion applications, from confirming simulations with extended-MHD effects are sufficiently resolved to describe reconnection, to quantifying local reconnection rates for purposes of understanding and predicting transport, not only at the q = 1 rational surface for sawteeth, but also at higher order rational surfaces that play a role in disruptions and edge-confinement degradation.
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-06-01
Full Text Available A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching/shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM. The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number on the dimensionless velocity, temperature, nanoparticle volume fraction as well as the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations.
Nonlinear Resistivity for Magnetohydrodynamical Models
Lingam, Manasvi; Pfefferlé, David; Comisso, Luca; Bhattacharjee, Amitava
2016-01-01
A nonlinear current-dependent resistivity that accurately accounts for the collisional electron-ion momentum transfer rate is derived. It is shown that the Spitzer resistivity overestimates the resistivity in certain observationally relevant regimes. The nonlinear resistivity computed herein is a strictly decreasing function of the current, in contrast to some notable previous proposals. The relative importance of the new expression with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of this current-dependent resistivity are discussed in the context of plasma systems and phenomena such as magnetic reconnection.
Using high performance Fortran for magnetohydrodynamic simulations
Keppens, R.; Toth, G.
2000-01-01
Two scientific application programs, the Versatile Advection Code (VAC) and the HEating by Resonant Absorption (HERA) code are adapted to parallel computer platforms. Both programs can solve the time-dependent nonlinear partial differential equations of magnetohydrodynamics (MHD) with different nume
Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence
Grete, Philipp; Schmidt, Wolfram; Schleicher, Dominik R G; Federrath, Christoph
2015-01-01
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pre...
Nonlinear magnetohydrodynamics of edge localized mode precursors
Energy Technology Data Exchange (ETDEWEB)
Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)
2015-02-15
A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.
Magnetohydrodynamics simulations on graphics processing units
Wong, Hon-Cheng; Feng, Xueshang; Tang, Zesheng
2009-01-01
Magnetohydrodynamics (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simulations. In this paper we present, to the authors' knowledge, the first implementation to accelerate computation of MHD simulations on GPUs. Numerical tests have been performed to validate the correctness of our GPU MHD code. Performance measurements show that our GPU-based implementation achieves speedups of 2 (1D problem with 2048 grids), 106 (2D problem with 1024^2 grids), and 43 (3D problem with 128^3 grids), respec...
Lattice kinetic simulation of nonisothermal magnetohydrodynamics.
Chatterjee, Dipankar; Amiroudine, Sakir
2010-06-01
In this paper, a lattice kinetic algorithm is presented to simulate nonisothermal magnetohydrodynamics in the low-Mach number incompressible limit. The flow and thermal fields are described by two separate distribution functions through respective scalar kinetic equations and the magnetic field is governed by a vector distribution function through a vector kinetic equation. The distribution functions are only coupled via the macroscopic density, momentum, magnetic field, and temperature computed at the lattice points. The novelty of the work is the computation of the thermal field in conjunction with the hydromagnetic fields in the lattice Boltzmann framework. A 9-bit two-dimensional (2D) lattice scheme is used for the numerical computation of the hydrodynamic and thermal fields, whereas the magnetic field is simulated in a 5-bit 2D lattice. Simulation of Hartmann flow in a channel provides excellent agreement with corresponding analytical results.
Nonlinear magnetohydrodynamics in the Dag confinement configuration
Strauss, H. R.
2004-03-01
The Dag magnetic fusion confinement configuration is a spheromak-like toroidal device. It consists of central vertical current channel, and an outer toroidal chamber with a toroidal current. It has a special magnetic topology. Whether this has consequences for plasma confinement is a motive for this study. A restricted class of computations, using the Multi-level 3D code [Park et al., Phys. Plasmas 6, 1796 (1999)], indicate stability for β<15%. For higher β, the simulations exhibit turbulent magnetic behavior similar to spheromaks and reverse field pinches. A reverse field pinch-like variant should be capable of a less turbulent start up and higher β than the spheromak-like Dag.
Nonlinear wave collapse, shock, and breather formation in an electron magnetohydrodynamic plasma.
Ghosh, Samiran; Chakrabarti, Nikhil
2014-12-01
Low-frequency nonlinear wave dynamics is investigated in a two-dimensional inhomogeneous electron magnetohydrodynamic (EMHD) plasma in the presence of electron viscosity. In the long-wavelength limit, the dynamics of the wave is found to be governed by a novel nonlinear equation. The result of the moving-frame nonlinear analysis is noteworthy, which shows that this nonlinear equation does have a breather solution and electron viscosity is responsible for the breather. A breather is a nonlinear wave in which energy accumulates in a localized and oscillatory manner. Analytical solution and time-dependent numerical simulation of this novel equation reveal the collapse of a soliton (localized pulse) into a weak noise shelf and formation of shocklike structures.
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
Zenitani, Seiji; Hesse, Michael; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten-Lan-van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv enic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond-chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet-Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Magnetohydrodynamic Simulation Code CANS+: Assessments and Applications
Matsumoto, Yosuke; Kudoh, Yuki; Kawashima, Tomohisa; Matsumoto, Jin; Takahashi, Hiroyuki R; Minoshima, Takashi; Zenitani, Seiji; Miyoshi, Takahiro; Matsumoto, Ryoji
2016-01-01
We present a new magnetohydrodynamic (MHD) simulation code with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the HLLD approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one- and two-dimensional problems showed the advantages of using the high-order scheme by comparing with results from a standard second-order TVD scheme. The present code enabled us to explore long-term evolution of a three-dimensional global accretion disk, in which compressible MHD turbulence saturated at much higher levels via the magneto-rotational instability than that given by the second-order scheme owing to the adoption of the high-resolution, nume...
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
Zenitani, Seiji; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten--Lan--van Leer (HLL) method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv\\'{e}nic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond--chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet--Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Computer simulation of a magnetohydrodynamic dynamo. II
Kageyama, Akira; Sato, Tetsuya; Complexity Simulation Group
1995-05-01
A computer simulation of a magnetohydrodynamic dynamo in a rapidly rotating spherical shell is performed. Extensive parameter runs are carried out changing electrical resistivity. When resistivity is sufficiently small, total magnetic energy can grow more than ten times larger than total kinetic energy of convection motion which is driven by an unlimited external energy source. When resistivity is relatively large and magnetic energy is comparable or smaller than kinetic energy, the convection motion maintains its well-organized structure. However, when resistivity is small and magnetic energy becomes larger than kinetic energy, the well-organized convection motion is highly irregular. The magnetic field is organized in two ways. One is the concentration of component parallel to the rotation axis and the other is the concentration of perpendicular component. The parallel component tends to be confined inside anticyclonic columnar convection cells, while the perpendicular component is confined outside convection cells.
NIMROD Resistive Magnetohydrodynamic Simulations of Spheromak Physics
Energy Technology Data Exchange (ETDEWEB)
Hooper, E B; Cohen, B I; McLean, H S; Wood, R D; Romero-Talamas, C A; Sovinec, C R
2007-12-11
The physics of spheromak plasmas is addressed by time-dependent, three-dimensional, resistive magneto-hydrodynamic simulations with the NIMROD code. Included in some detail are the formation of a spheromak driven electrostatically by a coaxial plasma gun with a flux-conserver geometry and power systems that accurately model the Sustained Spheromak Physics Experiment (SSPX) (R. D. Wood, et al., Nucl. Fusion 45, 1582 (2005)). The controlled decay of the spheromak plasma over several milliseconds is also modeled as the programmable current and voltage relax, resulting in simulations of entire experimental pulses. Reconnection phenomena and the effects of current profile evolution on the growth of symmetry-breaking toroidal modes are diagnosed; these in turn affect the quality of magnetic surfaces and the energy confinement. The sensitivity of the simulation results address variations in both physical and numerical parameters, including spatial resolution. There are significant points of agreement between the simulations and the observed experimental behavior, e.g., in the evolution of the magnetics and the sensitivity of the energy confinement to the presence of symmetry-breaking magnetic fluctuations.
Nonlinear Alfv\\'en waves in extended magnetohydrodynamics
Abdelhamid, Hamdi M
2015-01-01
Large-amplitude Alfv\\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfv\\'en wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfv\\'en waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \\small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat differ...
Energy Technology Data Exchange (ETDEWEB)
Greco, A.; Servidio, S. [Dipartimento di Fisica, Universita della Calabria, Rende (Italy); Matthaeus, W. H. [Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, DE (United States); D' Amicis, R. [INAF-Istituto di Fisica dello Spazio Interplanetario, Rome (Italy); Dmitruk, P. [Departamento de Fisica, FCEyN, Universidad de Buenos Aires and IFIBA, CONICET, Pabellon 1, Ciudad Universitaria, Buenos Aires (Argentina)
2012-04-20
The formation of coherent structures in turbulence is a signature of a developing cascade and therefore might be observable by analyzing inner heliospheric solar wind turbulence. To test this idea, data from the Helios 2 mission, for six streams of solar wind at different heliocentric distances and of different velocities, were subjected to statistical analysis using the partial variance of increments (PVI) approach. We see a clear increase of the PVI distribution function versus solar wind age for higher PVI cutoff, indicating development of non-Gaussian coherent structures. The plausibility of this interpretation is confirmed by a similar behavior observed in two-dimensional magnetohydrodynamics simulation data at corresponding dimensionless nonlinear times.
Magneto-hydrodynamics Simulation in Astrophysics
Pang, Bijia
2011-08-01
Magnetohydrodynamics (MHD) studies the dynamics of an electrically conducting fluid under the influence of a magnetic field. Many astrophysical phenomena are related to MHD, and computer simulations are used to model these dynamics. In this thesis, we conduct MHD simulations of non-radiative black hole accretion as well as fast magnetic reconnection. By performing large scale three dimensional parallel MHD simulations on supercomputers and using a deformed-mesh algorithm, we were able to conduct very high dynamical range simulations of black hole accretion of Sgr A* at the Galactic Center. We find a generic set of solutions, and make specific predictions for currently feasible observations of rotation measure (RM). The magnetized accretion flow is subsonic and lacks outward convection flux, making the accretion rate very small and having a density slope of around -1. There is no tendency for the flows to become rotationally supported, and the slow time variability of th! e RM is a key quantitative signature of this accretion flow. We also provide a constructive numerical example of fast magnetic reconnection in a three-dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines and the solution is intrinsically three-dimensional. Approximately 30% of the magnetic energy is released in an event which lasts about one Alfvén time, but only after a delay during which the field lines evolve into a critical configuration. In the co-moving frame of the reconnection regions, reconnection occurs through an X-like point, analogous to the Petschek reconnection. The dynamics appear to be driven by global flows rather than local processes. In addition to issues pertaining to physics, we present results on the acceleration of MHD simulations using heterogeneous computing systems te{shan2006heterogeneous}. We have implemented the MHD code on a variety of heterogeneous and multi-core architectures (multi-core x86, Cell, Nvidia and
Spectral magnetohydrodynamic simulations of the sun and stars
Brun, A. S.
The purpose of this lecture is two fold: first, to describe a powerful numerical technic, namely the spectral method, to solve the compressible (anelastic) magnetohydrodynamic (MHD) equations in spherical geometry and then to discuss some recent numerical applications to study stellar dynamics and magnetism. We thus start by describing the semi-implicit, anelastic spherical harmonic (ASH) code. In this code, the main field variables are projected into spherical harmonics for their horizontal dimensions and into Chebyshev polynomials for their radial direction. We then present, high resolution 3 D MHD simulations of the convective region of A- and G-type stars in spherical shells. We have chosen to model A and G-type stars because they represent good proxies to study and understand stellar dynamics and magnetism given their strikingly different internal “up-side-down” structure and magnetic activity level. In particular, we discuss the nonlinear interactions between turbulent convection, rotation and magnetic fields and the possibility for such flows and fields to lead to dynamo action. We find that both core and envelope turbulent convective zones are efficient at inducing strong mostly non-axisymmetric fields near equipartition but at the expense of damping the differential rotation present in the purely hydrodynamic progenitor solutions.
Ryu, D; Frank, A I; Ryu, Dongsu; Frank, Adam
2000-01-01
We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memo...
Lattice kinetic simulations in three-dimensional magnetohydrodynamics.
Breyiannis, G; Valougeorgis, D
2004-06-01
A lattice kinetic algorithm to simulate three-dimensional (3D) incompressible magnetohydrodynamics is presented. The fluid is monitored by a distribution function, which obeys a scalar kinetic equation, subject to an external force due to the imposed magnetic field. Following the work of J. Comput. Phys. 179, 95 (2002)], the magnetic field is represented by a different three-component vector distribution function, which obeys a corresponding vector kinetic equation. Discretization of the 3D phase space is based on a 19-bit scheme for the hydrodynamic part and on a 7-bit scheme for the magnetic part. Numerical results for magnetohydrodynamic (MHD) flow in a rectangular duct with insulating and conducting walls provide excellent agreement with corresponding analytical solutions. The scheme maintains in all cases tested the MHD constraint inverted Delta.B=0 within machine round-off error.
Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet
Directory of Open Access Journals (Sweden)
Lan Xu
2013-01-01
Full Text Available The variational iteration method (VIM is applied to solve the boundary layer problem of magnetohydrodynamic flow over a nonlinear stretching sheet. The combination of the VIM and the Padé approximants is shown to be a powerful method for solving two-point boundary value problems consisting of systems of nonlinear differential equations. And the comparison of the obtained results with other available results shows that the method is very effective and convenient for solving boundary layer problems.
Numerical Simulations and Diagnostics in Astrophysics:. a Few Magnetohydrodynamics Examples
Peres, Giovanni; Bonito, Rosaria; Orlando, Salvatore; Reale, Fabio
2007-12-01
We discuss some issues related to numerical simulations in Astrophysics and, in particular, to their use both as a theoretical tool and as a diagnostic tool, to gain insight into the physical phenomena at work. We make our point presenting some examples of Magneto-hydro-dynamic (MHD) simulations of astrophysical plasmas and illustrating their use. In particular we show the need for appropriate tools to interpret, visualize and present results in an adequate form, and the importance of spectral synthesis for a direct comparison with observations.
Modelling interplanetary CMEs using magnetohydrodynamic simulations
Directory of Open Access Journals (Sweden)
P. J. Cargill
Full Text Available The dynamics of Interplanetary Coronal Mass Ejections (ICMEs are discussed from the viewpoint of numerical modelling. Hydrodynamic models are shown to give a good zero-order picture of the plasma properties of ICMEs, but they cannot model the important magnetic field effects. Results from MHD simulations are shown for a number of cases of interest. It is demonstrated that the strong interaction of the ICME with the solar wind leads to the ICME and solar wind velocities being close to each other at 1 AU, despite their having very different speeds near the Sun. It is also pointed out that this interaction leads to a distortion of the ICME geometry, making cylindrical symmetry a dubious assumption for the CME field at 1 AU. In the presence of a significant solar wind magnetic field, the magnetic fields of the ICME and solar wind can reconnect with each other, leading to an ICME that has solar wind-like field lines. This effect is especially important when an ICME with the right sense of rotation propagates down the heliospheric current sheet. It is also noted that a lack of knowledge of the coronal magnetic field makes such simulations of little use in space weather forecasts that require knowledge of the ICME magnetic field strength.
Key words. Interplanetary physics (interplanetary magnetic fields Solar physics, astrophysics, and astronomy (flares and mass ejections Space plasma physics (numerical simulation studies
Mamatsashvili, G R; Gogichaishvili, D Z; Chagelishvili, G D; Horton, W
2014-04-01
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity), and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by a transient growth mechanism due to shear flow non-normality. This mechanism appears to be essentially anisotropic in the spectral (wave-number) plane and operates mainly for spatial Fourier harmonics with streamwise wave numbers less than the ratio of flow shear to Alfvén speed, kymagnetohydrodynamic (MHD) turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows: to the bypass concept of subcritical turbulence. The essence of the analyzed nonlinear MHD processes appears to be a transverse redistribution of kinetic and magnetic spectral energies in the wave-number plane [as occurs in the related hydrodynamic flow; see Horton et al., Phys. Rev. E 81, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows.
Smoothed Particle Magnetohydrodynamics Simulations of Protostellar Jets and Turbulent Dynamos
Tricco, Terrence S; Federrath, Christoph; Bate, Matthew R
2013-01-01
We presents results from Smoothed Particle Magnetohydrodynamics simulations of collapsing molecular cloud cores, and dynamo amplification of the magnetic field in the presence of Mach 10 magnetised turbulence. Our star formation simulations have produced, for the first time ever, highly collimated magnetised protostellar jets from the first hydrostatic core phase. Up to 40% of the initial core mass may be ejected through this outflow. The primary difficulty in performing these simulations is maintaining the divergence free constraint of the magnetic field, and to address this issue, we have developed a new divergence cleaning method which has allowed us to stably follow the evolution of these protostellar jets for long periods. The simulations performed of supersonic MHD turbulence are able to exponentially amplify magnetic energy by up to 10 orders of magnitude via turbulent dynamo. To reduce numerical dissipation, a new shock detection algorithm is utilised which is able to track magnetic shocks throughout ...
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Haverkort, J.W. [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam (Netherlands); Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Blank, H.J. de [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Huysmans, G.T.A. [ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance (France); Pratt, J. [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Koren, B., E-mail: b.koren@tue.nl [Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2016-07-01
Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.
Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions
Fang, Tiegang
2014-05-01
In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.
Rayleigh-Taylor instability in Magnetohydrodynamic Simulations of the Crab Nebula
Porth, Oliver; Keppens, Rony
2014-01-01
In this paper we discuss the development of Rayleigh-Taylor filaments in axisymmetric simulations of Pulsar wind nebulae (PWN). High-resolution adaptive mesh refinement magnetohydrodynamic (MHD) simulations are used to resolve the non-linear evolution of the instability. The typical separation of filaments is mediated by the turbulent flow in the nebula and hierarchical growth of the filaments. The strong magnetic dissipation and field-randomization found in recent global three-dimensional simulations of PWN suggests that magnetic tension is not strong enough to suppress the growth of RT filaments, in agreement with the observations of prominent filaments in the Crab nebula. The long-term axisymmetric results presented here confirm this finding.
Haverkort, J. W.; de Blank, H. J.; Huysmans, G. T. A.; Pratt, J.; Koren, B.
2016-01-01
Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more c
Efficient magnetohydrodynamic simulations on graphics processing units with CUDA
Wong, Hon-Cheng; Wong, Un-Hong; Feng, Xueshang; Tang, Zesheng
2011-10-01
Magnetohydrodynamic (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simulations. In this paper we present, to the best of the author's knowledge, the first implementation of MHD simulations entirely on GPUs with CUDA, named GPU-MHD, to accelerate the simulation process. GPU-MHD supports both single and double precision computations. A series of numerical tests have been performed to validate the correctness of our code. Accuracy evaluation by comparing single and double precision computation results is also given. Performance measurements of both single and double precision are conducted on both the NVIDIA GeForce GTX 295 (GT200 architecture) and GTX 480 (Fermi architecture) graphics cards. These measurements show that our GPU-based implementation achieves between one and two orders of magnitude of improvement depending on the graphics card used, the problem size, and the precision when comparing to the original serial CPU MHD implementation. In addition, we extend GPU-MHD to support the visualization of the simulation results and thus the whole MHD simulation and visualization process can be performed entirely on GPUs.
A new framework for magnetohydrodynamic simulations with anisotropic pressure
Hirabayashi, Kota; Amano, Takanobu
2016-01-01
We describe a new theoretical and numerical framework of the magnetohydrodynamic simulation incorporated with an anisotropic pressure tensor, which can play an important role in a collisionless plasma. A classical approach to handle the anisotropy is based on the double adiabatic approximation assuming that a pressure tensor is well described only by the components parallel and perpendicular to the local magnetic field. This gyrotropic assumption, however, fails around a magnetically neutral region, where the cyclotron period may get comparable to or even longer than a dynamical time in a system, and causes a singularity in the mathematical expression. In this paper, we demonstrate that this singularity can be completely removed away by the combination of direct use of the 2nd-moment of the Vlasov equation and an ingenious gyrotropization model. Numerical tests also verify that the present model properly reduces to the standard MHD or the double adiabatic formulation in an asymptotic manner under an appropria...
Zaliznyak, Yu A; Goedbloed, J P; Zaliznyak, Yu.
2003-01-01
We present a numerical study of an idealized magnetohydrodynamic (MHD) configuration consisting of a planar wake flow embedded into a three-dimensional (3D) sheared magnetic field. Our simulations investigate the possibility for in-situ development of large-scale compressive disturbances at cospatial current sheet -- velocity shear regions in the heliosphere. Using a linear MHD solver, we first systematically chart the destabilized wavenumbers, corresponding growth rates, and physical parameter ranges for dominant 3D sinuous-type instabilities in an equilibrium wake--current sheet system. Wakes bounded by sufficiently supersonic (Mach number $M_s > 2.6$) flow streams are found to support dominant fully 3D sinuous instabilities when the plasma beta is of order unity. Fully nonlinear, compressible 2.5D and 3D MHD simulations show the self-consistent formation of shock fronts of fast magnetosonic type. They carry density perturbations far away from the wake's center. Shock formation conditions are identified in ...
COMPARISONS OF COSMOLOGICAL MAGNETOHYDRODYNAMIC GALAXY CLUSTER SIMULATIONS TO RADIO OBSERVATIONS
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Xu Hao; Li Hui; Collins, David C. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Govoni, Federica; Murgia, Matteo [INAF-Osservatorio Astronomico di Cagliari, Poggio dei Pini, Strada 54, I-09012 Capoterra (Italy); Norman, Michael L. [Center for Astrophysics and Space Science, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States); Cen Renyue [Department of Astrophysical Science, Princeton University, Princeton, NJ 08544 (United States); Feretti, Luigina; Giovannini, Gabriele, E-mail: hao_xu@lanl.gov, E-mail: hli@lanl.gov, E-mail: dccollins@lanl.gov, E-mail: mlnorman@ucsd.edu, E-mail: fgovoni@oa-cagliari.inaf.it, E-mail: matteo@oa-cagliari.inaf.it, E-mail: cen@astro.princeton.edu, E-mail: lferetti@ira.inaf.it, E-mail: ggiovann@ira.inaf.it [INAF-Istituto di Radioastronomia, Via P.Gobetti 101, I-40129 Bologna (Italy)
2012-11-01
Radio observations of galaxy clusters show that there are {mu}G magnetic fields permeating the intracluster medium (ICM), but it is hard to accurately constrain the strength and structure of the magnetic fields without the help of advanced computer simulations. We present qualitative comparisons of synthetic Very Large Array observations of simulated galaxy clusters to radio observations of Faraday rotation measure (RM) and radio halos. The cluster formation is modeled using adaptive mesh refinement magnetohydrodynamic simulations with the assumption that the initial magnetic fields are injected into the ICM by active galactic nuclei (AGNs) at high redshift. In addition to simulated clusters in Xu et al., we present a new simulation with magnetic field injections from multiple AGNs. We find that the cluster with multiple injection sources is magnetized to a similar level as in previous simulations with a single AGN. The RM profiles from simulated clusters, both |RM| and the dispersion of RM ({sigma}{sub RM}), are consistent at a first order with the radial distribution from observations. The correlations between the {sigma}{sub RM} and X-ray surface brightness from simulations are in a broad agreement with the observations, although there is an indication that the simulated clusters could be slightly overdense and less magnetized with respect to those in the observed sample. In addition, the simulated radio halos agree with the observed correlations between the radio power versus the cluster X-ray luminosity and between the radio power versus the radio halo size. These studies show that the cluster-wide magnetic fields that originate from AGNs and are then amplified by the ICM turbulence match observations of magnetic fields in galaxy clusters.
Nonlinear magnetohydrodynamics. Progress report, December 15, 1977--December 14, 1978
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Vahala, G.
1978-01-01
Incompressible MHD turbulence is considered for both 2D and 3D plasmas in cylindrical geometry. It is found that for virtually all initial conditions (including quiescent ones) the plasma is nonlinearly unstable in that mean square turbulent velocity fields develop. However, there is a unique stable state of extremal magnetic helicity/energy ratio for which no turbulent fields develop (in 2D with B/sub z/ = const., it is the state of extremal mean square vector potential/energy). It is force free and is just the Taylor state. A conjecture can be put forward (based on a dual cascade argument for resistive MHD) to explain Taylor's hypothesis. In spherical geometry, the stable axisymmetric state is the spheromak.
Simulations and Transport Models for Imbalanced Magnetohydrodynamic Turbulence
Ng, Chung-Sang; Dennis, T.
2016-10-01
We present results from a series of three-dimensional simulations of magnetohydrodynamic (MHD) turbulence based on reduced MHD equations. Alfven waves are launched from both ends of a long tube along the background uniform magnetic field so that turbulence develops due to collision between counter propagating Alfven waves in the interior region. Waves are launched randomly with specified correlation time Tc such that the length of the tube, L, is greater than (but of the same order of) VA *Tc such that turbulence can fill most of the tube. While waves at both ends are launched with equal power, turbulence generated is imbalanced in general, with normalized cross-helicity gets close to -1 at one end and 1 at the other end. This simulation setup allows easier comparison of turbulence properties with one-dimensional turbulence transport models, which have been applied rather successfully in modeling solar wind turbulence. However, direct comparison of such models with full simulations of solar wind turbulence is difficult due to much higher level of complexity involved. We will present our latest simulations at different resolutions with decreasing dissipation (resistivity and viscosity) levels and compare with model outputs from turbulence transport models. This work is supported by a NASA Grant NNX15AU61G.
Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow
Hagan, Jonathan
2013-01-01
The present study is concerned with the stability of a flow of viscous conducting liquid driven by pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Although the magnetic field has a strong stabilizing effect, this flow, similarly to its hydrodynamic counterpart -- plane Poiseuille flow, is known to become turbulent significantly below the threshold predicted by linear stability theory. We investigate the effect of the magnetic field on 2D nonlinear travelling-wave states which are found at substantially subcritical Reynolds numbers starting from $Re_n=2939$ without the magnetic field and from $Re_n\\sim6.50\\times10^3Ha$ in a sufficiently strong magnetic field defined by the Hartmann number $Ha.$ Although the latter value is by a factor of seven lower than the linear stability threshold $Re_l\\sim4.83\\times10^4Ha$,it is still more by an order of magnitude higher than the experimentally observed value for the onset of turbulence in this flow.
Observations and Simulations of Magnetohydrodynamic Turbulence in the Solar Wind
Goldstein, M. L.
2006-12-01
Alfvénic fluctuations are a ubiquitous component of the solar wind. Evidence from many spacecraft indicates that the fluctuations are convected out of the solar corona with relatively flat power spectra and constitute a source of free energy for a turbulent cascade of magnetic and kinetic energy to high wave numbers. Observations and simulations support the conclusion that the cascade evolves most rapidly in the vicinity of velocity shears and current sheets. Numerical solutions of the magnetohydrodynamic equations have elucidated the role of expansion on the evolution of the turbulence. Such studies are clarifying not only how a turbulent cascade develops, but also the nature of the symmetries of the turbulence. Of particular interest is the origin of the two-component correlation function of magnetic fluctuations that was deduced from ISEE-3 data. A central issue to be resolved is whether the correlation function indicates the existence of a quasi-two- dimensional component of the turbulence, or reflects another origin, such as pressure-balanced structures or small velocity shears. In our efforts to simulate solar wind turbulence we have included a tilted rotating current heliospheric sheet as well as variety of waves (e.g., Alfvénic, quasi-two-dimensional, pressure balance structures) and microstreams. These simulations have replicated many of the observations, but challenges remain.
Three-Dimensional Magnetohydrodynamic Simulations of the Crab Nebula
Porth, Oliver; Keppens, Rony
2013-01-01
In this paper we give a detailed account of the first 3D relativistic magnetohydrodynamic (MHD) simulations of Pulsar Wind Nebulae (PWN), with parameters most suitable for the Crab Nebula. In order to clarify the new features specific to 3D models, reference 2D simulations have been carried out as well. Compared to the previous 2D simulations, we considered pulsar winds with much stronger magnetisation, up to \\sigma=3, and accounted more accurately for the anticipated magnetic dissipation in the striped zone of these winds. While the 3D models preserve the separation of the post termination shock flow into the equatorial and polar components, their relative strength and significance differ. Whereas the highly magnetised 2D models produce highly coherent and well collimated polar jets capable of efficient "drilling" through the supernova shell, in the corresponding 3D models the jets are disrupted by the kink mode current driven instability and "dissolve" into the main body of PWN after propagation of several ...
On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir
2016-06-01
This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter.
Analytical Investigation of Magnetohydrodynamic Flow over a Nonlinear Porous Stretching Sheet
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Fazle Mabood
2016-01-01
Full Text Available We investigated the magnetohydrodynamic (MHD boundary layer flow over a nonlinear porous stretching sheet with the help of semianalytical method known as optimal homotopy asymptotic method (OHAM. The effects of different parameters on fluid flow are investigated and discussed. The obtained results are compared with numerical Runge-Kutta-Fehlberg fourth-fifth-order method. It is found that the OHAM solution agrees well with numerical as well as published data for different assigned values of parameters; this thus indicates the feasibility of the proposed method (OHAM.
Flux canceling in three-dimensional radiative magnetohydrodynamic simulations
Thaler, Irina; Spruit, H. C.
2017-05-01
We aim to study the processes involved in the disappearance of magnetic flux between regions of opposite polarity on the solar surface using realistic three-dimensional (3D) magnetohydrodynamic (MHD) simulations. "Retraction" below the surface driven by magnetic forces is found to be a very effective mechanism of flux canceling of opposite polarities. The speed at which flux disappears increases strongly with initial mean flux density. In agreement with existing inferences from observations we suggest that this is a key process of flux disappearance within active complexes. Intrinsic kG strength concentrations connect the surface to deeper layers by magnetic forces, and therefore the influence of deeper layers on the flux canceling process is studied. We do this by comparing simulations extending to different depths. For average flux densities of 50 G, and on length scales on the order of 3 Mm in the horizontal and 10 Mm in depth, deeper layers appear to have only a mild influence on the effective rate of diffusion.
SOLAR WIND COLLISIONAL AGE FROM A GLOBAL MAGNETOHYDRODYNAMICS SIMULATION
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Chhiber, R; Usmanov, AV; Matthaeus, WH [Department of Physics and Astronomy and Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Goldstein, ML [NASA Goddard Space Flight Center, Greenbelt MD 20771 (United States)
2016-04-10
Simple estimates of the number of Coulomb collisions experienced by the interplanetary plasma to the point of observation, i.e., the “collisional age”, can be usefully employed in the study of non-thermal features of the solar wind. Usually these estimates are based on local plasma properties at the point of observation. Here we improve the method of estimation of the collisional age by employing solutions obtained from global three-dimensional magnetohydrodynamics simulations. This enables evaluation of the complete analytical expression for the collisional age without using approximations. The improved estimation of the collisional timescale is compared with turbulence and expansion timescales to assess the relative importance of collisions. The collisional age computed using the approximate formula employed in previous work is compared with the improved simulation-based calculations to examine the validity of the simplified formula. We also develop an analytical expression for the evaluation of the collisional age and we find good agreement between the numerical and analytical results. Finally, we briefly discuss the implications for an improved estimation of collisionality along spacecraft trajectories, including Solar Probe Plus.
General relativistic magnetohydrodynamic simulations of collapsars: Rotating black hole cases
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Mizuno, Y. [Kyoto Univ., Kyoto (Japan). Department of Astronomy; Yamada, S. [Waseda Univ., Tokyo (Japan). Science and Engineering; Koide, S. [Toyama Univ., Toyama (Japan). Department of Engineering; Shibata, K. [Kyoto Univ., Kyoto (Japan). Kwasan and Hida Observatory
2005-06-01
We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of coIIapsars including a rotating black hole. InitiaIIy, we assume that the care collapse has failed in this star. A rotating black hole of a few solar masses is inserted by hand into the calculation. The simulation results show the formation of a diskIike structure and the generation of a jetIike outflow near the central black hole. The jetIike outflow propagates and accelerated mainly by the magnetic field. The total jet velocity is {approx} 0.3c. When the rotation of the black hole is faster, the magnetic field is twisted strongly owing to the frame-dragging effect. The magnetic energy stored by the twisting magnetic field is directly converted to kinetic energy of the jet rather than propagating as an Alfven wave. Thus, as the rotation of the black hole becomes faster, the poloidal velocity of the jet becomes faster.
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Raphaldini, Breno; Raupp, Carlos F. M., E-mail: brenorfs@gmail.com, E-mail: carlos.raupp@iag.usp.br [Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Geofísica, Rua do Matão, 1226-Cidade Universitária São Paulo-SP 05508-090 (Brazil)
2015-01-20
The solar dynamo is known to be associated with several periodicities, with the nearly 11/22 yr cycle being the most pronounced one. Even though these quasiperiodic variations of solar activity have been attributed to the underlying dynamo action in the Sun's interior, a fundamental theoretical description of these cycles is still elusive. Here, we present a new possible direction in understanding the Sun's cycles based on resonant nonlinear interactions among magnetohydrodynamic (MHD) Rossby waves. The WKB theory for dispersive waves is applied to magnetohydrodynamic shallow-water equations describing the dynamics of the solar tachocline, and the reduced dynamics of a resonant triad composed of MHD Rossby waves embedded in constant toroidal magnetic field is analyzed. In the conservative case, the wave amplitudes evolve periodically in time, with periods on the order of the dominant solar activity timescale (∼11 yr). In addition, the presence of linear forcings representative of either convection or instabilities of meridionally varying background states appears to be crucial in balancing dissipation and thus sustaining the periodic oscillations of wave amplitudes associated with resonant triad interactions. Examination of the linear theory of MHD Rossby waves embedded in a latitudinally varying mean flow demonstrates that MHD Rossby waves propagate toward the equator in a waveguide from –35° to 35° in latitude, showing a remarkable resemblance to the structure of the butterfly diagram of the solar activity. Therefore, we argue that resonant nonlinear magnetohydrodynamic Rossby wave interactions might significantly contribute to the observed cycles of magnetic solar activity.
Magnetohydrodynamical simulations of a tidal disruption in general relativity
Sadowski, A; Gafton, E; Rosswog, S; Abarca, D
2015-01-01
We perform hydro- and magnetohydrodynamical general relativistic simulations of a tidal disruption of a $0.1\\,M_\\odot$ red dwarf approaching a $10^5\\,M_\\odot$ non-rotating massive black hole on a close (impact parameter $\\beta=10$) elliptical (eccentricity $e=0.97$) orbit. We track the debris self-interaction, circularization, and the accompanying accretion through the black hole horizon. We find that the relativistic precession leads to the formation of a self-crossing shock. The dissipated kinetic energy heats up the incoming debris and efficiently generates a quasi-spherical outflow. The self-interaction is modulated because of the feedback exerted by the flow on itself. The debris quickly forms a thick, almost marginally bound disc that remains turbulent for many orbital periods. Initially, the accretion through the black hole horizon results from the self-interaction, while in the later stages it is dominated by the debris originally ejected in the shocked region, as it gradually falls back towards the h...
Magnetohydrodynamic simulation of the inverse-pinch plasma discharge
Esaulov, A.; Bauer, B. S.; Lindemuth, I. R.; Makhin, V.; Presura, R.; Ryutov, D. D.; Sheehey, P. T.; Siemon, R. E.; Sotnikov, V. I.
2004-04-01
A wall confined plasma in an inverse-pinch configuration holds potential as a plasma target for Magnetized Target Fusion (MTF) as well as a simple geometry to study wall-confined plasma. An experiment is planned to study the inverse-pinch configuration using the Zebra Z pinch [B. S. Bauer et al., AIP Conference Proceedings Vol. 409 (American Institute of Physics, Melville, 1997), p. 153] of the Nevada Terawatt Facility at the University of Nevada, Reno (UNR). The dynamics of the discharge formation have been analyzed using analytic models and numerical methods. Strong heating occurs by thermalization of directed energy when an outward moving current sheet (the inverse pinch effect) collides with the outer wall of the experimental chamber. Two-dimensional magnetohydrodynamic simulations show Rayleigh-Taylor and Richtmyer-Meshkov like modes of instability, as expected because of the shock acceleration during plasma formation phase. The instabilities are not disruptive, but give rise to a mild level of turbulence. The conclusion from this work is that an interesting experiment relevant to wall confinement for MTF could be done using existing equipment at UNR.
Coupled neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
Lyons, Brendan C.
2014-10-01
Neoclassical effects (e.g., the bootstrap current and neoclassical toroidal viscosity [NTV]) have a profound impact on many magnetohydrodynamic (MHD) instabilities, including tearing modes, edge-localized modes (ELMs), and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We present the first results of the DK4D code, a dynamic drift-kinetic equation (DKE) solver being developed for this application. In this study, DK4D solves a set of time-dependent, axisymmetric DKEs for the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The plasma is formally assumed to be in the low- to finite-collisionality regimes. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by an appropriate set of extended MHD equations. We will discuss computational methods used and benchmarks to other neoclassical models and codes. Furthermore, DK4D has been coupled to a reduced, transport-timescale MHD code, allowing for self-consistent simulations of the dynamic formation of the ohmic and bootstrap currents. Several applications of this hybrid code will be presented, including an ELM-like pressure collapse. We will also discuss plans for coupling to the spatially three-dimensional, extended MHD code M3D-C1 and generalizing to nonaxisymmetric geometries, with the goal of performing self-consistent hybrid simulations of tokamak instabilities and calculations of NTV torque. This work supported by the U.S. Department of Energy (DOE) under Grant Numbers DE-FC02-08ER54969 and DE-AC02-09CH11466.
Time-dependent magnetohydrodynamic simulations of the inner heliosphere
Merkin, V. G.; Lyon, J. G.; Lario, D.; Arge, C. N.; Henney, C. J.
2016-04-01
This paper presents results from a simulation study exploring heliospheric consequences of time-dependent changes at the Sun. We selected a 2 month period in the beginning of year 2008 that was characterized by very low solar activity. The heliosphere in the equatorial region was dominated by two coronal holes whose changing structure created temporal variations distorting the classical steady state picture of the heliosphere. We used the Air Force Data Assimilate Photospheric Flux Transport (ADAPT) model to obtain daily updated photospheric magnetograms and drive the Wang-Sheeley-Arge (WSA) model of the corona. This leads to a formulation of a time-dependent boundary condition for our three-dimensional (3-D) magnetohydrodynamic (MHD) model, LFM-helio, which is the heliospheric adaptation of the Lyon-Fedder-Mobarry MHD simulation code. The time-dependent coronal conditions were propagated throughout the inner heliosphere, and the simulation results were compared with the spacecraft located near 1 astronomical unit (AU) heliocentric distance: Advanced Composition Explorer (ACE), Solar Terrestrial Relations Observatory (STEREO-A and STEREO-B), and the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft that was in cruise phase measuring the heliospheric magnetic field between 0.35 and 0.6 AU. In addition, during the selected interval MESSENGER and ACE aligned radially allowing minimization of the effects of temporal variation at the Sun versus radial evolution of structures. Our simulations show that time-dependent simulationsreproduce the gross-scale structure of the heliosphere with higher fidelity, while on smaller spatial and faster time scales (e.g., 1 day) they provide important insights for interpretation of the data. The simulations suggest that moving boundaries of slow-fast wind transitions at 0.1 AU may result in the formation of inverted magnetic fields near pseudostreamers which is an intrinsically time-dependent process
Nonlinear tearing mode study using the almost ideal magnetohydrodynamics (MHD) constraint
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Ren, C.; Callen, J.D. [Univ. of Wisconsin, Madison, WI (United States); Jensen, T.H. [General Atomics, San Diego, CA (United States)
1998-12-31
The tearing mode is an important resistive magnetohydrodynamics (MHD) mode. It perturbs the initial equilibrium magnetic flux surfaces through magnetic field line reconnection to form new flux surfaces with magnetic islands. In the study of the tearing mode, usually the initial equilibria are one dimensional with two ignorable coordinates and the perturbed equilibria are two dimensional with one ignorable coordinate. The tearing mode can be linearly unstable and its growth saturates at a fine amplitude. The neoclassical tearing mode theory shows that the mode can be nonlinearly driven by the bootstrap current even when it is linearly stable to the classical tearing mode. It is important to study the nonlinear behavior of the tearing mode. As an intrinsically nonlinear approach, the use of the almost ideal MHD constraint is suited to study the nonlinear properties of the tearing mode. In this paper, as a validation of the method, the authors study two characteristics of the tearing mode using the almost ideal MHD constraint: (1) the linear stability condition for the initial one dimensional equilibrium; and (2) the final saturation level for the unstable case. In this work, they only consider the simplest case where no gradient of pressure or current density exists at the mode resonant surface.
Energy Technology Data Exchange (ETDEWEB)
Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2015-07-01
Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.
On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet
Energy Technology Data Exchange (ETDEWEB)
Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Aziz, Arsalan [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Ahmad, Bashir [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2016-06-15
This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter. - Highlights: • Constitutive relation for second grade fluid is employed. • Flow is caused by a nonlinear stretching surface. • Magnetic field applied is in transverse direction. • Nanofluid model consists of Brownian motion and thermophoresis. • Magnetic Reynolds number is assumed small.
Yuan, Xingqiu; Trichtchenko, Larisa; Boteler, David
Propagation of coronal mass ejections from solar surface to the Earth magnetosphere is strongly influenced by the conditions in solar corona and ambient solar wind. Thus, reliable simulation of the background solar wind is the primary task toward the development of numerical model for the transient events. In this paper we introduce a new numerical model which has been specifically designed for numerical study of the solar corona and ambient solar wind. This model is based on our recently developed three-dimensional Spherical Coordinate Adaptive Magneto-Hydro-Dynamic (MHD) code (SCA-MHD-3D) [Yuan et al., 2009]. Modifications has been done to include the observed magnetic field at the photosphere as inner boundary conditions. The energy source term together with reduced plasma gamma are used in the nonlinear MHD equations in order to simulate the solar wind acceleration from subsonic speed at solar surface to supersonic speed at the inter-heliosphere region, and the absorbing boundary conditions are used at the solar surface. This model has been applied to simulate the background solar wind condition for several different solar rotations, and comparison between the observation and model output have shown that it reproduces many features of solar wind, including open and closed magnetic fields, fast and slow solar wind speed, sector boundaries, etc.
Liu, Wei; Li, Hui; Li, Shengtai; Lynn, Alan G
2008-01-01
Nonlinear ideal magnetohydrodynamic (MHD) simulations of the propagation and expansion of a magnetic "bubble" plasma into a lower density, weakly-magnetized background plasma are presented. These simulations mimic the geometry and parameters of the Plasma Bubble Expansion Experiment (PBEX) [A. G. Lynn, Y. Zhang, S. C. Hsu, H. Li, W. Liu, M. Gilmore, and C. Watts, Bull. Amer. Phys. Soc. {\\bf 52}, 53 (2007)], which is studying magnetic bubble expansion as a model for extra-galactic radio lobes. The simulations predict several key features of the bubble evolution. First, the direction of bubble expansion depends on the ratio of the bubble toroidal to poloidal magnetic field, with a higher ratio leading to expansion predominantly in the direction of propagation and a lower ratio leading to expansion predominantly normal to the direction of propagation. Second, an MHD shock and a trailing slow-mode compressible MHD wavefront are formed ahead of the bubble as it propagates into the background plasma. Third, the bub...
Makwana, K D; Li, H; Daughton, W; Cattaneo, F
2014-01-01
Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfv\\'{e}n waves, which interfere and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of $k_{\\perp}^{-1.3}$. The kinetic code shows a spectral slope of $k_{\\perp}^{-1.5}$ for smaller simulation domain, and $k_{\\perp}^{-1.3}$ for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. T...
Comparison of magnetic island stabilization strategies from magneto-hydrodynamic simulations
Février, O.; Maget, P.; Lütjens, H.; Beyer, P.
2017-04-01
The degradation of plasma confinement in tokamaks caused by magnetic islands motivates to better understand their possible suppression using electron cyclotron current drive (ECCD) and to investigate the various strategies relevant for this purpose. In this work, we evaluate the efficiency of several control methods through nonlinear simulations of this process with the toroidal magneto-hydro-dynamic (MHD) code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), which has been extended to incorporate in Ohm’s law a source term modeling the driven current resulting from the interaction of the EC waves with the plasma. A basic control system has been implemented in the code, allowing testing of advanced strategies that require feedback on island position or phase. We focus in particular on the robustness of the control strategies towards uncertainties that apply to the control and ECCD systems, such as the risk of misalignment of the current deposition or the possible inability to generate narrow current deposition.
Subramaniam, Vivek; Raja, Laxminarayan L.
2017-06-01
Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this paper, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and the resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. This also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.
VizieR Online Data Catalog: Solar wind 3D magnetohydrodynamic simulation (Chhiber+, 2017)
Chhiber, R.; Subedi, P.; Usmanov, A. V.; Matthaeus, W. H.; Ruffolo, D.; Goldstein, M. L.; Parashar, T. N.
2017-08-01
We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic-ray diffusion coefficients throughout the inner heliosphere (2Rȯ-3au). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path (mfp) is evaluated using quasi-linear theory, while the perpendicular mfp is determined from nonlinear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mfp is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp. In the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5au; our estimations of the parallel mfp in the ecliptic region at 1 au agree well with the Palmer "consensus" range of 0.08-0.3au. Solar activity increases perpendicular diffusion and reduces parallel diffusion. The parallel mfp mostly varies with rigidity (P) as P.33, and the perpendicular mfp is weakly dependent on P. The mfps are weakly influenced by the choice of long-wavelength power spectra. (2 data files).
Energy Technology Data Exchange (ETDEWEB)
Gaur, Gurudatt; Das, Amita [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2012-07-15
The study of electron velocity shear driven instability in electron magnetohydrodynamics (EMHD) regime in three dimensions has been carried out. It is well known that the instability is non-local in the plane defined by the flow direction and that of the shear, which is the usual Kelvin-Helmholtz mode, often termed as the sausage mode in the context of EMHD. On the other hand, a local instability with perturbations in the plane defined by the shear and the magnetic field direction exists which is termed as kink mode. The interplay of these two modes for simple sheared flow case as well as that when an external magnetic field exists has been studied extensively in the present manuscript in both linear and nonlinear regimes. Finally, these instability processes have been investigated for the exact 2D dipole solutions of EMHD equations [M. B. Isichenko and A. N. Marnachev, Sov. Phys. JETP 66, 702 (1987)] for which the electron flow velocity is sheared. It has been shown that dipoles are very robust and stable against the sausage mode as the unstable wavelengths are typically longer than the dipole size. However, we observe that they do get destabilized by the local kink mode.
Mininni, P; Dmitruk, P; Odier, P; Pinton, J-F; Plihon, N; Verhille, G; Volk, R; Bourgoin, M
2014-05-01
We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von Kármán swirling flow between two counterrotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field and a case with self-sustained magnetic fields. Evidence of long-term memory and 1/f noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von Kármán flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large-scale magnetic field.
Mininni, Pablo; Odier, Philippe; Pinton, Jean-François; Plihon, Nicolas; Verhille, Gautier; Volk, Romain; Bourgoin, Mickael
2014-01-01
We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von K\\'arm\\'an swirling flow between two counter-rotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field, and a case with self-sustained magnetic fields. Evidence of long-term memory and $1/f$ noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von K\\'arm\\'an flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large scale magnetic field.
Large-eddy simulations of fluid and magnetohydrodynamic turbulence using renormalized parameters
Indian Academy of Sciences (India)
Mahendra K Verma; Shishir Kumar
2004-09-01
In this paper a procedure for large-eddy simulation (LES) has been devised for fluid and magnetohydrodynamic turbulence in Fourier space using the renormalized parameters; The parameters calculated using field theory have been taken from recent papers by Verma [1, 2]. We have carried out LES on 643 grid. These results match quite well with direct numerical simulations of 1283. We show that proper choice of parameter is necessary in LES.
Predictive simulation of nonlinear ultrasonics
Shen, Yanfeng; Giurgiutiu, Victor
2012-04-01
Most of the nonlinear ultrasonic studies to date have been experimental, but few theoretical predictive studies exist, especially for Lamb wave ultrasonic. Compared with nonlinear bulk waves and Rayleigh waves, nonlinear Lamb waves for structural health monitoring become more challenging due to their multi-mode dispersive features. In this paper, predictive study of nonlinear Lamb waves is done with finite element simulation. A pitch-catch method is used to interrogate a plate with a "breathing crack" which opens and closes under tension and compression. Piezoelectric wafer active sensors (PWAS) used as transmitter and receiver are modeled with coupled field elements. The "breathing crack" is simulated via "element birth and death" technique. The ultrasonic waves generated by the transmitter PWAS propagate into the structure, interact with the "breathing crack", acquire nonlinear features, and are picked up by the receiver PWAS. The features of the wave packets at the receiver PWAS are studied and discussed. The received signal is processed with Fast Fourier Transform to show the higher harmonics nonlinear characteristics. A baseline free damage index is introduced to assess the presence and the severity of the crack. The paper finishes with summary, conclusions, and suggestions for future work.
Nonlinear Multigrid for Reservoir Simulation
DEFF Research Database (Denmark)
Christensen, Max la Cour; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter
2016-01-01
A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy...... modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical...... efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning...
Magneto-acoustic waves in sunspots: first results from a new 3D nonlinear magnetohydrodynamic code
Felipe, T; Collados, M
2010-01-01
Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional non-linear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here we present the first results of such modeling. We have developed a 3D non-linear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of three and five minutes. We present a detailed description of the three-d...
Matsumoto, Jin; Masada, Youhei; Asano, Eiji; Shibata, Kazunari
2011-06-01
The nonlinear dynamics of the outflow driven by magnetic explosion on the surface of compact object is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as an initial equilibrium state, a spherical stellar object embedded in the hydrostatic plasma which has a density ρ(r) ~ r-α and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of compact star breaks the dynamical equilibrium and triggers two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly in time around the stellar surface, initiating a magnetically driven outflow. Then it excites a strong forward shock, shock driven outflow. The expansion velocity of the magnetically driven outflow is characterized by the Alfvén velocity on the stellar surface, and follows a simple scaling relation υmag ~ υA1/2. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that the evolution of the strong forward shock can be described by a self-similar relation Γsh ~ rsh, where Γsh is the Lorentz factor of the plasma measured at the shock surface rsh. It should be stressed that the pure hydrodynamic process is responsible for the acceleration of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, would deepen the understanding of the magnetic active phenomena on various magnetized stellar objects.
Energy Technology Data Exchange (ETDEWEB)
Khan, Masood [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hashim, E-mail: hashim_alik@yahoo.com [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hussain, M. [Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad 44000 (Pakistan); Azam, M. [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan)
2016-08-15
This paper presents a study of the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Carreau fluid over a convectively heated surface. The analysis of heat transfer is further performed in the presence of non-linear thermal radiation. The appropriate transformations are employed to bring the governing equations into dimensionless form. The numerical solutions of the partially coupled non-linear ordinary differential equations are obtained by using the Runge-Kutta Fehlberg integration scheme. The influence of non-dimensional governing parameters on the velocity, temperature, local skin friction coefficient and local Nusselt number is studied and discussed with the help of graphs and tables. Results proved that there is significant decrease in the velocity and the corresponding momentum boundary layer thickness with the growth in the magnetic parameter. However, a quite the opposite is true for the temperature and the corresponding thermal boundary layer thickness. - Highlights: • We investigated the Magnetohydrodynamic flow of Carreau constitutive fluid model. • Impact of non-linear thermal radiation is further taken into account. • Runge-Kutta Fehlberg method is employed to obtain the numerical solutions. • Fluid velocity is higher in case of hydromagnetic flow in comparison with hydrodynamic flow. • The local Nusselt number is a decreasing function of the thermal radiation parameter.
Klimachkov, D. A.; Petrosyan, A. S.
2016-09-01
Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the
Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows
Matsuoka, C.; Nishihara, K.; Sano, T.
2016-10-01
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.
Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows
Matsuoka, C.; Nishihara, K.; Sano, T.
2017-04-01
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.
Magnetohydrodynamic simulation of reconnection in turbulent astrophysical plasmas
Energy Technology Data Exchange (ETDEWEB)
Widmer, Fabien
2016-07-19
Turbulence is ubiquitous at large-Reynolds-number astrophysical plasmas like in the Solar corona. In such environments, the turbulence is thought to enhance the energy conversion rate by magnetic reconnection above the classical model predictions. Since turbulence cannot be simulated together with the large scale behaviour of the plasma, magnetic reconnection is studied through the average properties of turbulence. A Reynolds-averaged turbulence model is explored in which turbulence is self-sustained and -generated by the large scales (mean-) field inhomogeneities. Employing that model, the influence of turbulence is investigated by large-scale MHD numerical simulations solving evolution equations of the energy and cross-helicity of the turbulence together with the MHD equations. Magnetic reconnection is found to be either rapidly enhanced or suppressed by turbulence depending on the turbulence timescale. If the turbulence timescale is self-consistently calculated, reconnection is always strongly enhanced. Since the solar corona bears strong guide magnetic fields perpendicular to the reconnecting magnetic fields, the influences of a strong guide field on turbulent reconnection is separately investigated. A slow down of reconnection, obtained in the presence of a finite guide field, can be understood by a finite residual helicity working against the enhancement of reconnection by the turbulence. The influence of turbulence on magnetic reconnection is further studied by means of high resolution simulations of plasmoid-unstable current sheets. These simulations revealed the importance of turbulence for reaching fast reconnection.
Observations of "wisps" in magnetohydrodynamic simulations of the Crab Nebula
Camus, N F; Buccantini, N; Hughes, P A
2009-01-01
In this letter, we describe results of new high-resolution axisymmetric relativistic MHD simulations of Pulsar Wind Nebulae. The simulations reveal strong breakdown of the equatorial symmetry and highly variable structure of the pulsar wind termination shock. The synthetic synchrotron maps, constructed using a new more accurate approach, show striking similarity with the well known images of the Crab Nebula obtained by Chandra, and the Hubble Space Telescope. In addition to the \\textit{jet-torus} structure, these maps reproduce the Crab's famous moving wisps whose speed and rateof production agree with the observations. The variability is then analyzed using various statistical methods, including the method of structure function and wavelet transform. The results point towards the quasi-periodic behaviour with the periods of 1.5-3yr and MHD turbulence on scales below 1yr. The full account of this study will be presented in a follow up paper.
Three-Dimensional Magnetohydrodynamic Simulation of Slapper Initiation Systems
Energy Technology Data Exchange (ETDEWEB)
Christensen, J S; Hrousis, C A
2010-03-09
Although useful information can be gleaned from 2D and even 1D simulations of slapper type initiation systems, these systems are inherently three-dimensional and therefore require full 3D representation to model all relevant details. Further, such representation provides additional insight into optimizing the design of such devices from a first-principles perspective and can thereby reduce experimental costs. We discuss in this paper several ongoing efforts in modeling these systems, our pursuit of validation, and extension of these methods to other systems. Our results show the substantial dependence upon highly accurate global equations of state and resistivity models in these analyses.
Fil, A.; Nardon, E.; Hoelzl, M.; Huijsmans, G. T. A.; Orain, F.; Becoulet, M.; Beyer, P.; Dif-Pradalier, G.; Guirlet, R.; Koslowski, H. R.; Lehnen, M.; Morales, J.; Pamela, S.; Passeron, C.; Reux, C.; Saint-Laurent, F.
2015-06-01
JOREK 3D non-linear MHD simulations of a D2 Massive Gas Injection (MGI) triggered disruption in JET are presented and compared in detail to experimental data. The MGI creates an overdensity that rapidly expands in the direction parallel to the magnetic field. It also causes the growth of magnetic islands ( m / n = 2 / 1 and 3/2 mainly) and seeds the 1/1 internal kink mode. O-points of all island chains (including 1/1) are located in front of the MGI, consistently with experimental observations. A burst of MHD activity and a peak in plasma current take place at the same time as in the experiment. However, the magnitude of these two effects is much smaller than in the experiment. The simulated radiation is also much below the experimental level. As a consequence, the thermal quench is not fully reproduced. Directions for progress are identified. Radiation from impurities is a good candidate.
Fragile, P Chris
2008-01-01
(Abridged) We present one of the first physically-motivated two-dimensional general relativistic magnetohydrodynamic (GRMHD) numerical simulations of a radiatively-cooled black-hole accretion disk. The fiducial simulation combines a total-energy-conserving formulation with a radiative cooling function, which includes bremsstrahlung, synchrotron, and Compton effects. By comparison with other simulations we show that in optically thin advection-dominated accretion flows, radiative cooling can significantly affect the structure, without necessarily leading to an optically thick, geometrically thin accretion disk. We further compare the results of our radiatively-cooled simulation to the predictions of a previously developed analytic model for such flows. For the very low stress parameter and accretion rate found in our simulated disk, we closely match a state called the "transition" solution between an outer advection-dominated accretion flow and what would be a magnetically-dominated accretion flow (MDAF) in th...
Energy Technology Data Exchange (ETDEWEB)
Haas, Fernando; Pascoal, Kellen Alves [Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS (Brazil); Mendonça, José Tito [IPFN, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal and Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo, SP (Brazil)
2016-01-15
A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the neutrino coupling is shown to be responsible for breaking the frozen-in magnetic field lines condition even in infinite conductivity plasmas. Simplified and ideal NMHD assumptions were adopted and analyzed in detail.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Two dimensional Magnetohydrodynamic (MHD) equations with and without the momentum addi-tion respectively have been used to simulate the solar wind structure on the meridian plane. The results show that far away from the sun it isn't solar magnetic field that induces the concave solar wind speed. Instead, there may be the fast speed streamer driven by the momentum addition and an interface between high and low speed streamers. The interaction between high and low speed streamers causes the sharp division.
Simulated annealing applied to two-dimensional low-beta reduced magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Chikasue, Y., E-mail: chikasue@ppl.k.u-tokyo.ac.jp [Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8561 (Japan); Furukawa, M., E-mail: furukawa@damp.tottori-u.ac.jp [Graduate School of Engineering, Tottori University, Minami 4-101, Koyama-cho, Tottori-shi, Tottori 680-8552 (Japan)
2015-02-15
The simulated annealing (SA) method is applied to two-dimensional (2D) low-beta reduced magnetohydrodynamics (R-MHD). We have successfully obtained stationary states of the system numerically by the SA method with Casimir invariants preserved. Since the 2D low-beta R-MHD has two fields, the relaxation process becomes complex compared to a single field system such as 2D Euler flow. The obtained stationary state can have fine structure. We have found that the fine structure appears because the relaxation processes are different between kinetic energy and magnetic energy.
Inoue, S; Magara, T; Choe, G S; Park, Y D
2014-01-01
We performed a magnetohydrodynamic (MHD) simulation using a nonlinear force-free field (NLFFF) in solar active region 11158 to clarify the dynamics of an X2.2-class solar flare. We found that the NLFFF never shows the drastic dynamics seen in observations, i.e., it is in stable state against the perturbations. On the other hand, the MHD simulation shows that when the strongly twisted lines are formed at close to the neutral line, which are produced via tether-cutting reconnection in the twisted lines of the NLFFF, consequently they erupt away from the solar surface via the complicated reconnection. This result supports the argument that the strongly twisted lines formed in NLFFF via tether-cutting reconnection are responsible for breaking the force balance condition of the magnetic fields in the lower solar corona. In addition to this the dynamical evolution of these field lines reveals that at the initial stage the spatial pattern of the footpoints caused by the reconnection of the twisted lines appropriatel...
Yuan, Xuefei
2012-07-01
Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.
Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.
Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Ng, C. S.; Bhattacharjee, A.
2006-10-01
A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate the problem of island coalescence instability (ICI) in 2D. The MHD solver is explicit, and uses the Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described in [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys., 215, 59-80 (2006)], allowing both statically refined and dynamically refined grids. ICI is a MHD process that can produce strong current sheets and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [cf., Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Thus, it is desirable to use adaptive refinement grids to increase resolution, and to maintain accuracy at the same time. Results are compared with simulations using finite difference method with the same refinement grid, as well as pesudo-spectral simulations using uniform grid.
Energy Technology Data Exchange (ETDEWEB)
Moawad, S. M., E-mail: smmoawad@hotmail.com [Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt)
2015-02-15
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
Liu, Wei
2010-01-01
We present results from three-dimensional ideal magnetohydrodynamic simulations of unmagnetized dense plasma jet injection into a hot strongly magnetized plasma, with the aim of providing insight into core fueling of a tokamak with parameters relevant for ITER (International Thermonuclear Experimental Reactor) and NSTX (National Spherical Torus Experiment). Unmagnetized jet injection is similar to compact toroid injection but with higher possible injection density and total mass, as well as a potentially smaller footprint for the injector hardware. Our simulation results show that the unmagnetized dense jet is quickly magnetized upon injection. The penetration depth of the jet into the tokamak plasma is mostly dependent on the jet's initial kinetic energy while the jet's magnetic field determines its interior evolution. A key requirement for spatially precise fueling is for the jet's slowing-down time to be less than the time for the perturbed tokamak magnetic flux to relax due to magnetic reconnection. Thus ...
Reconnection-Driven Magnetohydrodynamic Turbulence in a Simulated Coronal-Hole Jet
Uritsky, Vadim M; DeVore, C Richard; Karpen, Judith T
2016-01-01
Extreme-ultraviolet and X-ray jets occur frequently in magnetically open coronal holes on the Sun, especially at high solar latitudes. Some of these jets are observed by white-light coronagraphs as they propagate through the outer corona toward the inner heliosphere, and it has been proposed that they give rise to microstreams and torsional Alfv\\'{e}n waves detected in situ in the solar wind. To predict and understand the signatures of coronal-hole jets, we have performed a detailed statistical analysis of such a jet simulated with an adaptively refined magnetohydrodynamics model. The results confirm the generation and persistence of three-dimensional, reconnectiondriven magnetic turbulence in the simulation. We calculate the spatial correlations of magnetic fluctuations within the jet and find that they agree best with the M\\"{u}ller - Biskamp scaling model including intermittent current sheets of various sizes coupled via hydrodynamic turbulent cascade. The anisotropy of the magnetic fluctuations and the sp...
Proga, Daniel
2007-05-15
I present results from magnetohydrodynamic (MHD) simulations of a gaseous envelope collapsing onto a black hole (BH). These results support the notion that the collapsar model is one of the most promising scenarios to explain the huge release of energy in a matter of seconds associated with gamma-ray bursts (GRBs). Additionally, the MHD simulations show that at late times, when the mass supply rate is expected to decrease, the region in the vicinity of the BH can play an important role in determining the rate of accretion, its time behaviour and ultimately the energy output. In particular, the magnetic flux accumulated around the BH can repeatedly stop and then restart the energy release. As proposed by Proga & Zhang, the episode or episodes of reoccurrence of accretion processes can correspond to X-ray flares discovered recently in a number of GRBs.
Onofri, M; Malara, F; Veltri, P
2010-11-19
A compressible magnetohydrodynamics simulation of the reversed-field pinch is performed including anisotropic thermal conductivity. When the thermal conductivity is much larger in the direction parallel to the magnetic field than in the perpendicular direction, magnetic field lines become isothermal. As a consequence, as long as magnetic surfaces exist, a temperature distribution is observed displaying a hotter confined region, while an almost uniform temperature is produced when the magnetic field lines become chaotic. To include this effect in the numerical simulation, we use a multiple-time-scale analysis, which allows us to reproduce the effect of a large parallel thermal conductivity. The resulting temperature distribution is related to the existence of closed magnetic surfaces, as observed in experiments. The magnetic field is also affected by the presence of an anisotropic thermal conductivity.
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Energy Technology Data Exchange (ETDEWEB)
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)
2013-10-15
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Huijsmans, G.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A.; Chapman, I.; Kirk, A.; Thornton, A.; Hoelzl, M.; Cahyna, P.
2013-10-01
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
Matsumoto, Jin; Masada, Youhei; Asano, Eiji; Shibata, Kazunari
2011-05-01
The nonlinear dynamics of outflows driven by magnetic explosion on the surface of a compact star is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as the initial equilibrium state, a spherical stellar object embedded in hydrostatic plasma which has a density ρ(r) vprop r -α and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of a compact star breaks the equilibrium and triggers a two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly around the stellar surface, initiating a magnetically driven outflow. A strong forward shock driven outflow is then excited. The expansion velocity of the magnetically driven outflow is characterized by the Alfvén velocity on the stellar surface and follows a simple scaling relation v mag vprop v A 1/2. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that it evolves according to a self-similar relation Γsh vprop r sh, where Γsh is the Lorentz factor of the plasma measured at the shock surface r sh. A purely hydrodynamic process would be responsible for the acceleration mechanism of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, can provide a better understanding of the magnetic active phenomena on various magnetized compact stars.
Nakamura, T K M; Hasegawa, H; Shinohara, I
2010-04-01
Ion-to-magnetohydrodynamic scale physics of the transverse velocity shear layer and associated Kelvin-Helmholtz instability (KHI) in a homogeneous, collisionless plasma are investigated by means of full particle simulations. The shear layer is broadened to reach a kinetic equilibrium when its initial thickness is close to the gyrodiameter of ions crossing the layer, namely, of ion-kinetic scale. The broadened thickness is larger in B⋅Ω0 case, where Ω is the vorticity at the layer. This is because the convective electric field, which points out of (into) the layer for B⋅Ω0), extends (reduces) the gyrodiameters. Since the kinetic equilibrium is established before the KHI onset, the KHI growth rate depends on the broadened thickness. In the saturation phase of the KHI, the ion vortex flow is strengthened (weakened) for B⋅Ω0), due to ion centrifugal drift along the rotational plasma flow. In ion inertial scale vortices, this drift effect is crucial in altering the ion vortex size. These results indicate that the KHI at Mercury-like ion-scale magnetospheric boundaries could show clear dawn-dusk asymmetries in both its linear and nonlinear growth.
A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition
Nishikawa, K. I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fushman, G. J.
2004-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity sim 0.3c) is created as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The 3-D simulation ran over one hundred light-crossing time units which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted due in part to magnetic pressure from the twisting the initially uniform magnetic field and from gas pressure associated with shock formation. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outwards with a wider angle than the initial jet. The widening of the jet is consistent with the outward moving shock wave. This evolution of jet-disk coupling suggests that the low/hard state of the jet system may switch to the high/soft state with a wind, as the accretion rate diminishes.
Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.
2010-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.
Energy Technology Data Exchange (ETDEWEB)
Sovinec, C.R.
1995-12-31
Numerical computation is used to investigate resistive magnetohydrodynamic (MHD) fluctuations in the reversed-field pinch (RFP) and in tokamak-like configurations driven solely by direct current (DC) helicity injection. A Lundquist number (S) scan of RFP turbulence without plasma pressure produces the weak scaling of S{sup -0.18} for the root-mean-square magnetic fluctuation level for 2.5x10{sup 3}{le}S{le}4x10{sup 4}. The temporal behavior of fluctuations and the reversal parameter becomes more regular as S is increased, acquiring a {open_quotes}sawtooth{close_quotes} shape at the largest value of S. Simulations with plasma pressure and anisotropic thermal conduction demonstrate energy transport resulting from parallel heat fluctuations. To investigate means of improving RFP energy confinement, three forms of current profile modification are tested. Radio frequency (RF) current drive is modeled with an auxiliary electron force, and linear stability calculations are used.
Energy Technology Data Exchange (ETDEWEB)
Sovinec, Carl R. [Univ. of Wisconsin, Madison, WI (United States)
1995-11-01
Numerical computation is used to investigate resistive magnetohydrodynamic (MHD) fluctuations in the reversed-field pinch (RFP) and in tokamak-like configurations driven solely by direct current (DC) helicity injection. A Lundquist number (S) scan of RFP turbulence without plasma pressure produces the weak scaling of S^{-0.18} for the root-mean-square magnetic fluctuation level for 2.5x10^{3}≤S≤4x10^{4}. The temporal behavior of fluctuations and the reversal parameter becomes more regular as S is increased, acquiring a "sawtooth" shape at the largest value of S. Simulations with plasma pressure and anisotropic thermal conduction demonstrate energy transport resulting from parallel heat fluctuations. To investigate means of improving RFP energy confinement, three forms of current profile modification are tested. Radio frequency (RF) current drive is modeled with an auxiliary electron force, and linear stability calculations are used.
Energy Technology Data Exchange (ETDEWEB)
Liu, Wei [Los Alamos National Laboratory; Hsu, Scott [Los Alamos National Laboratory; Li, Hui [Los Alamos National Laboratory
2009-01-01
We present results from three-dimensional ideal magnetohydrodynamic simulations of low {beta} compact toroid (CT) injection into a hot strongly magnetized plasma, with the aim of providing insight into CT fueling of a tokamak with parameters relevant for ITER (International Thermonuclear Experimental Reactor). A regime is identified in terms of CT injection speed and CT-to-background magnetic field ratio that appears promising for precise core fueling. Shock-dominated regimes, which are probably unfavorable for tokamak fueling, are also identified. The CT penetration depth is proportional to the CT injection speed and density. The entire CT evolution can be divided into three stages: (1) initial penetration, (2) compression in the direction of propagation and reconnection, and (3) coming to rest and spreading in the direction perpendicular to injection. Tilting of the CT is not observed due to the fast transit time of the CT across the background plasma.
Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations.
Hotta, H; Rempel, M; Yokoyama, T
2016-03-25
The 11-year solar magnetic cycle shows a high degree of coherence in spite of the turbulent nature of the solar convection zone. It has been found in recent high-resolution magnetohydrodynamics simulations that the maintenance of a large-scale coherent magnetic field is difficult with small viscosity and magnetic diffusivity (≲10 (12) square centimenters per second). We reproduced previous findings that indicate a reduction of the energy in the large-scale magnetic field for lower diffusivities and demonstrate the recovery of the global-scale magnetic field using unprecedentedly high resolution. We found an efficient small-scale dynamo that suppresses small-scale flows, which mimics the properties of large diffusivity. As a result, the global-scale magnetic field is maintained even in the regime of small diffusivities-that is, large Reynolds numbers.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
Penna, Robert F; Sadowski, Aleksander
2013-01-01
Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, while ignoring the accretion disk leads to a further ~50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures f...
Resistive magnetohydrodynamic simulations of X-line retreat during magnetic reconnection
Murphy, N A
2010-01-01
To investigate the impact of current sheet motion on the reconnection process, we perform resistive magnetohydrodynamic (MHD) simulations of two closely located reconnection sites which move apart from each other as reconnection develops. This simulation develops less quickly than an otherwise equivalent single perturbation simulation but eventually exhibits a higher reconnection rate. The unobstructed outflow jets are faster and longer than the outflow jets directed towards the magnetic island that forms between the two current sheets. The X-line and flow stagnation point are located near the trailing end of each current sheet very close to the obstructed exit. The speed of X-line retreat ranges from ~0.02-0.06 while the speed of stagnation point retreat ranges from ~0.03-0.07, in units of the initial upstream Alfven velocity. Early in time, the flow stagnation point is located closer to the center of the current sheet than the X-line, but later on the relative positions of these two points switch. Consequen...
Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics
Bakhsh, Abeer
2016-03-09
Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability(RMI) is suppressed in ideal magnetohydrodynamics(MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2p/B^2_r) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.
Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics
Miesch, Mark; Matthaeus, William; Brandenburg, Axel; Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank; Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli, Marco
2015-11-01
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.
Energy Technology Data Exchange (ETDEWEB)
Wang, Peng; Abel, Tom; /KIPAC, Menlo Park /Santa Barbara, KITP
2007-12-18
Using magnetohydrodynamic (MHD) adaptive mesh refinement simulations, we study the formation and early evolution of disk galaxies with a magnetized interstellar medium. For a 10{sup 10} M{sub {circle_dot}} halo with initial NFW dark matter and gas profiles, we impose a uniform 10{sup -9} G magnetic field and follow its collapse, disk formation and evolution up to 1 Gyr. Comparing to a purely hydrodynamic simulation with the same initial condition, we find that a protogalactic field of this strength does not significantly influence the global disk properties. At the same time, the initial magnetic fields are quickly amplified by the differentially rotating turbulent disk. After the initial rapid amplification lasting {approx} 500 Myr, subsequent field amplification appears self-regulated. As a result, highly magnetized material begin to form above and below the disk. Interestingly, the field strengths in the self-regulated regime agrees well with the observed fields in the Milky Way galaxy both in the warm and the cold HI phase and do not change appreciably with time. Most of the cold phase shows a dispersion of order ten in the magnetic field strength. The global azimuthal magnetic fields reverse at different radii and the amplitude declines as a function of radius of the disk. By comparing the estimated star formation rate (SFR) in hydrodynamic and MHD simulations, we find that after the magnetic field strength saturates, magnetic forces provide further support in the cold gas and lead to a decline of the SFR.
Energy Technology Data Exchange (ETDEWEB)
Wang, Peng; Abel, Tom; /KIPAC, Menlo Park /Santa Barbara, KITP
2007-12-18
Using magnetohydrodynamic (MHD) adaptive mesh refinement simulations, we study the formation and early evolution of disk galaxies with a magnetized interstellar medium. For a 10{sup 10} M{sub {circle_dot}} halo with initial NFW dark matter and gas profiles, we impose a uniform 10{sup -9} G magnetic field and follow its collapse, disk formation and evolution up to 1 Gyr. Comparing to a purely hydrodynamic simulation with the same initial condition, we find that a protogalactic field of this strength does not significantly influence the global disk properties. At the same time, the initial magnetic fields are quickly amplified by the differentially rotating turbulent disk. After the initial rapid amplification lasting {approx} 500 Myr, subsequent field amplification appears self-regulated. As a result, highly magnetized material begin to form above and below the disk. Interestingly, the field strengths in the self-regulated regime agrees well with the observed fields in the Milky Way galaxy both in the warm and the cold HI phase and do not change appreciably with time. Most of the cold phase shows a dispersion of order ten in the magnetic field strength. The global azimuthal magnetic fields reverse at different radii and the amplitude declines as a function of radius of the disk. By comparing the estimated star formation rate (SFR) in hydrodynamic and MHD simulations, we find that after the magnetic field strength saturates, magnetic forces provide further support in the cold gas and lead to a decline of the SFR.
Energy Technology Data Exchange (ETDEWEB)
Chang, S.L.; Lottes, S.A.; Bouillard, J.X.; Petrick, M.
1997-11-01
This report covers application of Argonne National Laboratory`s (ANL`s) computer codes to simulation and analysis of components of the magnetohydrodynamic (MHD) power train system at the Component Development and Integration Facility (CDIF). Major components of the system include a 50-MWt coal-fired, two-stage combustor and an MHD channel. The combustor, designed and built by TRW, includes a deswirl section between the first and the second-stage combustor and a converging nozzle following the second-stage combustor, which connects to the MHD channel. ANL used computer codes to simulate and analyze flow characteristics in various components of the MHD system. The first-stage swirl combustor was deemed a mature technology and, therefore, was not included in the computer simulation. Several versions of the ICOMFLO computer code were used for the deswirl section and second-stage combustor. The MGMHD code, upgraded with a slag current leakage submodel, was used for the MHD channel. Whenever possible data from the test facilities were used to aid in calibrating parameters in the computer code, to validate the computer code, or to set base-case operating conditions for computations with the computer code. Extensive sensitivity and parametric studies were done on cold-flow mixing in the second-stage combustor, reacting flow in the second-stage combustor and converging nozzle, and particle-laden flow in the deswirl zone of the first-stage combustor, the second-stage combustor, and the converging nozzle. These simulations with subsequent analysis were able to show clearly in flow patterns and various computable measures of performance a number of sensitive and problematical areas in the design of the power train. The simulations of upstream components also provided inlet parameter profiles for simulation of the MHD power generating channel. 86 figs., 18 tabs.
Nonlinear simulations with and computational issues for NIMROD
Energy Technology Data Exchange (ETDEWEB)
Sovinec, C.R. [Los Alamos National Lab., NM (United States)
1998-12-31
The NIMROD (Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion) code development project was commissioned by the US Department of Energy in February, 1996 to provide the fusion research community with a computational tool for studying low-frequency behavior in experiments. Specific problems of interest include the neoclassical evolution of magnetic islands and the nonlinear behavior of tearing modes in the presence of rotation and nonideal walls in tokamaks; they also include topics relevant to innovative confinement concepts such as magnetic turbulence. Besides having physics models appropriate for these phenomena, an additional requirement is the ability to perform the computations in realistic geometries. The NIMROD Team is using contemporary management and computational methods to develop a computational tool for investigating low-frequency behavior in plasma fusion experiments. The authors intend to make the code freely available, and are taking steps to make it as easy to learn and use as possible. An example application for NIMROD is the nonlinear toroidal RFP simulation--the first in a series to investigate how toroidal geometry affects MHD activity in RFPs. Finally, the most important issue facing the project is execution time, and they are exploring better matrix solvers and a better parallel decomposition to address this.
Xiong, Ming; Wang, Yuming; Wang, Shui; 10.1029/2005JA011593
2009-01-01
Numerical studies have been performed to interpret the observed "shock overtaking magnetic cloud (MC)" event by a 2.5 dimensional magnetohydrodynamic (MHD) model in heliospheric meridional plane. Results of an individual MC simulation show that the MC travels with a constant bulk flow speed. The MC is injected with very strong inherent magnetic field over that in the ambient flow and expands rapidly in size initially. Consequently, the diameter of MC increases in an asymptotic speed while its angular width contracts gradually. Meanwhile, simulations of MC-shock interaction are also presented, in which both a typical MC and a strong fast shock emerge from the inner boundary and propagate along heliospheric equator, separated by an appropriate interval. The results show that the shock firstly catches up with the preceding MC, then penetrates through the MC, and finally merges with the MC-driven shock into a stronger compound shock. The morphologies of shock front in interplanetary space and MC body behave as a ...
Endrizzi, A.; Ciolfi, R.; Giacomazzo, B.; Kastaun, W.; Kawamura, T.
2016-08-01
We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.
Endrizzi, Andrea; Giacomazzo, Bruno; Kastaun, Wolfgang; Kawamura, Takumu
2016-01-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state (EOS) for cold matter, together with a "hybrid" part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole (BH) is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the "standard" and in the "time-reversal" scenarios) and other electro...
Wang, Peng
2007-01-01
Using magnetohydrodynamic (MHD) adaptive mesh refinement simulations, we study the formation and early evolution of disk galaxies with a magnetized interstellar medium. For a $10^{10}$ \\msun halo with initial NFW dark matter and gas profiles, we impose a uniform $10^{-9}$ G magnetic field and follow its collapse, disk formation and evolution up to 1 Gyr. Comparing to a purely hydrodynamic simulation with the same initial condition, we find that a protogalactic field of this strength does not significantly influence the global disk properties. At the same time, the initial magnetic fields are quickly amplified by the differentially rotating turbulent disk. After the initial rapid amplification lasting $\\sim500$ Myr, subsequent field amplification appears self-regulated. As a result, highly magnetized material begin to form above and below the disk. Interestingly, the field strengths in the self-regulated regime agrees well with the observed fields in the Milky Way galaxy both in the warm and the cold HI phase ...
Magnetohydrodynamics with Embedded Particle-in-Cell Simulation of Mercury's Magnetosphere
Chen, Y.; Toth, G.; Jia, X.; Gombosi, T. I.; Markidis, S.
2015-12-01
Mercury's magnetosphere is much more dynamic than other planetary magnetospheres because of Mercury's weak intrinsic magnetic field and its proximity to the Sun. Magnetic reconnection and Kelvin-Helmholtz phenomena occur in Mercury's magnetopause and magnetotail at higher frequencies than in other planetary magnetosphere. For instance, chains of flux transfer events (FTEs) on the magnetopause, have been frequentlyobserved by the the MErcury Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) spacecraft (Slavin et al., 2012). Because ion Larmor radius is comparable to typical spatial scales in Mercury's magnetosphere, finite Larmor radius effects need to be accounted for. In addition, it is important to take in account non-ideal dissipation mechanisms to accurately describe magnetic reconnection. A kinetic approach allows us to model these phenomena accurately. However, kinetic global simulations, even for small-size magnetospheres like Mercury's, are currently unfeasible because of the high computational cost. In this work, we carry out global simulations of Mercury's magnetosphere with the recently developed MHD-EPIC model, which is a two-way coupling of the extended magnetohydrodynamic (XMHD) code BATS-R-US with the implicit Particle-in-Cell (PIC) model iPIC3D. The PIC model can cover the regions where kinetic effects are most important, such as reconnection sites. The BATS-R-US code, on the other hand, can efficiently handle the rest of the computational domain where the MHD or Hall MHD description is sufficient. We will present our preliminary results and comparison with MESSENGER observations.
Directory of Open Access Journals (Sweden)
Andrew N. Guarendi
2013-01-01
Full Text Available Numerical simulations of magnetohydrodynamic (MHD hypersonic flow over a cylinder are presented for axial- and transverse-oriented dipoles with different strengths. ANSYS CFX is used to carry out calculations for steady, laminar flows at a Mach number of 6.1, with a model for electrical conductivity as a function of temperature and pressure. The low magnetic Reynolds number (≪1 calculated based on the velocity and length scales in this problem justifies the quasistatic approximation, which assumes negligible effect of velocity on magnetic fields. Therefore, the governing equations employed in the simulations are the compressible Navier-Stokes and the energy equations with MHD-related source terms such as Lorentz force and Joule dissipation. The results demonstrate the ability of the magnetic field to affect the flowfield around the cylinder, which results in an increase in shock stand-off distance and reduction in overall temperature. Also, it is observed that there is a noticeable decrease in drag with the addition of the magnetic field.
Chatterjee, Dipankar; Amiroudine, Sakir
2011-02-01
A comprehensive non-isothermal Lattice Boltzmann (LB) algorithm is proposed in this article to simulate the thermofluidic transport phenomena encountered in a direct-current (DC) magnetohydrodynamic (MHD) micropump. Inside the pump, an electrically conducting fluid is transported through the microchannel by the action of an electromagnetic Lorentz force evolved out as a consequence of the interaction between applied electric and magnetic fields. The fluid flow and thermal characteristics of the MHD micropump depend on several factors such as the channel geometry, electromagnetic field strength and electrical property of the conducting fluid. An involved analysis is carried out following the LB technique to understand the significant influences of the aforementioned controlling parameters on the overall transport phenomena. In the LB framework, the hydrodynamics is simulated by a distribution function, which obeys a single scalar kinetic equation associated with an externally imposed electromagnetic force field. The thermal history is monitored by a separate temperature distribution function through another scalar kinetic equation incorporating the Joule heating effect. Agreement with analytical, experimental and other available numerical results is found to be quantitative.
Numerical Simulation of 2D Supersonic Magnetohydrodynamic Channel and Study on Hall Effect
Institute of Scientific and Technical Information of China (English)
ZHENG Xiaomei; LU Haoyu; XU Dajun; CAI Guobiao
2011-01-01
In this research effort, numerical simulation of two-dimensional magnetohydrodynamic (MHD) channel is performed and Hall effect is studied.The computational model consists of the Navier-Stokes (N-S) equations coupled with electrical-magnetic source terms, Maxwell equations and the generalized Ohm's law.Boundary conditions for the electrical potential equation considering Hall effect are derived.To start with, the MHD channel with single-pair electrodes is studied and flow of the electric current is in accordance with physical principle.Then the MHD channel with five-pair electrodes is numerically simulated.The results show that the electrical current concentrates on the downstream of the anode and the upstream of the cathode due to Hall effect, and the flow field becomes asymmetrical.At the current value of the magnetic interaction parameter, the electrical-magnetic force affects the flow remarkably, decreasing the outlet Mach number and increasing the outlet pressure; what's more, the flow structure in the channel becomes extremely complex.Performances of MHD channels with continual electrodes and segmented electrodes are compared.The results show that performance of the MHD channel with segmented electrodes is better than that with continual electrodes with the increase of Hall parameter.
Zhang, Haocheng; Li, Hui; Guo, Fan; Taylor, Greg
2017-02-01
Kink instabilities are likely to occur in the current-carrying magnetized plasma jets. Recent observations of the blazar radiation and polarization signatures suggest that the blazar emission region may be considerably magnetized. While the kink instability has been studied with first-principle magnetohydrodynamic (MHD) simulations, the corresponding time-dependent radiation and polarization signatures have not been investigated. In this paper, we perform comprehensive polarization-dependent radiation modeling of the kink instability in the blazar emission region based on relativistic MHD (RMHD) simulations. We find that the kink instability may give rise to strong flares with polarization angle (PA) swings or weak flares with polarization fluctuations, depending on the initial magnetic topology and magnetization. These findings are consistent with observations. Compared with the shock model, the kink model generates polarization signatures that are in better agreement with the general polarization observations. Therefore, we suggest that kink instabilities may widely exist in the jet environment and provide an efficient way to convert the magnetic energy and produce multiwavelength flares and polarization variations.
Guarendi, Andrew N; Chandy, Abhilash J
2013-01-01
Numerical simulations of magnetohydrodynamic (MHD) hypersonic flow over a cylinder are presented for axial- and transverse-oriented dipoles with different strengths. ANSYS CFX is used to carry out calculations for steady, laminar flows at a Mach number of 6.1, with a model for electrical conductivity as a function of temperature and pressure. The low magnetic Reynolds number (<1) calculated based on the velocity and length scales in this problem justifies the quasistatic approximation, which assumes negligible effect of velocity on magnetic fields. Therefore, the governing equations employed in the simulations are the compressible Navier-Stokes and the energy equations with MHD-related source terms such as Lorentz force and Joule dissipation. The results demonstrate the ability of the magnetic field to affect the flowfield around the cylinder, which results in an increase in shock stand-off distance and reduction in overall temperature. Also, it is observed that there is a noticeable decrease in drag with the addition of the magnetic field.
Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.
2014-12-01
We study super-Eddington accretion flows onto black holes using a global three-dimensional radiation magneto-hydrodynamical simulation. We solve the time-dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220 L Edd/c 2 and forms a radiation-driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10 L Edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.
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Jiang, Yan-Fei [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Stone, James M. [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Davis, Shane W. [Canadian Institute for Theoretical Astrophysics. Toronto, ON M5S3H4 (Canada)
2014-12-01
We study super-Eddington accretion flows onto black holes using a global three-dimensional radiation magneto-hydrodynamical simulation. We solve the time-dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ∼220 L {sub Edd}/c {sup 2} and forms a radiation-driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ∼20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ∼10 L {sub Edd}. This yields a radiative efficiency ∼4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.
Elements of magnetohydrodynamic stability theory
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Spies, G O
1976-11-01
The nonlinear equations of ideal magnetohydrodynamics are discussed along with the following topics: (1) static equilibrium, (2) strict linear theory, (3) stability of a system with one degree of freedom, (4) spectrum and variational principles in magnetohydrodynamics, (5) elementary proof of the modified energy principle, (6) sufficient stability criteria, (7) local stability, and (8) normal modes. (MOW)
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Shiokawa, Hotaka; Dolence, Joshua C.; Gammie, Charles F. [Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States); Noble, Scott C. [Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623 (United States)
2012-01-10
Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 Multiplication-Sign 96 Multiplication-Sign 64 to 384 Multiplication-Sign 384 Multiplication-Sign 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma {beta}; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma {beta} decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model ({sup s}hearing box{sup )} calculations and with the recent non-relativistic global convergence studies of Hawley et al.
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Le Chat, G.; Cohen, O. [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Kasper, J. C. [Atmospheric, Oceanic and Space Sciences Department, University of Michigan, Ann Arbor, MI (United States); Spangler, S. R., E-mail: gaetan.lechat@obspm.fr [Department of Physics and Astronomy, University of Iowa, Iowa City, IA (United States)
2014-07-10
Polarized natural radio sources passing behind the Sun experience Faraday rotation as a consequence of the electron density and magnetic field strength in coronal plasma. Since Faraday rotation is proportional to the product of the density and the component of the magnetic field along the line of sight of the observer, a model is required to interpret the observations and infer coronal structures. Faraday rotation observations have been compared with relatively ad hoc models of the corona. Here for the first time we compare these observations with magnetohydrodynamic (MHD) models of the solar corona driven by measurements of the photospheric magnetic field. We use observations made with the NRAO Very Large Array of 34 polarized radio sources occulted by the solar corona between 5 and 14 solar radii. The measurements were made during 1997 May, and 2005 March and April. We compare the observed Faraday rotation values with values extracted from MHD steady-state simulations of the solar corona. We find that (1) using a synoptic map of the solar magnetic field just one Carrington rotation off produces poorer agreements, meaning that the outer corona changes in the course of one month, even in solar minimum; (2) global MHD models of the solar corona driven by photospheric magnetic field measurements are generally able to reproduce Faraday rotation observations; and (3) some sources show significant disagreement between the model and the observations, which appears to be a function of the proximity of the line of sight to the large-scale heliospheric current sheet.
Multi-ion, multi-fluid 3-D magnetohydrodynamic simulation of the outer heliosphere
Prested, Christina; Toth, Gabor
2012-01-01
Data from the Voyager probes and the Interstellar Boundary Explorer have revealed the importance of pick-up ions (PUIs) in understanding the character and behavior of the outer heliosphere, the region of interaction between the solar wind and the interstellar medium. In the outer heliosphere PUIs carry a large fraction of the thermal pressure, which effects the nature of the termination shock, and they are a dominate component of pressure in the heliosheath. This paper describes the development of a new multi-ion, multi-fluid 3-D magnetohydrodynamic model of the outer heliosphere. This model has the added capability of tracking the individual fluid properties of multiple ion populations. For this initial study two ion populations are modeled: the thermal solar wind ions and PUIs produced in the supersonic solar wind. The model also includes 4 neutral fluids that interact through charge-exchange with the ion fluids. The new multi-ion simulation reproduces the significant heating of PUIs at the termination shoc...
Resistivity profile effects in numerical magnetohydrodynamic simulations of the reversed-field pinch
Sätherblom, H.-E.; Mazur, S.; Nordlund, P.
1996-12-01
The influence of the resistivity profile on reversed-field pinch (RFP) dynamics is investigated numerically using a three-dimensional resistive magnetohydrodynamic code. This investigation is motivated by experimental observations on the EXTRAP-T1 RFP (Nordlund P et al 1994 Int. Conf. Plasma Physics and Controlled Nuclear Fusion Research IAEA-CN-60/A6/C-P-6). Two cases with profiles mainly differing in the edge region, i.e. in the region outside the reversal surface, are simulated. It is found that increasing the resistivity in this region results in a factor of two increase in magnetic fluctuation energy and an equal amount in the fluctuation-induced electric field. In spite of this, the parallel current decreases in the edge region, resulting in a factor two reduction of the field reversal ratio. The dynamics become more irregular and the characteristic timescale is reduced. The final state is characterized by a higher loop voltage, slightly lower values of the total (fluctuating plus mean part) magnetic energy and the magnetic helicity, but almost unchanged Taylor relaxation ratio. The results indicate that the edge region can be important for RFP confinement since cooling of the plasma in this region can lead to an increased fluctuation level and degraded performance.
Multispectral Emission of the Sun during the First Whole Sun Month: Magnetohydrodynamic Simulations
Lionello, Roberto; Linker, Jon A.; Mikic, Zoran
2008-01-01
We demonstrate that a three-dimensional magnetohydrodynamic (MHD) simulation of the corona can model its global plasma density and temperature structure with sufficient accuracy to reproduce many of the multispectral properties of the corona observed in extreme ultraviolet (EW) and X-ray emission. The key ingredient to this new type of global MHD model is the inclusion of energy transport processes (coronal heating, anisotropic thermal conduction, and radiative losses) in the energy equation. The calculation of these processes has previously been confined to one-dimensional loop models, idealized two-dimensional computations, and three-dimensional active region models. We refer to this as the thermodynamic MHD model, and we apply it to the time period of Carrington rotation 1913 (1996 August 22 to September 18). The form of the coronal heating term strongly affects the plasma density and temperature of the solutions. We perform our calculation for three different empirical heating models: (1) a heating function exponentially decreasing in radius; (2) the model of Schrijver et al.; and (3) a model reproducing the heating properties of the quiet Sun and active regions. We produce synthetic emission images from the density and temperature calculated with these three heating functions and quantitatively compare them with observations from E W Imaging Telescope on the Solar and Heliospheric Observatory and the soft X-ray telescope on Yohkoh. Although none of the heating models provide a perfect match, heating models 2 and 3 provide a reasonable match to the observations.
Magnetohydrodynamic Simulations of A Rotating Massive Star Collapsing to A Black Hole
Fujimoto, S; Kotake, K; Sato, K; Yamada, S; Fujimoto, Shin-ichiro; Hashimoto, Masa-aki; Kotake, Kei; Sato, Katsuhiko; Yamada, Shoichi
2006-01-01
We perform two-dimensional, axisymmetric, magnetohydrodynamic simulations of the collapse of a rotating star of 40 Msun and in the light of the collapsar model of gamma-ray burst. Considering two distributions of angular momentum, up to \\sim 10^{17} cm^2/s, and the uniform vertical magnetic field, we investigate the formation of an accretion disk around a black hole and the jet production near the hole. After material reaches to the black hole with the high angular momentum, the disk is formed inside a surface of weak shock. The disk becomes in a quasi-steady state for stars whose magnetic field is less than 10^{10} G before the collapse. We find that the jet can be driven by the magnetic fields even if the central core does not rotate as rapidly as previously assumed and outer layers of the star has sufficiently high angular momentum. The magnetic fields are chiefly amplified inside the disk due to the compression and the wrapping of the field. The fields inside the disk propagate to the polar region along t...
Borissov, A.; Kontar, E. P.; Threlfall, J.; Neukirch, T.
2017-09-01
The conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and non-thermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucial role in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of two-dimensional (2D) X-point reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivity-independent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the
Magnetohydrodynamic simulation of solid-deuterium-initiated Z-pinch experiments
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Sheehey, Peter Trogdon [Univ. of California, Los Angeles, CA (United States)
1994-02-01
Solid-deuterium-initiated Z-pinch experiments are numerically simulated using a two-dimensional resistive magnetohydrodynamic model, which includes many important experimental details, such as ``cold-start`` initial conditions, thermal conduction, radiative energy loss, actual discharge current vs. time, and grids of sufficient size and resolution to allow realistic development of the plasma. The alternating-direction-implicit numerical technique used meets the substantial demands presented by such a computational task. Simulations of fiber-initiated experiments show that when the fiber becomes fully ionized rapidly developing m=0 instabilities, which originated in the coronal plasma generated from the ablating fiber, drive intense non-uniform heating and rapid expansion of the plasma column. The possibility that inclusion of additional physical effects would improve stability is explored. Finite-Larmor-radius-ordered Hall and diamagnetic pressure terms in the magnetic field evolution equation, corresponding energy equation terms, and separate ion and electron energy equations are included; these do not change the basic results. Model diagnostics, such as shadowgrams and interferograms, generated from simulation results, are in good agreement with experiment. Two alternative experimental approaches are explored: high-current magnetic implosion of hollow cylindrical deuterium shells, and ``plasma-on-wire`` (POW) implosion of low-density plasma onto a central deuterium fiber. By minimizing instability problems, these techniques may allow attainment of higher temperatures and densities than possible with bare fiber-initiated Z-pinches. Conditions for significant D-D or D-T fusion neutron production may be realizable with these implosion-based approaches.
Tsai, T. C.; Yu, H.-S.; Hsieh, M.-S.; Lai, S. H.; Yang, Y.-H.
2015-11-01
Nowadays most of supercomputers are based on the frame of PC cluster; therefore, the efficiency of parallel computing is of importance especially with the increasing computing scale. This paper proposes a high-order implicit predictor-corrector central finite difference (iPCCFD) scheme and demonstrates its high efficiency in parallel computing. Of special interests are the large scale numerical studies such as the magnetohydrodynamic (MHD) simulations in the planetary magnetosphere. An iPCCFD scheme is developed based on fifth-order central finite difference method and fourth-order implicit predictor-corrector method in combination with elimination-of-the-round-off-errors (ERE) technique. We examine several numerical studies such as one-dimensional Brio-Wu shock tube problem, two-dimensional Orszag-Tang vortex system, vortex type K-H instability, kink type K-H instability, field loop advection, and blast wave. All the simulation results are consistent with many literatures. iPCCFD can minimize the numerical instabilities and noises along with the additional diffusion terms. All of our studies present relatively small numerical errors without employing any divergence-free reconstruction. In particular, we obtain fairly stable results in the two-dimensional Brio-Wu shock tube problem which well conserves ∇ ṡ B = 0 throughout the simulation. The ERE technique removes the accumulation of roundoff errors in the uniform or non-disturbed system. We have also shown that iPCCFD is characterized by the high order of accuracy and the low numerical dissipation in the circularly polarized Alfvén wave tests. The proposed iPCCFD scheme is a parallel-efficient and high precision numerical scheme for solving the MHD equations in hyperbolic conservation systems.
Magnetohydrodynamic simulations of mechanical stellar feedback in a sheet-like molecular cloud
Wareing, C. J.; Pittard, J. M.; Falle, S. A. E. G.
2017-03-01
We have used the adaptive-mesh-refinement hydrodynamic code, MG, to perform 3D magnetohydrodynamic simulations with self-gravity of stellar feedback in a sheet-like molecular cloud formed through the action of the thermal instability. We simulate the interaction of the mechanical energy input from a 15 star and a 40 M⊙ star into a 100 pc-diameter 17 000 M⊙ cloud with a corrugated sheet morphology that in projection appears filamentary. The stellar winds are introduced using appropriate Geneva stellar evolution models. In the 15 M⊙ star case, the wind forms a narrow bipolar cavity with minimal effect on the parent cloud. In the 40 M⊙ star case, the more powerful stellar wind creates a large cylindrical cavity through the centre of the cloud. After 12.5 and 4.97 Myr, respectively, the massive stars explode as supernovae (SNe). In the 15 M⊙ star case, the SN material and energy is primarily deposited into the molecular cloud surroundings over ∼105 yr before the SN remnant escapes the cloud. In the 40 M⊙ star case, a significant fraction of the SN material and energy rapidly escapes the molecular cloud along the wind cavity in a few tens of kiloyears. Both SN events compress the molecular cloud material around them to higher densities (so may trigger further star formation), and strengthen the magnetic field, typically by factors of 2-3 but up to a factor of 10. Our simulations are relevant to observations of bubbles in flattened ring-like molecular clouds and bipolar H II regions.
Graham, Jonathan Pietarila; Mininni, Pablo D; Pouquet, Annick
2005-10-01
We present direct numerical simulations and Lagrangian averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.
Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas
Lyons, Brendan Carrick
Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literatureAB that is appropriate for such studies. In particular, the formulation uses a set of time-dependent drift-kinetic equations (DKEs) to advance the non-Maxwellian part of the electron and ion distribution functions (fNM) with linearized Fokker-Planck-Landau collision operators. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by a set of MHD equations which are closed by moments of fNM . We then present two DKE solvers based upon this formulation in axisymmetric toroidal geometries. The Neoclassical Ion-Electron Solver (NIES) solves the steady-state DKEs in the low-collisionality limit. Convergence and benchmark studies are discussed, providing a proof-of-principle that this new formulation can accurately reproduce results from the literature in the limit considered. We then present the DK4D code which evolves the finite-collisionality DKEs time-dependently. Computational methods used and successful benchmarks to other neoclassical models and codes are discussed. Furthermore, we couple DK4D to a reduced, transport-timescale MHD code. The resulting hybrid code is used to simulate the evolution of the current density in a large-aspect-ratio plasma in the presence of several different time-dependent pressure profiles. These simulations demonstrate the self-consistent, dynamic formation of the ohmic and bootstrap currents. In the slowly-evolving plasmas considered
Wareing, C. J.; Pittard, J. M.; Falle, S. A. E. G.; Van Loo, S.
2016-06-01
We have used the adaptive mesh refinement hydrodynamic code, MG, to perform idealized 3D magnetohydrodynamical simulations of the formation of clumpy and filamentary structure in a thermally unstable medium without turbulence. A stationary thermally unstable spherical diffuse atomic cloud with uniform density in pressure equilibrium with low density surroundings was seeded with random density variations and allowed to evolve. A range of magnetic field strengths threading the cloud have been explored, from β = 0.1 to 1.0 to the zero magnetic field case (β = ∞), where β is the ratio of thermal pressure to magnetic pressure. Once the density inhomogeneities had developed to the point where gravity started to become important, self-gravity was introduced to the simulation. With no magnetic field, clouds and clumps form within the cloud with aspect ratios of around unity, whereas in the presence of a relatively strong field (β = 0.1) these become filaments, then evolve into interconnected corrugated sheets that are predominantly perpendicular to the magnetic field. With magnetic and thermal pressure equality (β = 1.0), filaments, clouds and clumps are formed. At any particular instant, the projection of the 3D structure on to a plane parallel to the magnetic field, i.e. a line of sight perpendicular to the magnetic field, resembles the appearance of filamentary molecular clouds. The filament densities, widths, velocity dispersions and temperatures resemble those observed in molecular clouds. In contrast, in the strong field case β = 0.1, projection of the 3D structure along a line of sight parallel to the magnetic field reveals a remarkably uniform structure.
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Skillman, Samuel W.; Hallman, Eric J.; Burns, Jack O. [Center for Astrophysics and Space Astronomy, Department of Astrophysical and Planetary Science, University of Colorado, Boulder, CO 80309 (United States); Xu, Hao; Li, Hui; Collins, David C. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544 (United States); O' Shea, Brian W. [Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Norman, Michael L., E-mail: samuel.skillman@colorado.edu [Center for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92093 (United States)
2013-03-01
Non-thermal radio emission from cosmic-ray electrons in the vicinity of merging galaxy clusters is an important tracer of cluster merger activity, and is the result of complex physical processes that involve magnetic fields, particle acceleration, gas dynamics, and radiation. In particular, objects known as radio relics are thought to be the result of shock-accelerated electrons that, when embedded in a magnetic field, emit synchrotron radiation in the radio wavelengths. In order to properly model this emission, we utilize the adaptive mesh refinement simulation of the magnetohydrodynamic evolution of a galaxy cluster from cosmological initial conditions. We locate shock fronts and apply models of cosmic-ray electron acceleration that are then input into radio emission models. We have determined the thermodynamic properties of this radio-emitting plasma and constructed synthetic radio observations to compare observed galaxy clusters. We find a significant dependence of the observed morphology and radio relic properties on the viewing angle of the cluster, raising concerns regarding the interpretation of observed radio features in clusters. We also find that a given shock should not be characterized by a single Mach number. We find that the bulk of the radio emission comes from gas with T > 5 Multiplication-Sign 10{sup 7} K, {rho} {approx} 10{sup -28}-10{sup -27} g cm{sup -3}, with magnetic field strengths of 0.1-1.0 {mu}G, and shock Mach numbers of M {approx} 3-6. We present an analysis of the radio spectral index which suggests that the spatial variation of the spectral index can mimic synchrotron aging. Finally, we examine the polarization fraction and position angle of the simulated radio features, and compare to observations.
Nonlinear distortion in wireless systems modeling and simulation with Matlab
Gharaibeh, Khaled M
2011-01-01
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems
Rubin, M.; Jia, X.; Altwegg, K.; Combi, M. R.; Daldorff, L. K. S.; Gombosi, T. I.; Khurana, K. K.; Kivelson, M.; Tenishev, V.; Toth, G.; van der Holst, B.; Wurz, P.
2015-12-01
Jupiter's moon Europa is believed to contain a subsurface water ocean whose finite electrical conductance imposes clear induction signatures on the magnetic field in its surroundings. The evidence rests heavily on measurements performed by the magnetometer on board the Galileo spacecraft during multiple flybys of the moon. Europa's interaction with the Jovian magnetosphere has become a major target of research in planetary science, partly because of the potential of a salty ocean to harbor life outside our own planet. Thus it is of considerable interest to develop numerical simulations of the Europa-Jupiter interaction that can be compared with data in order to refine our knowledge of Europa's subsurface structure. In this presentation we show aspects of Europa's interaction with the Jovian magnetosphere extracted from a multifluid magnetohydrodynamics (MHD) code BATS-R-US recently developed at the University of Michigan. The model dynamically separates magnetospheric and pick-up ions and is capable of capturing some of the physics previously accessible only to kinetic approaches. The model utilizes an adaptive grid to maintain the high spatial resolution on the surface required to resolve the portion of Europa's neutral atmosphere with a scale height of a few tens of kilometers that is in thermal equilibrium. The model also derives the electron temperature, which is crucial to obtain the local electron impact ionization rates and hence the plasma mass loading in Europa's atmosphere. We compare our results with observations made by the plasma particles and fields instruments on the Galileo spacecraft to validate our model. We will show that multifluid MHD is able to reproduce the basic features of the plasma moments and magnetic field observations obtained during the Galileo E4 and E26 flybys at Europa.
Nonlinear Epigenetic Variance: Review and Simulations
Kan, Kees-Jan; Ploeger, Annemie; Raijmakers, Maartje E. J.; Dolan, Conor V.; van Der Maas, Han L. J.
2010-01-01
We present a review of empirical evidence that suggests that a substantial portion of phenotypic variance is due to nonlinear (epigenetic) processes during ontogenesis. The role of such processes as a source of phenotypic variance in human behaviour genetic studies is not fully appreciated. In addition to our review, we present simulation studies…
Data assimilation for magnetohydrodynamics systems
Mendoza, O. Barrero; de Moor, B.; Bernstein, D. S.
2006-05-01
Prediction of solar storms has become a very important issue due to the fact that they can affect dramatically the telecommunication and electrical power systems at the earth. As a result, a lot of research is being done in this direction, space weather forecast. Magnetohydrodynamics systems are being studied in order to analyse the space plasma dynamics, and techniques which have been broadly used in the prediction of earth environmental variables like the Kalman filter (KF), the ensemble Kalman filter (EnKF), the extended Kalman filter (EKF), etc., are being studied and adapted to this new framework. The assimilation of a wide range of space environment data into first-principles-based global numerical models will improve our understanding of the physics of the geospace environment and the forecasting of its behaviour. Therefore, the aim of this paper is to study the performance of nonlinear observers in magnetohydrodynamics systems, namely, the EnKF.The EnKF is based on a Monte Carlo simulation approach for propagation of process and measurement errors. In this paper, the EnKF for a nonlinear two-dimensional magnetohydrodynamic (2D-MHD) system is considered. For its implementation, two software packages are merged, namely, the Versatile Advection Code (VAC) written in Fortran and Matlab of Mathworks. The 2D-MHD is simulated with the VAC code while the EnKF is computed in Matlab. In order to study the performance of the EnKF in MHD systems, different number of measurement points as well as ensemble members are set.
Energy Technology Data Exchange (ETDEWEB)
McKinney, Jonathan C.; Tchekhovskoy, Alexander; Blandford, Roger D.
2012-04-26
Black hole (BH) accretion flows and jets are qualitatively affected by the presence of ordered magnetic fields. We study fully three-dimensional global general relativistic magnetohydrodynamic (MHD) simulations of radially extended and thick (height H to cylindrical radius R ratio of |H/R| {approx} 0.2-1) accretion flows around BHs with various dimensionless spins (a/M, with BH mass M) and with initially toroidally-dominated ({phi}-directed) and poloidally-dominated (R-z directed) magnetic fields. Firstly, for toroidal field models and BHs with high enough |a/M|, coherent large-scale (i.e. >> H) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate transient relativistic jets. Secondly, for poloidal field models, poloidal magnetic flux readily accretes through the disk from large radii and builds-up to a natural saturation point near the BH. While models with |H/R| {approx} 1 and |a/M| {le} 0.5 do not launch jets due to quenching by mass infall, for sufficiently high |a/M| or low |H/R| the polar magnetic field compresses the inflow into a geometrically thin highly non-axisymmetric 'magnetically choked accretion flow' (MCAF) within which the standard linear magneto-rotational instability is suppressed. The condition of a highly-magnetized state over most of the horizon is optimal for the Blandford-Znajek mechanism that generates persistent relativistic jets with and 100% efficiency for |a/M| {approx}> 0.9. A magnetic Rayleigh-Taylor and Kelvin-Helmholtz unstable magnetospheric interface forms between the compressed inflow and bulging jet magnetosphere, which drives a new jet-disk oscillation (JDO) type of quasi-periodic oscillation (QPO) mechanism. The high-frequency QPO has spherical harmonic |m| = 1 mode period of {tau} {approx} 70GM/c{sup 3} for a/M {approx} 0.9 with coherence quality factors Q {approx}> 10. Overall, our models are qualitatively distinct from most prior MHD simulations (typically, |H/R| << 1 and poloidal flux is
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Masson, S.
2010-10-15
Solar activity manifests itself through highly dynamical events, such as flares and coronal mass ejections, which result in energy release by magnetic reconnection. This thesis focuses on two manifestations of this energy release: solar energetic particles and dynamics of magnetic reconnection. The first part of my work consists in the detailed temporal analysis of several electromagnetic signatures, produced by energetic particles in the solar atmosphere, with respect to the energetic particle flux at Earth. Using multi-instrument observations, I highlighted that particles can be accelerated by the flare to relativistic energies during a specific episode of acceleration in the impulsive phase. This showed that particles traveled a longer path length than the theoretical length generally assumed. Using in-situ measurements of magnetic field and plasma, I identified the interplanetary magnetic field for 10 particle events, and performing a velocity dispersion analysis I obtained the interplanetary length traveled by particles. I showed that the magnetic structure of the interplanetary medium play a crucial role in the association of the particle flux at Earth and the acceleration signatures of particles at the Sun. The second part of my work focuses on the dynamics of magnetic reconnection. Observationally, the best evidence for magnetic reconnection is the appearance of brightnesses at the solar surface. Performing the first data-driven 3 dimensional magneto-hydrodynamic (MHD) simulation of an observed event, I discovered that the evolution of brightnesses can be explained by the succession of two different reconnection regimes, induced by a new topological association where null-point separatrix lines are embedded in quasi-separatrix layers. This new topological association induces a change of field line connectivity, but also a continuous reconnection process, leading to an apparent slipping motion of reconnected field lines. From a MHD simulation I showed that
Mumford, S J; Erdélyi, R
2013-01-01
Aims. Recent ground- and space-based observations reveal the presence of small-scale motions between convection cells in the solar photosphere. In these regions small-scale magnetic flux tubes are generated due to the interaction of granulation motion and background magnetic field. This paper aims to study the effects of these motions, in regions of enhanced magnetic field, on magnetohydrodynamic wave excitation, propagation and energy flux from the solar photosphere up towards the solar corona. Methods. Numerical experiments of magnetohydrodynamic wave propagation in a realistic gravitationally stratified solar atmosphere from five different modelled photospheric drivers are performed. Horizontal and vertical drivers to mimic granular buffeting and solar global oscillations, a uniform torsional driver, an Archimedean spiral and a logarithmic spiral to mimic observed torsional motions in the solar photosphere are investigated. The numerical results are analysed using a novel method for extracting the parallel...
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2017-03-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2016-12-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Nonlinear PIC Simulations for Nonneutral Plasmas
Lapenta, Giovanni; Luca Delzanno, Gian; Finn, John M.
2002-11-01
We present nonlinear simulations of the low frequency dynamics of electrons in a Malmberg-Penning trap, including compressional and thermal effects [1,2]. First, we consider a 2D model where we assume the effective plasma length constant in time. In this framework, we further neglect the thermal effect on the velocity field, and show with the PIC code KANDINSKY that Penning traps could be used to perform geophysical fluid dynamics experiments [3]. We also observe that, due to the presence of the nonlinear m=1 instability, the initially hollow density profile becomes peaked, as in the experiments. Then, we show 2D results including thermal effects. In this case, the development of the m=1 instability is slowed since the equilibrium plasma length profile is closer to the integrable profile, namely the length profile for which there are no discrete unstable modes [4]. Finally, we present simulations of the 3D fluiddynamics model of Ref. [2]. In particular, we investigate the evolution of a m=1 perturbation for different electron temperatures, when compressional and thermal effects are included. [1] J.M. Finn, D. del-Castillo-Negrete, D.C. Barnes,Phys. Plasmas, 6, 3744, 1999. [2] G.G.M. Coppa, A. D'Angola, G.L. Delzanno, G. Lapenta, Phys. Plasmas, 8, 1133, 2001. [3] G.L. Delzanno, J.M. Finn, G. Lapenta, "Nonlinear Phase of the Compressional m=1 Diocotron Instability: Saturation and Analogy with Geophysical Fluid Dynamics", submitted to Phys. Plasmas. [4] G.L. Delzanno, V.I. Pariev, J.M. Finn, G. Lapenta, "Stability Analysis of Hollow Electron Columns Including Compression and Thermal Effects: Integrability Condition and Numerical Simulations", submitted to Phys. Plasmas.
Adventures in magnetohydrodynamics
Johnson, John L.
1988-03-01
The material in the report was presented in a series of three lectures presented on two days, October 29 and 30, 1987, at Nagoya University. A survey of magnetohydrodynamic theory was given as it applies to toroidal confinement. The material was broken down into four sections: (1) the derivation and justification of the MHD equations; (2) the equilibrium problem; (3) linearized stability; and (4) comments on nonlinear evolution, magnetic islands and transport theory.
Radiation magnetohydrodynamic simulation of plasma formed on a surface by a megagauss field.
Esaulov, A A; Bauer, B S; Makhin, V; Siemon, R E; Lindemuth, I R; Awe, T J; Reinovsky, R E; Struve, K W; Desjarlais, M P; Mehlhorn, T A
2008-03-01
Radiation magnetohydrodynamic modeling is used to study the plasma formed on the surface of a cylindrical metallic load, driven by megagauss magnetic field at the 1MA Zebra generator (University of Nevada, Reno). An ionized aluminum plasma is used to represent the "core-corona" behavior in which a heterogeneous Z-pinch consists of a hot low-density corona surrounding a dense low-temperature core. The radiation dynamics model included simultaneously a self-consistent treatment of both the opaque and transparent plasma regions in a corona. For the parameters of this experiment, the boundary of the opaque plasma region emits the major radiation power with Planckian black-body spectrum in the extreme ultraviolet corresponding to an equilibrium temperature of 16 eV. The radiation heat transport significantly exceeds the electron and ion kinetic heat transport in the outer layers of the opaque plasma. Electromagnetic field energy is partly radiated (13%) and partly deposited into inner corona and core regions (87%). Surface temperature estimates are sensitive to the radiation effects, but the surface motion in response to pressure and magnetic forces is not. The general results of the present investigation are applicable to the liner compression experiments at multi-MA long-pulse current accelerators such as Atlas and Shiva Star. Also the radiation magnetohydrodynamic model discussed in the paper may be useful for understanding key effects of wire array implosion dynamics.
Energy Technology Data Exchange (ETDEWEB)
Nishida, Keisuke; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto 607-8471 (Japan); Nishizuka, Naoto, E-mail: nishida@kwasan.kyoto-u.ac.jp [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan)
2013-10-01
We investigated the dynamic evolution of a three-dimensional (3D) flux rope eruption and magnetic reconnection process in a solar flare by simply extending the two-dimensional (2D) resistive magnetohydrodynamic simulation model of solar flares with low β plasma to a 3D model. We succeeded in reproducing a current sheet and bi-directional reconnection outflows just below the flux rope during the eruption in our 3D simulations. We calculated four cases of a strongly twisted flux rope and a weakly twisted flux rope in 2D and 3D simulations. The time evolution of a weakly twisted flux rope in the 3D simulation shows behaviors similar to those of the 2D simulation, while a strongly twisted flux rope in the 3D simulation clearly shows a different time evolution from the 2D simulation except for the initial phase evolution. The ejection speeds of both strongly and weakly twisted flux ropes in 3D simulations are larger than in the 2D simulations, and the reconnection rates in 3D cases are also larger than in the 2D cases. This indicates positive feedback between the ejection speed of a flux rope and the reconnection rate even in the 3D simulation, and we conclude that the plasmoid-induced reconnection model can be applied to 3D. We also found that small-scale plasmoids are formed inside a current sheet and make it turbulent. These small-scale plasmoid ejections have a role in locally increasing the reconnection rate intermittently as observed in solar flares, coupled with a global eruption of a flux rope.
2-D viscous magnetohydrodynamics simulation of plasma armatures with the CE/SE method
Institute of Scientific and Technical Information of China (English)
LI Xin; WENG ChunSheng
2009-01-01
A possible two-dimensional viscous magnetohydrodynamics (MHD) model is applied to investigating the plasma armature in a railgun. The space-time conservation element and solution element (CE/SE) method for solving the coupled Navier-Stokes equations and Maxwell equations was devised. The dis-tributions of physical parameters of the plasma may thus be evaluated. The results show that extremely high pressure can always be observed ahead of the projectile, and the Lorentz force is the main pro-puIsion. The distribution of temperature is in a good agreement with the results predicted by the law of radiation at the boundaries. Due to convection, the circulation patterns of velocity are evident in both the cases considering inviscid and viscous effect. Furthermore, the velocity and acceleration oscillate over time until a new steady state is achieved. This model efficiently captures the salient features of the physical phenomena, and contributes to further studies of MHD problems in plasma armature.
Mikellides, Ioannis G; Yorke, Harold W
2010-01-01
We present results from numerical simulations of the cooling-core cluster A2199 produced by the two-dimensional (2-D) resistive magnetohydrodynamics (MHD) code MACH2. In our simulations we explore the effect of anisotropic thermal conduction on the energy balance of the system. The results from idealized cases in 2-D axisymmetric geometry underscore the importance of the initial plasma density in ICM simulations, especially the near-core values since the radiation cooling rate is proportional to ${n_e}^2$. Heat conduction is found to be non-effective in preventing catastrophic cooling in this cluster. In addition we performed 2-D planar MHD simulations starting from initial conditions deliberately violating both thermal balance and hydrostatic equilibrium in the ICM, to assess contributions of the convective terms in the energy balance of the system against anisotropic thermal conduction. We find that in this case work done by the pressure on the plasma can dominate the early evolution of the internal energy ...
Energy Technology Data Exchange (ETDEWEB)
Zhao, J. S.; Wu, D. J. [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing (China); Voitenko, Y.; De Keyser, J., E-mail: js_zhao@pmo.ac.cn [Solar-Terrestrial Centre of Excellence, Space Physics Division, Belgian Institute for Space Aeronomy, Ringlaan-3-Avenue Circulaire, B-1180 Brussels (Belgium)
2014-04-20
We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigate two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.
Nonlinear PIC simulation in a Penning trap
Lapenta, G.; Delzanno, G. L.; Finn, J. M.
2002-01-01
We study the nonlinear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column. A new cylindrical PIC code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as it is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a reference Eulerian fluid code. We compare the dynamics of three different models: a model with compression effects, the standard Euler model and a geophysical fluid dynamics model. The results of our investigation prove that Penning traps can really be used to simulate geophysical fluids.
Weakly nonlinear simulation of planar stratified flows
Energy Technology Data Exchange (ETDEWEB)
King, Michael R. [Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States); McCready, Mark J. [Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States)
2000-01-01
The interfacial behavior of two-fluid, planar flows is studied by numerical integration of weakly-nonlinear amplitude equations derived via eigenfunction expansion of the governing equations. This study extends the range of classic Stuart-Landau theories by the inclusion of a spectrum of modes allowing all possible quadratic and cubic interactions. Results are obtained for four cases where linear and Stuart-Landau theories do not give a complete description; gas-liquid and oil-water pressure driven flow, matched-density liquid-liquid Couette flow, and the region of gas-liquid flow near resonance that switches from supercritical to subcritical. It is found that integration of amplitude equations gives better qualitative and quantitative agreement with experiments than Stuart-Landau theory. Further, the distinctively different behaviors of these systems can be understood in terms of the spectrum of nonlinear coefficients. In gas-liquid channel flow a low wave number wave is destabilized through quadratic interaction with the mean flow mode. For liquid-liquid Poiseuille flow, a low wave number wave is destabilized through cubic interactions with higher modes. For depth and viscosity ratios where liquid-liquid Couette flow is unstable to long waves and for which the growth rates are not too large, simulation results predict that the waves grow to a statistically steady state where there is no preferred wave number. Stabilization is provided by an apparently self-similar cascade of energy to higher modes that are linearly stable, explaining why no visible waves occur in experiments done in this region. While Stuart-Landau theory provides no prediction of wave amplitude above criticality for subcritical cases, simulations show that wave saturation at small amplitude is possible and suggests that subcritical predictions may not mean that steady waves do not exist. (c) 2000 American Institute of Physics.
Hayashi, Keiji; Liu, Yang; Bobra, Monica G; Sun, Xudong D; Norton, Aimee A
2015-01-01
Time-dependent three-dimensional magnetohydrodynamics (MHD) simulation modules are implemented at the Joint Science Operation Center (JSOC) of Solar Dynamics Observatory (SDO). The modules regularly produce three-dimensional data of the time-relaxed minimum-energy state of the solar corona using global solar-surface magnetic-field maps created from Helioseismic Magnetic Imager (HMI) full-disk magnetogram data. With the assumption of polytropic gas with specific heat ratio of 1.05, three types of simulation products are currently generated: i) simulation data with medium spatial resolution using the definitive calibrated synoptic map of the magnetic field with a cadence of one Carrington rotation, ii) data with low spatial resolution using the definitive version of the synchronic frame format of the magnetic field, with a cadence of one day, and iii) low-resolution data using near-real-time (NRT) synchronic format of the magnetic field on daily basis. The MHD data available in the JSOC database are three-dimen...
Krumholz, Mark R; Klein, Richard I; McKee, Christopher F
2016-01-01
As star-forming clouds collapse, the gas within them fragments to ever-smaller masses, until the cascade of fragmentation is arrested at some mass scale, making smaller objects progressively less likely to form. This scale defines the peak of the initial mass function (IMF). In this paper we analyse radiation-magnetohydrodynamics simulations of star cluster formation in typical Milky Way environments in order to determine what physical process limits fragmentation in them. We examine the regions in the vicinity of stars that form in the simulations to determine the amounts of mass that are prevented from fragmenting by thermal and magnetic pressure. We show that, on small scales, thermal pressure enhanced by stellar radiation heating is the dominant mechanism limiting the ability of the gas to further fragment. In the brown dwarf mass regime, $\\sim 0.01$ $M_\\odot$, the typical object that forms in the simulations is surrounded by gas whose mass is several times its own that is unable to escape or fragment, an...
Baczynski, C; Klessen, R S
2015-01-01
We introduce a radiative transfer code module for the magnetohydrodynamical adaptive mesh refinement code FLASH 4. It is coupled to an efficient chemical network which explicitly tracks the three hydrogen species H, H_2, H+ as well as C+ and CO. The module is geared towards modeling all relevant thermal feedback processes of massive stars, and is able to follow the non-equilibrium time-dependent thermal and chemical state of the present-day interstellar medium as well as that of dense molecular clouds. We describe in detail the implementation of all relevant thermal stellar feedback mechanisms, i.e. photoelectric, photoionization and H_2 dissociation heating as well as pumping of molecular hydrogen by UV photons. All included radiative feedback processes are extensively tested. We also compare our module to dedicated photon-dominated region (PDR) codes and find good agreement in our modeled hydrogen species once our radiative transfer solution reaches equilibrium. In addition, we show that the implemented rad...
A Collection of Nonlinear Aircraft Simulations in MATLAB
Garza, Frederico R.; Morelli, Eugene A.
2003-01-01
Nonlinear six degree-of-freedom simulations for a variety of aircraft were created using MATLAB. Data for aircraft geometry, aerodynamic characteristics, mass / inertia properties, and engine characteristics were obtained from open literature publications documenting wind tunnel experiments and flight tests. Each nonlinear simulation was implemented within a common framework in MATLAB, and includes an interface with another commercially-available program to read pilot inputs and produce a three-dimensional (3-D) display of the simulated airplane motion. Aircraft simulations include the General Dynamics F-16 Fighting Falcon, Convair F-106B Delta Dart, Grumman F-14 Tomcat, McDonnell Douglas F-4 Phantom, NASA Langley Free-Flying Aircraft for Sub-scale Experimental Research (FASER), NASA HL-20 Lifting Body, NASA / DARPA X-31 Enhanced Fighter Maneuverability Demonstrator, and the Vought A-7 Corsair II. All nonlinear simulations and 3-D displays run in real time in response to pilot inputs, using contemporary desktop personal computer hardware. The simulations can also be run in batch mode. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. Since all the nonlinear simulations are implemented entirely in MATLAB, user-defined control laws can be added in a straightforward fashion, and the simulations are portable across various computing platforms. Routines for trim, linearization, and numerical integration are included. The general nonlinear simulation framework and the specifics for each particular aircraft are documented.
Akcay, Cihan
A comparative study of 3-D pressureless resistive (single-fluid) magnetohydrodynamic (rMHD) and 3-D pressureless two-fluid magnetohydrodynamic (2fl-MHD) models of the Helicity Injected Torus experiment (HIT-SI) is presented. HIT-SI is a spheromak current-drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The goal of the experiment is to demonstrate that steady inductive helicity injection (SIHI) is a viable method for driving and sustaining a magnetized plasma for the eventual purpose of electricity production with magnetic fusion power. The experiment has achieved sustainment of nearly 100 kA of plasma current for ˜1~ms. Fusion power plants are expected to sustain a burning plasma for many minutes to hours with more than 10~MA of plasma current. The purpose of project is to determine the validity of the single-fluid and two-fluid MHD models of HIT-SI. The comparable size of the collisionless ion skin depth to the diameter of the injectors and resistive skin depth predicates the importance of two-fluid effects. The simulations are run with NIMROD (non-ideal magnetohydrodynamics code with rotation-open discussion), an initial-value, 3-D extended MHD code. A constant and uniform plasma density and temperature are assumed. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification and formation time
Grete, P; Schmidt, W; Schleicher, D R G
2016-01-01
Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics (MHD). We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number $\\mathrm{M_s} = 0.2$ to $20$ as reference data for the most extensive \\textit{a priori} tests performed so far in literature. In these tests we explicitly filter the reference data and compare the performance of the new closures against th...
Hayashi, K.; Hoeksema, J. T.; Liu, Y.; Bobra, M. G.; Sun, X. D.; Norton, A. A.
2015-05-01
Time-dependent three-dimensional magnetohydrodynamics (MHD) simulation modules are implemented at the Joint Science Operation Center (JSOC) of the Solar Dynamics Observatory (SDO). The modules regularly produce three-dimensional data of the time-relaxed minimum-energy state of the solar corona using global solar-surface magnetic-field maps created from Helioseismic and Magnetic Imager (HMI) full-disk magnetogram data. With the assumption of a polytropic gas with specific-heat ratio of 1.05, three types of simulation products are currently generated: i) simulation data with medium spatial resolution using the definitive calibrated synoptic map of the magnetic field with a cadence of one Carrington rotation, ii) data with low spatial resolution using the definitive version of the synchronic frame format of the magnetic field, with a cadence of one day, and iii) low-resolution data using near-real-time (NRT) synchronic format of the magnetic field on a daily basis. The MHD data available in the JSOC database are three-dimensional, covering heliocentric distances from 1.025 to 4.975 solar radii, and contain all eight MHD variables: the plasma density, temperature, and three components of motion velocity, and three components of the magnetic field. This article describes details of the MHD simulations as well as the production of the input magnetic-field maps, and details of the products available at the JSOC database interface. To assess the merits and limits of the model, we show the simulated data in early 2011 and compare with the actual coronal features observed by the Atmospheric Imaging Assembly (AIA) and the near-Earth in-situ data.
Hayashi, K; Hoeksema, J T; Liu, Y; Bobra, M G; Sun, X D; Norton, A A
Time-dependent three-dimensional magnetohydrodynamics (MHD) simulation modules are implemented at the Joint Science Operation Center (JSOC) of the Solar Dynamics Observatory (SDO). The modules regularly produce three-dimensional data of the time-relaxed minimum-energy state of the solar corona using global solar-surface magnetic-field maps created from Helioseismic and Magnetic Imager (HMI) full-disk magnetogram data. With the assumption of a polytropic gas with specific-heat ratio of 1.05, three types of simulation products are currently generated: i) simulation data with medium spatial resolution using the definitive calibrated synoptic map of the magnetic field with a cadence of one Carrington rotation, ii) data with low spatial resolution using the definitive version of the synchronic frame format of the magnetic field, with a cadence of one day, and iii) low-resolution data using near-real-time (NRT) synchronic format of the magnetic field on a daily basis. The MHD data available in the JSOC database are three-dimensional, covering heliocentric distances from 1.025 to 4.975 solar radii, and contain all eight MHD variables: the plasma density, temperature, and three components of motion velocity, and three components of the magnetic field. This article describes details of the MHD simulations as well as the production of the input magnetic-field maps, and details of the products available at the JSOC database interface. To assess the merits and limits of the model, we show the simulated data in early 2011 and compare with the actual coronal features observed by the Atmospheric Imaging Assembly (AIA) and the near-Earth in-situ data.
Lorenzo, Maibys Sierra; Domingues, Margarete Oliveira; Mecías, Angela León; Menconi, Varlei Everton; Mendes, Odim
2016-12-01
A global magnetohydrodynamic (MHD) model describes the solar-terrestrial system and the physical processes that live in it. Information obtained from satellites provides input to MHD model to compose a more realistic initial state for the equations and, therefore, more accurate simulations. However, the use of high resolution in time data can produce numerical instabilities that quickly interrupt the simulations. Moreover, satellite time series may have gaps which could be a problem in this context. In order to contribute to the overcoming of such challenges, we propose in this work a methodology based on a variant of the continuous wavelet transform to introduce environmental satellite data on the global resistive MHD model originally developed by Prof. Ogino at the University of Nagoya. Our methodology uses a simplified time-scale version of the original data that preserves the most important spectral features of the phenomena of interest. Then, we can do a long-term integration using this MHD model without any computational instability, while preserving the main time-scale features of the original data set and even overcome possible occurrence of gaps on the satellite data. This methodology also contributes to keeping more realistic physical results.
Wareing, C J; Falle, S A E G
2016-01-01
We have used the AMR hydrodynamic code, MG, to perform 3D magnetohydrodynamic simulations with self-gravity of stellar feedback in a sheet-like molecular cloud formed through the action of the thermal instability. We simulate the interaction of the mechanical energy input from a 15Msun star and a 40Msun star into a 100pc-diameter 17000Msun cloud with a corrugated sheet morphology that in projection appears filamentary. The stellar winds are introduced using appropriate Geneva stellar evolution models. In the 15Msun star case, the wind forms a narrow bipolar cavity with minimal effect on the parent cloud. In the 40Msun star case, the more powerful stellar wind creates a large cylindrical cavity through the centre of the cloud. After 12.5Myrs and 4.97Myrs respectively, the massive stars explode as supernovae (SNe). In the 15Msun star case, the SN material and energy is primarily deposited into the molecular cloud surroundings over 10^5 years before the SN remnant escapes the cloud. In the 40Msun star case, the ...
Magnetohydrodynamic Simulation of the Chordal Wire-Array Plasma Flow Switch
Domonkos, Matthew; Amdahl, David
2015-11-01
The coaxial plasma flow switch (PFS) using a chordal wire array armature was first studied experimentally and computationally in the 1980's. That work revealed significant current interruption (dI/dt ~ 5 MA/ μs) as well as continuum x-ray emission representative of 30-45 keV bremsstrahlung. The work concluded that the voltage spike associated with the current interruption accelerated highly magnetized ions downstream at high velocity, and that energy exchange between the ions and electrons and their subsequent acceleration at the downstream boundary of the apparatus were responsible for the x-ray production. This work revisits the PFS operation up to and just beyond the point of armature lift-off from the coaxial section, where the magnetohydrodynamic model is valid and relevant. The early-time energy deposition in the wires from the pulse discharge is modeled in high-resolution 1-D and is used to set the initial conditions for the full-scale 3-D calculation. The wire array is assumed to have expanded from the initial r =0.01 cm uniformly and only in the axial direction, while the areal mass density retains its intended variation with radius. 3-D calculations are used to examine the armature, including magnetic field diffusion, as it is propelled along the coaxial geometry. These calculations will be used to set the initial conditions for follow-on particle or particle-fluid hybrid calculations of the propagation of ions and electrons to downstream obstacles and to calculate the x-ray production from the interactions of the flowing plasma with the obstacles.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Energy Technology Data Exchange (ETDEWEB)
Gorlin, S.M.; Ljubimov, G.A.; Bitjurin, V.A.; Kovbasjuk, V.I.; Maximenko, V.I.; Medin, S.A.; Barshak, A.E.
1979-12-25
A magnetohydrodynamic device having a duct for a conducting gas to flow at an angle with the direction of the magnetic field induction vector is described. The duct is situated in the magnetic system and is provided with a plurality of electrodes adapted to interact electrically with the gas, whereas the cross-sectional shape of the duct working space is bounded by a closed contour formed by a curve inscribed into a rectangle. 1 claim.
Steady-state properties of driven magnetic reconnection in 2D electron magnetohydrodynamics.
Chacón, L; Simakov, Andrei N; Zocco, A
2007-12-07
We formulate a rigorous nonlinear analytical model that describes the dynamics of the diffusion (reconnection) region in driven systems in the context of electron magnetohydrodynamics (EMHD). A steady-state analysis yields allowed geometric configurations and associated reconnection rates. In addition to the well-known open X-point geometry, elongated configurations are found possible. The model predictions have been validated numerically with two-dimensional EMHD nonlinear simulations, and are in excellent agreement with previously published work.
Solar Flares: Magnetohydrodynamic Processes
Directory of Open Access Journals (Sweden)
Kazunari Shibata
2011-12-01
Full Text Available This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 10^32 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence, local enhancement of electric current in the corona (formation of a current sheet, and rapid dissipation of electric current (magnetic reconnection that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely, while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.
Nonlinear Simulation Studies of Tokamaks and STs
Energy Technology Data Exchange (ETDEWEB)
W. Park; J. Breslau; J. Chen; G.Y. Fu; S.C. Jardin; S. Klasky; J. Menard; A. Pletzer; B.C. Stratton; D. Stutman; H.R. Strauss; L.E. Sugiyama
2003-07-07
The multilevel physics, massively parallel plasma simulation code, M3D, has been used to study spherical tori (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX [National Spherical Torus Experiment] under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-beta disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g., through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion-driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.
Wong, Un-Hong; Aoki, Takayuki; Wong, Hon-Cheng
2014-07-01
Modern graphics processing units (GPUs) have been widely utilized in magnetohydrodynamic (MHD) simulations in recent years. Due to the limited memory of a single GPU, distributed multi-GPU systems are needed to be explored for large-scale MHD simulations. However, the data transfer between GPUs bottlenecks the efficiency of the simulations on such systems. In this paper we propose a novel GPU Direct-MPI hybrid approach to address this problem for overall performance enhancement. Our approach consists of two strategies: (1) We exploit GPU Direct 2.0 to speedup the data transfers between multiple GPUs in a single node and reduce the total number of message passing interface (MPI) communications; (2) We design Compute Unified Device Architecture (CUDA) kernels instead of using memory copy to speedup the fragmented data exchange in the three-dimensional (3D) decomposition. 3D decomposition is usually not preferable for distributed multi-GPU systems due to its low efficiency of the fragmented data exchange. Our approach has made a breakthrough to make 3D decomposition available on distributed multi-GPU systems. As a result, it can reduce the memory usage and computation time of each partition of the computational domain. Experiment results show twice the FLOPS comparing to common 2D decomposition MPI-only implementation method. The proposed approach has been developed in an efficient implementation for MHD simulations on distributed multi-GPU systems, called MGPU-MHD code. The code realizes the GPU parallelization of a total variation diminishing (TVD) algorithm for solving the multidimensional ideal MHD equations, extending our work from single GPU computation (Wong et al., 2011) to multiple GPUs. Numerical tests and performance measurements are conducted on the TSUBAME 2.0 supercomputer at the Tokyo Institute of Technology. Our code achieves 2 TFLOPS in double precision for the problem with 12003 grid points using 216 GPUs.
Tunable nonlinear superconducting metamaterials: Experiment and simulation
Trepanier, Melissa
I present experimental and numerical simulation results for two types of nonlinear tunable superconducting metamaterials: 2D arrays of rf SQUIDs (radio frequency superconducting quantum interference devices) as magnetic metamaterials and arrays of Josephson junction-loaded wires as electric metamaterials. The effective inductance of a Josephson junction is sensitive to dc current, temperature, and rf current. I took advantage of this property to design arrays of Josephson junction-loaded wires that present a tunable cutoff frequency and thus a tunable effective permittivity for propagating electromagnetic waves in a one-conductor waveguide. I measured the response of the metamaterial to each tuning parameter and found agreement with numerical simulations that employ the RCSJ (resistively and capacitively shunted junction) model. An rf SQUID is an analogue of an SRR (split ring resonator) with the gap capacitance replaced with a Josephson junction. Like the SRR the SQUID is a resonant structure with a frequency-dependent effective permeability. The difference between the SQUID and the SRR is that the effective inductance and thus effective permeability of the SQUID can be tuned with dc and rf flux, and temperature. Individual rf SQUID meta-atoms and two-dimensional arrays were designed and measured as a function of each tuning parameter and I have found excellent agreement with numerical simulations. There is also an interesting transparency feature that occurs for intermediate rf flux values. The tuning of SQUID arrays has a similar character to the tuning of individual rf SQUID meta-atoms. However, I found that the coupling between the SQUIDs increases the resonant frequency, decreases dc flux tuning, and introduces additional resonant modes. Another feature of arrays is disorder which suppresses the coherence of the response and negatively impacts the emergent properties of the metamaterial. The disorder was experimentally found to be mainly due to a dc flux
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Pacini, Benjamin Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mayes, Randall L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roettgen, Daniel R [Univ. of Wisconsin, Madison, WI (United States)
2015-10-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
Ohsuga, Ken
2011-01-01
We present the detailed global structure of black hole accretion flows and outflows through newly performed two-dimensional radiation-magnetohydrodynamic simulations. By starting from a torus threaded with weak toroidal magnetic fields and by controlling the central density of the initial torus, rho_0, we can reproduce three distinct modes of accretion flow. In model A with the highest central density, an optically and geometrically thick supercritical accretion disk is created. The radiation force greatly exceeds the gravity above the disk surface, thereby driving a strong outflow (or jet). Because of the mild beaming, the apparent (isotropic) photon luminosity is ~22L_E (where L_E is the Eddington luminosity) in the face-on view. Even higher apparent luminosity is feasible if we increase the flow density. In model B with a moderate density, radiative cooling of the accretion flow is so efficient that a standard-type, cold, and geometrically thin disk is formed at radii greater than ~7R_S (where R_S is the S...
Ohsuga, Ken; Mori, Masao; Kato, Yoshiaki
2009-01-01
Black-hole accretion systems are known to possess several distinct modes (or spectral states), such as low/hard state, high/soft state, and so on. Since the dynamics of the corresponding flows is distinct, theoretical models were separately discussed for each state. We here propose a unified model based on our new, global, two-dimensional radiation-magnetohydrodynamic simulations. By controlling a density normalization we could for the first time reproduce three distinct modes of accretion flow and outflow with one numerical code. When the density is large (model A), a geometrically thick, very luminous disk forms, in which photon trapping takes place. When the density is moderate (model B), the accreting gas can effectively cool by emitting radiation, thus generating a thin disk, i.e., the soft-state disk. When the density is too low for radiative cooling to be important (model C), a disk becomes hot, thick, and faint; i.e., the hard-state disk. The magnetic energy is amplified within the disk up to about tw...
Takahashi, Hiroyuki R; Kawashima, Tomohisa; Sekiguchi, Yuichiro
2016-01-01
Using three-dimensional general relativistic radiation magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk ($\\gtrsim 10^{7}$K) is truncated near the black hole. Hot and less-dense regions, of which the gas temperature is $ \\gtrsim 10^9$K and more than ten times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, and sandwich the cold disk, leading to the effective Compton upscattering. The truncation radius is $\\sim 30 r_{\\rm g}$ for $\\dot{M} \\sim L_{\\rm Edd}/c^2$, where $r_{\\rm g}, \\dot M, L_\\mathrm{Edd}, c$ are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed. Our results are consistent with observations of very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to $\\sim 10 r_{\\rm g}$ with increasing mass accret...
Boquist, Carl W.; Marchant, David D.
1978-01-01
A ceramic-metal composite suitable for use in a high-temperature environment consists of a refractory ceramic matrix containing 10 to 50 volume percent of a continuous high-temperature metal reinforcement. In a specific application of the composite, as an electrode in a magnetohydrodynamic generator, the one surface of the electrode which contacts the MHD fluid may have a layer of varying thickness of nonreinforced refractory ceramic for electrode temperature control. The side walls of the electrode may be coated with a refractory ceramic insulator. Also described is an electrode-insulator system for a MHD channel.
Energy Technology Data Exchange (ETDEWEB)
Takasao, Shinsuke; Nakamura, Naoki; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto 607-8471 (Japan); Matsumoto, Takuma, E-mail: takasao@kwasan.kyoto-u.ac.jp [Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), 3-1-1 Yoshinodai, Sagamihara, Kanagawa 252-5210 (Japan)
2015-06-01
Solar flares are an explosive phenomenon where super-sonic flows and shocks are expected in and above the post-flare loops. To understand the dynamics of post-flare loops, a two-dimensional magnetohydrodynamic (2D MHD) simulation of a solar flare has been carried out. We found new shock structures in and above the post-flare loops, which were not resolved in the previous work by Yokoyama and Shibata. To study the dynamics of flows along the reconnected magnetic field, the kinematics and energetics of the plasma are investigated along selected field lines. It is found that shocks are crucial to determine the thermal and flow structures in the post-flare loops. On the basis of the 2D MHD simulation, we developed a new post-flare loop model, which we defined as the pseudo-2D MHD model. The model is based on the one-dimensional (1D) MHD equations, where all variables depend on one space dimension, and all the three components of the magnetic and velocity fields are considered. Our pseudo-2D model includes many features of the multi-dimensional MHD processes related to magnetic reconnection (particularly MHD shocks), which the previous 1D hydrodynamic models are not able to include. We compared the shock formation and energetics of a specific field line in the 2D calculation with those in our pseudo-2D MHD model, and found that they give similar results. This model will allow us to study the evolution of the post-flare loops in a wide parameter space without expensive computational cost or neglecting important physics associated with magnetic reconnection.
Unified Nonlinear Flight Dynamics and Aeroelastic Simulator Tool Project
National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes a R&D effort to develop a Unified Nonlinear Flight Dynamics and Aeroelastic Simulator (UNFDAS) Tool that will combine...
Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Astrophysics and Space Physics
Miesch, Mark S; Brandenburg, Axel; Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank; Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli, Marco
2015-01-01
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in astrophysics and space physics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, astrophysical and heliophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and...
Three-dimensional Magnetohydrodynamic Simulations of Buoyant Bubbles in Galaxy Clusters
O'Neill, S M; Jones, T W
2009-01-01
We report results of 3D MHD simulations of the dynamics of buoyant bubbles in magnetized galaxy cluster media. The simulations are three dimensional extensions of two dimensional calculations reported by Jones & De Young (2005). Initially spherical bubbles and briefly inflated spherical bubbles all with radii a few times smaller than the intracluster medium (ICM) scale height were followed as they rose through several ICM scale heights. Such bubbles quickly evolve into a toroidal form that, in the absence of magnetic influences, is stable against fragmentation in our simulations. This ring formation results from (commonly used) initial conditions that cause ICM material below the bubbles to drive upwards through the bubble, creating a vortex ring; that is, hydrostatic bubbles develop into "smoke rings", if they are initially not very much smaller or very much larger than the ICM scale height. Even modest ICM magnetic fields with beta = P_gas/P_mag ~ 10^3 can influence the dynamics of the bubbles, provided...
MERIDIONAL CIRCULATION DYNAMICS FROM 3D MAGNETOHYDRODYNAMIC GLOBAL SIMULATIONS OF SOLAR CONVECTION
Energy Technology Data Exchange (ETDEWEB)
Passos, Dário [CENTRA, Instituto Superior Tecnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal); Charbonneau, Paul [Départment de Physique, Université de Montréal, C.P. 6128, Centre-ville, Montréal, QC H3C 3J7 (Canada); Miesch, Mark, E-mail: dariopassos@ist.utl.pt [High Altitude Observatory, NCAR, Boulder CO 80301-2252 (United States)
2015-02-10
The form of solar meridional circulation is a very important ingredient for mean field flux transport dynamo models. However, a shroud of mystery still surrounds this large-scale flow, given that its measurement using current helioseismic techniques is challenging. In this work, we use results from three-dimensional global simulations of solar convection to infer the dynamical behavior of the established meridional circulation. We make a direct comparison between the meridional circulation that arises in these simulations and the latest observations. Based on our results, we argue that there should be an equatorward flow at the base of the convection zone at mid-latitudes, below the current maximum depth helioseismic measures can probe (0.75 R{sub ⊙}). We also provide physical arguments to justify this behavior. The simulations indicate that the meridional circulation undergoes substantial changes in morphology as the magnetic cycle unfolds. We close by discussing the importance of these dynamical changes for current methods of observation which involve long averaging periods of helioseismic data. Also noteworthy is the fact that these topological changes indicate a rich interaction between magnetic fields and plasma flows, which challenges the ubiquitous kinematic approach used in the vast majority of mean field dynamo simulations.
A direct-numerical-simulation-based second-moment closure for turbulent magnetohydrodynamic flows
Kenjereš, S.; Hanjalić, K.; Bal, D.
2004-01-01
A magnetic field, imposed on turbulent flow of an electrically conductive fluid, is known to cause preferential damping of the velocity and its fluctuations in the direction of Lorentz force, thus leading to an increase in stress anisotropy. Based on direct numerical simulations (DNS), we have devel
Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method
Ma, Jun; Qin, Hong; Yu, Zhi; Li, Dehui
2016-07-01
A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and this trend continues through all scale-lengths. The physics of this interesting nonlinear dynamics is numerically analyzed. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB111002, 2013GB105003, 2013GB111000, 2014GB124005, 2015GB111003), National Natural Science Foundation of China (Nos. 11305171, 11405208), JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC-11261140328), the Science Foundation of the Institute of Plasma Physics, Chinese Academy of Sciences (DSJJ-15-JC02) and the CAS Program for the Interdisciplinary Collaboration Team
Numerical Simulation of Two-dimensional Nonlinear Sloshing Problems
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Numerical simulation of a two-dimensional nonlinearsloshing problem is preceded by the finite element method. Two theories are used. One is fully nonlinear theory; the other is time domain second order theory. A liquid sloshing in a rectangular container subjected to a horizontal excitation is simulated using these two theories. Numerical results are obtained and comparisons are made. It is found that a good agreement is obtained for the case of small amplitude oscillation. For the situation of large amplitude excitation, although the differences between using the two theories are obvious the second order solution can still exhibit typical nonlinear features of nonlinear wave.
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...
Fragile, P. Christopher Christopher; Etheridge, Sarina Marie; Anninos, Peter; Mishra, Bhupendra
2017-01-01
Many analytic, semi-analytic, and even some numerical treatments of black hole accretion parametrize the stresses within the disk as an effective viscosity, even though the true source of stresses is likely to be turbulence driven by the magneto-rotational instability. Despite some attempts to quantify the differences between these treatments, it remains unclear exactly what the consequences of a viscous treatment are, especially in the context of the temporal and spatial variability of global disk parameters. We use the astrophysics code, Cosmos++, to create two accretion disk simulations using alpha-viscosity, one thin and one thick. These simulations are then compared to similar work done using MHD in order to analyze the extent of the validity of the alpha-model. One expected result, which we, nevertheless, demonstrate is the greater spatial and temporal variability of MHD.
Toth, G.; Daldorff, L. K. S.; Jia, X.; Gombosi, T. I.; Lapenta, G.
2014-12-01
We have recently developed a new modeling capability to embed theimplicit Particle-in-Cell (PIC) model iPIC3D into the BATS-R-USmagnetohydrodynamic model. The PIC domain can cover the regions wherekinetic effects are most important, such as reconnection sites. TheBATS-R-US code, on the other hand, can efficiently handle the rest ofthe computational domain where the MHD or Hall MHD description issufficient. As one of the very first applications of the MHD-EPICalgorithm (Daldorff et al. 2014, JCP, 268, 236) we simulate theinteraction between Jupiter's magnetospheric plasma with Ganymede'smagnetosphere, where the separation of kinetic and global scalesappears less severe than for the Earth's magnetosphere. Because theexternal Jovian magnetic field remains in an anti-parallel orientationwith respect to Ganymede's intrinsic magnetic field, magneticreconnection is believed to be the major process that couples the twomagnetospheres. As the PIC model is able to describe self-consistentlythe electron behavior, our coupled MHD-EPIC model is well suited forinvestigating the nature of magnetic reconnection in thisreconnection-driven mini-magnetosphere. We will compare the MHD-EPICsimulations with pure Hall MHD simulations and compare both modelresults with Galileo plasma and magnetic field measurements to assess therelative importance of ion and electron kinetics in controlling theconfiguration and dynamics of Ganymede's magnetosphere.
Milroy, R. D.; Kim, C. C.; Sovinec, C. R.
2010-06-01
Three-dimensional simulations of field reversed configuration (FRC) formation and sustainment with rotating magnetic field (RMF) current drive have been performed with the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. The Hall term is a zeroth order effect with strong coupling between Fourier components, and recent enhancements to the NIMROD preconditioner allow much larger time steps than was previously possible. Boundary conditions to capture the effects of a finite length RMF antenna have been added, and simulations of FRC formation from a uniform background plasma have been performed with parameters relevant to the translation, confinement, and sustainment-upgrade experiment at the University of Washington [H. Y. Guo, A. L. Hoffman, and R. D. Milroy, Phys. Plasmas 14, 112502 (2007)]. The effects of both even-parity and odd-parity antennas have been investigated, and there is no evidence of a disruptive instability for either antenna type. It has been found that RMF effects extend considerably beyond the ends of the antenna, and that a large n =0 Bθ can develop in the open-field line region, producing a back torque opposing the RMF.
3D Radiation Nonideal Magnetohydrodynamical Simulations of the Inner Rim in Protoplanetary Disks
Flock, M.; Fromang, S.; Turner, N. J.; Benisty, M.
2017-02-01
Many planets orbit within 1 au of their stars, raising questions about their origins. Particularly puzzling are the planets found near the silicate sublimation front. We investigate conditions near the front in the protostellar disk around a young intermediate-mass star, using the first global 3D radiation nonideal MHD simulations in this context. We treat the starlight heating; the silicate grains’ sublimation and deposition at the local, time-varying temperature and density; temperature-dependent ohmic dissipation; and various initial magnetic fields. The results show magnetorotational turbulence around the sublimation front at 0.5 au. The disk interior to 0.8 au is turbulent, with velocities exceeding 10% of the sound speed. Beyond 0.8 au is the dead zone, cooler than 1000 K and with turbulence orders of magnitude weaker. A local pressure maximum just inside the dead zone concentrates solid particles, favoring their growth. Over many orbits, a vortex develops at the dead zone’s inner edge, increasing the disk’s thickness locally by around 10%. We synthetically observe the results using Monte Carlo transfer calculations, finding that the sublimation front is near-infrared bright. The models with net vertical magnetic fields develop extended, magnetically supported atmospheres that reprocess extra starlight, raising the near-infrared flux 20%. The vortex throws a nonaxisymmetric shadow on the outer disk. At wavelengths > 2 μ {{m}}, the flux varies several percent on monthly timescales. The variations are more regular when the vortex is present. The vortex is directly visible as an arc at ultraviolet through near-infrared wavelengths, given sub-au spatial resolution.
Triadic resonances in non-linear simulations of a fluid flow in a precessing cylinder
Giesecke, A; Gundrum, T; Herault, J; Stefani, F
2015-01-01
We present results from three-dimensional non-linear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which - in cylindrical geometry - form so-called Kelvin modes. For a precession ratio ${\\rm{Po}}=\\Omega_p/\\Omega_c=0.014$ the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of ${\\rm{Po}}$. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin m...
Strings and large scale magnetohydrodynamics
Olesen, P
1995-01-01
From computer simulations of magnetohydrodynamics one knows that a turbulent plasma becomes very intermittent, with the magnetic fields concentrated in thin flux tubes. This situation looks very "string-like", so we investigate whether strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the string equations (with non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields.
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.
2012-11-01
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.
Validating a quasi-linear transport model versus nonlinear simulations
Casati, A.; Bourdelle, C.; Garbet, X.; Imbeaux, F.; Candy, J.; Clairet, F.; Dif-Pradalier, G.; Falchetto, G.; Gerbaud, T.; Grandgirard, V.; Gürcan, Ö. D.; Hennequin, P.; Kinsey, J.; Ottaviani, M.; Sabot, R.; Sarazin, Y.; Vermare, L.; Waltz, R. E.
2009-08-01
In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.
Computation simulation of the nonlinear response of suspension bridges
Energy Technology Data Exchange (ETDEWEB)
McCallen, D.B.; Astaneh-Asl, A.
1997-10-01
Accurate computational simulation of the dynamic response of long- span bridges presents one of the greatest challenges facing the earthquake engineering community The size of these structures, in terms of physical dimensions and number of main load bearing members, makes computational simulation of transient response an arduous task. Discretization of a large bridge with general purpose finite element software often results in a computational model of such size that excessive computational effort is required for three dimensional nonlinear analyses. The aim of the current study was the development of efficient, computationally based methodologies for the nonlinear analysis of cable supported bridge systems which would allow accurate characterization of a bridge with a relatively small number of degrees of freedom. This work has lead to the development of a special purpose software program for the nonlinear analysis of cable supported bridges and the methodologies and software are described and illustrated in this paper.
Nonlinear instability in simulations of Large Plasma Device turbulence
Friedman, B; Umansky, M V; Schaffner, D; Joseph, I
2013-01-01
Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wall mode instability which is just as unstable as the drift waves. Nevertheless, the turbulence in all the simulations is relatively similar because it is primarily driven by a robust nonlinear instability that is the same for all cases. The nonlinear instability preferentially drives $k_\\parallel = 0$ potential energy fluctuations, which then three-wave couple to $k_\\parallel \
Nonlinear Processes in Magnetic Nanodots under Perpendicular Pumping: Micromagnetic Simulations
Directory of Open Access Journals (Sweden)
D.V. Slobodiainuk
2013-03-01
Full Text Available Processes that take place in permalloy nanodots under external electromagnetic pumping are considered. It is shown that in such system similar to bulk samples Suhl and kinetic instability processes are possible. Using micromagnetic simulations approach key features of mode excitation with an external pumping power increase were revealed. Results of the simulations were compared with published experimental data dedicated to investigation of magnetic nanodotes in nonlinear regime.
Nonlinear Simulation of the Tooth Enamel Spectrum for EPR Dosimetry
Kirillov, V. A.; Dubovsky, S. V.
2016-07-01
Software was developed where initial EPR spectra of tooth enamel were deconvoluted based on nonlinear simulation, line shapes and signal amplitudes in the model initial spectrum were calculated, the regression coefficient was evaluated, and individual spectra were summed. Software validation demonstrated that doses calculated using it agreed excellently with the applied radiation doses and the doses reconstructed by the method of additive doses.
Simulation of Chaos in Asymmetric Nonlinear Chua's Circuit
Institute of Scientific and Technical Information of China (English)
WANG Yu-fei; QIAO Shu-tong; JIANG Jian-guo
2008-01-01
In order to describe practical chaotic systems exactly, we presented a simple modified Chua's circuit,which contains an asymmetric nonlinear resistive element. Mathematical analysis was made, and simulation study was performed by MATLAB. By varying the value of linear resistor in the circuit, rich variety dynamical behaviors were observed, such as DC equilibrium point, Hopf bifurcation, period-doubling bifurcation,single-scroll strange attractor, periodic windows, and asymmetric double-scroll strange attractor. The extreme sensitivity in the state trajectory with respect to the initial conditions was exhibited; the special characteristic of asymmetric nonlinear Chua's circuit was found also.
Energy Technology Data Exchange (ETDEWEB)
Jenkins, Thomas G. [Tech–X Corporation, 5621 Arapahoe Avenue, Boulder, CO, 80303; Kruger, Scott E. [Tech–X Corporation, 5621 Arapahoe Avenue, Boulder, CO, 80303
2013-03-25
Work carried out by Tech-X Corporation for the DoE SciDAC Center for Simulation of RF Wave Interactions with Magnetohydrodynamics (SWIM; U.S. DoE Office of Science Award Number DE-FC02-06ER54899) is summarized and is shown to fulfil the project objectives. The Tech-X portion of the SWIM work focused on the development of analytic and computational approaches to study neoclassical tearing modes and their interaction with injected electron cyclotron current drive. Using formalism developed by Hegna, Callen, and Ramos [Phys. Plasmas 16, 112501 (2009); Phys. Plasmas 17, 082502 (2010); Phys. Plasmas 18, 102506 (2011)], analytic approximations for the RF interaction were derived and the numerical methods needed to implement these interactions in the NIMROD extended MHD code were developed. Using the SWIM IPS framework, NIMROD has successfully coupled to GENRAY, an RF ray tracing code; additionally, a numerical control system to trigger the RF injection, adjustment, and shutdown in response to tearing mode activity has been developed. We discuss these accomplishments, as well as prospects for ongoing future research that this work has enabled (which continue in a limited fashion under the SciDAC Center for Extended Magnetohydrodynamic Modeling (CEMM) project and under a baseline theory grant). Associated conference presentations, published articles, and publications in progress are also listed.
Two-fluid sub-grid-scale viscosity in nonlinear simulation of ballooning modes in a heliotron device
Miura, H.; Hamba, F.; Ito, A.
2017-07-01
A large eddy simulation (LES) approach is introduced to enable the study of the nonlinear growth of ballooning modes in a heliotron-type device, by solving fully 3D two-fluid magnetohydrodynamic (MHD) equations numerically over a wide range of parameter space, keeping computational costs as low as possible. A model to substitute the influence of scales smaller than the grid size, at sub-grid scale (SGS), and at the scales larger than it—grid scale (GS)—has been developed for LES. The LESs of two-fluid MHD equations with SGS models have successfully reproduced the growth of the ballooning modes in the GS and nonlinear saturation. The numerical results show the importance of SGS effects on the GS components, or the effects of turbulent fluctuation at small scales in low-wavenumber unstable modes, over the course of the nonlinear saturation process. The results also show the usefulness of the LES approach in studying instability in a heliotron device. It is shown through a parameter survey over many SGS model coefficients that turbulent small-scale components in experiments can contribute to keeping the plasma core pressure from totally collapsing.
Hybrid simulation theory for a classical nonlinear dynamical system
Drazin, Paul L.; Govindjee, Sanjay
2017-03-01
Hybrid simulation is an experimental and computational technique which allows one to study the time evolution of a system by physically testing a subset of it while the remainder is represented by a numerical model that is attached to the physical portion via sensors and actuators. The technique allows one to study large or complicated mechanical systems while only requiring a subset of the complete system to be present in the laboratory. This results in vast cost savings as well as the ability to study systems that simply can not be tested due to scale. However, the errors that arise from splitting the system in two requires careful attention, if a valid simulation is to be guaranteed. To date, efforts to understand the theoretical limitations of hybrid simulation have been restricted to linear dynamical systems. In this work we consider the behavior of hybrid simulation when applied to nonlinear dynamical systems. As a model problem, we focus on the damped, harmonically-driven nonlinear pendulum. This system offers complex nonlinear characteristics, in particular periodic and chaotic motions. We are able to show that the application of hybrid simulation to nonlinear systems requires a careful understanding of what one expects from such an experiment. In particular, when system response is chaotic we advocate the need for the use of multiple metrics to characterize the difference between two chaotic systems via Lyapunov exponents and Lyapunov dimensions, as well as correlation exponents. When system response is periodic we advocate the use of L2 norms. Further, we are able to show that hybrid simulation can falsely predict chaotic or periodic response when the true system has the opposite characteristic. In certain cases, we are able to show that control system parameters can mitigate this issue.
Simulations of coherent nonlinear optical response of molecular vibronic dimers
Perlík, Václav
2016-01-01
We have implemented vibronic dynamics for simulations of the third order coherent response of electronic dimers. In the present communication we provide the full and detailed description of the dynamical model, recently used for simulations of chlorophyll-carotenoid dyads, terylene dimers, or hypericin. We allow for explicit vibronic level structure, by including selected vibrational modes into a "system". Bath dynamics include the Landau-Teller vibrational relaxation, electronic dephasing, and nonlinear vibronic (to bath) coupling. Simulations combine effects of transport and dephasing between vibronic levels. Transport is described by master equation within secular approximation, phase is accumulated in cumulants and its calculation follows the transport pathways during waiting time period.
Nonlinear numerical simulation on extreme-wave kinematics
Institute of Scientific and Technical Information of China (English)
NING Dezhi; TENG Bin; LIU Shuxue
2009-01-01
A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is "adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.
An adaptive nonlinear solution scheme for reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Lett, G.S. [Scientific Software - Intercomp, Inc., Denver, CO (United States)
1996-12-31
Numerical reservoir simulation involves solving large, nonlinear systems of PDE with strongly discontinuous coefficients. Because of the large demands on computer memory and CPU, most users must perform simulations on very coarse grids. The average properties of the fluids and rocks must be estimated on these grids. These coarse grid {open_quotes}effective{close_quotes} properties are costly to determine, and risky to use, since their optimal values depend on the fluid flow being simulated. Thus, they must be found by trial-and-error techniques, and the more coarse the grid, the poorer the results. This paper describes a numerical reservoir simulator which accepts fine scale properties and automatically generates multiple levels of coarse grid rock and fluid properties. The fine grid properties and the coarse grid simulation results are used to estimate discretization errors with multilevel error expansions. These expansions are local, and identify areas requiring local grid refinement. These refinements are added adoptively by the simulator, and the resulting composite grid equations are solved by a nonlinear Fast Adaptive Composite (FAC) Grid method, with a damped Newton algorithm being used on each local grid. The nonsymmetric linear system of equations resulting from Newton`s method are in turn solved by a preconditioned Conjugate Gradients-like algorithm. The scheme is demonstrated by performing fine and coarse grid simulations of several multiphase reservoirs from around the world.
Prediction and simulation errors in parameter estimation for nonlinear systems
Aguirre, Luis A.; Barbosa, Bruno H. G.; Braga, Antônio P.
2010-11-01
This article compares the pros and cons of using prediction error and simulation error to define cost functions for parameter estimation in the context of nonlinear system identification. To avoid being influenced by estimators of the least squares family (e.g. prediction error methods), and in order to be able to solve non-convex optimisation problems (e.g. minimisation of some norm of the free-run simulation error), evolutionary algorithms were used. Simulated examples which include polynomial, rational and neural network models are discussed. Our results—obtained using different model classes—show that, in general the use of simulation error is preferable to prediction error. An interesting exception to this rule seems to be the equation error case when the model structure includes the true model. In the case of error-in-variables, although parameter estimation is biased in both cases, the algorithm based on simulation error is more robust.
Nonlinear simulations of the convection-pulsation coupling
Gastine, T
2011-01-01
In cold Cepheids close to the red edge of the classical instability strip, a strong coupling between the stellar pulsations and the surface convective motions occurs. This coupling is by now poorly described by 1-D models of convection, the so-called "time-dependent convection models" (TDC). The intrinsic weakness of such models comes from the large number of unconstrained free parameters entering in the description of turbulent convection. A way to overcome these limits is to compute two-dimensional direct simulations (DNS), in which all the nonlinearities are correctly solved. Two-dimensional DNS of the convection-pulsation coupling are presented here. In an appropriate parameter regime, convective motions can actually quench the radial pulsations of the star, as suspected in Cepheids close to the red edge of the instability strip. These nonlinear simulations can also be used to determine the limits and the relevance of the TDC models.
McKinney, Jonathan C; Sadowski, Aleksander; Narayan, Ramesh
2013-01-01
Black hole (BH) accretion flows and jets are dynamic hot relativistic magnetized plasma flows whose radiative opacity can significantly affect flow structure and behavior. We describe a numerical scheme, tests, and an astrophysically relevant application using the M1 radiation closure within a new three-dimensional (3D) general relativistic (GR) radiation (R) magnetohydrodynamics (MHD) massively parallel code called HARMRAD. Our 3D GRRMHD simulation of super-Eddington accretion (about $20$ times Eddington) onto a rapidly rotating BH (dimensionless spin $j=0.9375$) shows sustained non-axisymmemtric disk turbulence, a persistent electromagnetic jet driven by the Blandford-Znajek effect, and a total radiative output consistently near the Eddington rate. The total accretion efficiency is of order $20\\%$, the large-scale electromagnetic jet efficiency is of order $10\\%$, and the total radiative efficiency that reaches large distances remains low at only order $1\\%$. However, the radiation jet and the electromagnet...
Dynamic grid adaptation for computational magnetohydrodynamics
Keppens, R.; Nool, M.; Zegeling, P. A.; Goedbloed, J. P.; Bubak, M.; Williams, R.; Afsarmanesh, H.; Hertzberger, B.
2000-01-01
In many plasma physical and astrophysical problems, both linear and nonlinear effects can lead to global dynamics that induce, or occur simultaneously with, local phenomena. For example, a magnetically confined plasma column can potentially posses global magnetohydrodynamic (MHD) eigenmodes with an
Xiong, Ming; Wang, Yuming; Wang, Shui; 10.1029/2006JA011901
2009-01-01
Numerical studies of the interplanetary "shock overtaking magnetic cloud (MC)" event are continued by a 2.5 dimensional magnetohydrodynamic (MHD) model in heliospheric meridional plane. Interplanetary direct collision (DC)/oblique collision (OC) between an MC and a shock results from their same/different initial propagation orientations. For radially erupted MC and shock in solar corona, the orientations are only determined respectively by their heliographic locations. OC is investigated in contrast with the results in DC \\citep{Xiong2006}. The shock front behaves as a smooth arc. The cannibalized part of MC is highly compressed by the shock front along its normal. As the shock propagates gradually into the preceding MC body, the most violent interaction is transferred sideways with an accompanying significant narrowing of the MC's angular width. The opposite deflections of MC body and shock aphelion in OC occur simultaneously through the process of the shock penetrating the MC. After the shock's passage, the...
Cunningham, Andrew J.; Frank, Adam; Varnière, Peggy; Mitran, Sorin; Jones, Thomas W.
2009-06-01
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh-refinement code for ideal magnetohydrodynamics. The code provides several high-resolution shock-capturing schemes which are constructed to maintain conserved quantities of the flow in a finite-volume sense. Divergence-free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across collocated grids of different resolutions. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.
Parametric resonance in ideal magnetohydrodynamics
Zaqarashvili
2000-08-01
We show that an external nonelectromagnetic periodic inhomogeneous force sets up a parametric resonance in an ideal magnetohydrodynamics. Alfven waves with certain wavelengths grow exponentially in amplitude. Nonlinear interaction between the resonant harmonics produces the long-term modulation of amplitudes. The mechanism of the energy transformation from an external nonelectromagnetic force to magnetic oscillations of the system presented here can be used in understanding the physical background of the gravitational action on the magnetized medium. Future application of this theory to several astrophysical problems is briefly discussed.
The inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
Müller, Wolf-Christian; Busse, Angela
2012-01-01
The nonlinear dynamics of magnetic helicity, $H^M$, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of $H^M$ is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. \\textbf{77} 321 (1976)]. By revisiting this theory a universal dynamical balance relation is found that includes effects of kinetic helicity, as well as kinetic and magnetic energy on the inverse cascade of $H^M$ and explains the above-mentioned discrepancy. Considering the result in the context of mean-field dynamo theory suggests a nonlinear modification of the $\\alpha$-dynamo effect important in the context of magnetic field excitation in turbulent plasmas.
Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence.
Müller, Wolf-Christian; Malapaka, Shiva Kumar; Busse, Angela
2012-01-01
The nonlinear dynamics of magnetic helicity HM, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media, is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high-resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of HM is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. 77, 321 (1976)]. By revisiting this theory, a universal dynamical balance relation is found that includes the effects of kinetic helicity as well as kinetic and magnetic energies on the inverse cascade of HM and explains the above-mentioned discrepancy. Consideration of the result in the context of mean-field dynamo theory suggests a nonlinear modification of the α-dynamo effect, which is important in the context of magnetic-field excitation in turbulent plasmas.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1980-01-01
Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
Li, H; Wendroff, B; Liska, R
2000-01-01
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed due to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortic...
Simulation of Fully Nonlinear 3-D Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
张晓兔; 滕斌; 宁德志
2004-01-01
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
Nonlinear Compensation of Solar Array Simulators with Dual Power Regulation
Mizrah, E. A.; Tkachev, S. B.; Poymanov, D. N.; Fedchenko, A. S.
2016-11-01
During the tests of the spacecraft electrical systems there is a need for simulators of individual parts of the spacecrafts, in particular, solar array simulators (SAS). One of the topologies of medium and high power SAS simulators has dual control of consumed power and contains series or parallel connected linear and switching regulators. This topology allows to provide wide bandwidth and high efficiency, but the range of the resistance change of periodically switched SAS load is limited to the value of the stabilized attribute. Nonlinear compensator (NC) allows to reduce the average feedback voltage of the switching regulator in case of periodic load switching, which, in turn, allows to increase the average value of the stabilized attribute. The describing function method provides a mathematical description of the NC electrical circuit, which allows to select parameters of NC that eliminate the excitation of self-oscillation based on the SAS load switching frequency range and to study the switching regulator stability.
Kessar, M.; Balarac, G.; Plunian, F.
2016-10-01
In this work, the accuracy of various models used in large-eddy simulations (LES) of incompressible magnetohydrodynamic (MHD) turbulence is evaluated. Particular attention is devoted to the capabilities of models to reproduce the transfers between resolved grid- and subgrid-scales. The exact global balance of MHD turbulent flows is first evaluated from direct numerical simulation (DNS) database. This balance is controlled by the transfers between scales and between kinetic and magnetic energies. Two cases of forced homogeneous isotropic MHD turbulent flows are considered, with and without injecting large scale helicity. The strong helical case leads to domination of the magnetic energy due to an inverse cascade [A. Brandenburg, Astrophys. J. 550(2), 824 (2001); N. E. Haugen et al., Phys. Rev. E 70(1), 016308 (2004)]. The energy transfers predicted by various models are then compared with the transfer extracted from DNS results. This allows to discriminate models classically used for LES of MHD turbulence. In the non-helical case, the Smagorinsky-like model [M. L. Theobald et al., Phys. Plasmas 1, 3016 (1994)] and a mixed model are able to perform stable LES, but the helical case is a more demanding test and all the models lead to unstable simulations.
Initial Synthetic Diagnostics of Nonlinear Simulation of CSDX
Vaezi, Payam; Holland, Christopher; Thakur, Saikat; Tynan, George
2015-11-01
The Controlled Shear Decorrelation Experiment (CSDX) linear plasma device provides a simple system for nonlinear studies of coupled drift-wave/zonal flow dynamics. We present numerical simulations of a minimal model of 3D collisional drift-wave physics in CSDX which evolves density, vorticity and electron temperature perturbations, implemented in the BOUndary Turbulence (BOUT++) framework. Equilibrium electron density and temperature profiles are taken from experimental measurements. We have verified the model with both linear analytical theory and nonlinear energy balance analysis. Results show that retaining the radial profile variation of plasma parameters has a significant impact on the simulation results. Application of synthetic Langmuir probes to simulation results reveals that the effect of electron temperature fluctuations is significant for validation of model results against measurements of turbulence characteristics (e.g. fluctuation levels, flux, frequency spectra). Both of these effects are found to be needed for model predictions to be comparable to experimental observations. This work is supported by US DoE under DE-FG02-06ER54871.
Simulation of non-linear coaxial line using ferrite beads
Energy Technology Data Exchange (ETDEWEB)
Furuya, S.; Matsumoto, H.; Tachi, K.; Takano, S.; Irisawa, J. [Nagaoka Univ. of Technology, Niigata (Japan)
2002-06-01
A ferrite sharpener is a non-linear coaxial line using ferrite beads, which produces high-voltage, high-dV/dt pulses. We have been examining the characteristics of ferrite sharpeners experimentally, varying various parameters. Also we have made the simulation of the ferrite sharpener and compared the predictions with the experimental results in detail to analyze the characteristics of the sharpener. In this report, calculating the magnetization M of the ferrite bead, we divide the bead into n sections radially instead of adopting M at the average radius in the previous report. (author)
Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis Project
National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...
Fast recursive filters for simulating nonlinear dynamic systems.
van Hateren, J H
2008-07-01
A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities may depend on system variables, and the topology of the system may be complex, including feedback. Several examples taken from neuroscience are given: phototransduction, photopigment bleaching, and spike generation according to the Hodgkin-Huxley equations. The scheme uses two slightly different forms of autoregressive filters, with an implicit delay of zero for feedforward control and an implicit delay of half a sample distance for feedback control. On a fairly complex model of the macaque retinal horizontal cell, it computes, for a given level of accuracy, one to two orders of magnitude faster than the fourth-order Runge-Kutta. The computational scheme has minimal memory requirements and is also suited for computation on a stream processor, such as a graphical processing unit.
Simulation of an optomechanical quantum memory in the nonlinear regime
Teh, R. Y.; Kiesewetter, S.; Reid, M. D.; Drummond, P. D.
2017-07-01
Optomechanical systems cooled to the quantum level provide a promising mechanism for a high-fidelity quantum memory that is faithful to a given temporal mode structure, and can be recovered synchronously. We carry out full, probabilistic quantum simulation of a quantum optomechanical memory, including nonlinear effects that are usually ignored. This is achieved using both the approximate truncated Wigner and the exact positive P phase-space representations. By considering the nonlinear quantum optomechanical Hamiltonian, our simulations allow us to probe the regime where the linearization approximation fails to hold. We show evidence for large spectral overlap between the quantum signal and the transfer field in typical optomechanical quantum memory experiments. Methods for eliminating this overlap to accurately recover the quantum signal are discussed. This allows us to give a complete model for the quantum storage of a coherent state. We treat the mode matching that is necessary to accurately retrieve the stored quantum state, by including the internal dynamics of the mechanical system as well as the optical system. We also include the finite switching time of the control transfer field. The fidelity for the storage of a coherent state is computed numerically using currently realistic experimental parameters in the electromechanical case. We find the expected fidelity is lower than required to demonstrate true quantum state transfers. Significant improvements in the quality factor of the cavity and mechanical systems will, however, increase the fidelity beyond the quantum threshold.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Adams, Mark F.
2010-09-01
Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations so-called "textbook" multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations. (C) 2010 Elsevier Inc. All rights reserved.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Adams, Mark F. [Columbia Univ., New York, NY (United States); Samtaney, Ravi [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Brandt, Achi [Weizmann Inst. of Science, Rehovot (Israel)
2013-12-14
Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called “textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.
Gorelick, S.M.; Voss, C.I.; Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1984-01-01
A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. -from Authors
The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics
Wheatley, V.
2014-01-10
The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers.
Flight Dynamic Simulation with Nonlinear Aeroelastic Interaction using the ROM-ROM Procedure Project
National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes to develop an integrated flight dynamics simulation capability with nonlinear aeroelastic interactions by combining a flight...
Flight Dynamic Simulation with Nonlinear Aeroelastic Interaction using the ROM-ROM Procedure Project
National Aeronautics and Space Administration — ZONA Technology, Inc. proposes to develop an integrated flight dynamics simulation capability with nonlinear aeroelastic interactions by combining a flight dynamics...
Experiments in Magnetohydrodynamics
Rayner, J. P.
1970-01-01
Describes three student experiments in magnetohydrodynamics (MHD). In these experiments, it was found that the electrical conductivity of the local water supply was sufficient to demonstrate effectively some of the features of MHD flowmeters, generators, and pumps. (LC)
Effects of seed magnetic fields on magnetohydrodynamic implosion structure and dynamics
Mostert, W.
2014-12-01
The effects of various seed magnetic fields on the dynamics of cylindrical and spherical implosions in ideal magnetohydrodynamics are investigated. Here, we present a fundamental investigation of this problem utilizing cylindrical and spherical Riemann problems under three seed field configurations to initialize the implosions. The resulting flows are simulated numerically, revealing rich flow structures, including multiple families of magnetohydrodynamic shocks and rarefactions that interact non-linearly. We fully characterize these flow structures, examine their axi- and spherisymmetry-breaking behaviour, and provide data on asymmetry evolution for different field strengths and driving pressures for each seed field configuration. We find that out of the configurations investigated, a seed field for which the implosion centre is a saddle point in at least one plane exhibits the least degree of asymmetry during implosion.
Center for Extended Magnetohydrodynamic Modeling Cooperative Agreement
Energy Technology Data Exchange (ETDEWEB)
Carl R. Sovinec
2008-02-15
The Center for Extended Magnetohydrodynamic Modeling (CEMM) is developing computer simulation models for predicting the behavior of magnetically confined plasmas. Over the first phase of support from the Department of Energy’s Scientific Discovery through Advanced Computing (SciDAC) initiative, the focus has been on macroscopic dynamics that alter the confinement properties of magnetic field configurations. The ultimate objective is to provide computational capabilities to predict plasma behavior—not unlike computational weather prediction—to optimize performance and to increase the reliability of magnetic confinement for fusion energy. Numerical modeling aids theoretical research by solving complicated mathematical models of plasma behavior including strong nonlinear effects and the influences of geometrical shaping of actual experiments. The numerical modeling itself remains an area of active research, due to challenges associated with simulating multiple temporal and spatial scales. The research summarized in this report spans computational and physical topics associated with state of the art simulation of magnetized plasmas. The tasks performed for this grant are categorized according to whether they are primarily computational, algorithmic, or application-oriented in nature. All involve the development and use of the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion (NIMROD) code, which is described at http://nimrodteam.org. With respect to computation, we have tested and refined methods for solving the large algebraic systems of equations that result from our numerical approximations of the physical model. Collaboration with the Terascale Optimal PDE Solvers (TOPS) SciDAC center led us to the SuperLU_DIST software library [http://crd.lbl.gov/~xiaoye/SuperLU/] for solving large sparse matrices using direct methods on parallel computers. Switching to this solver library boosted NIMROD’s performance by a factor of five in typical large
Magnetohydrodynamic fluidic system
Lee, Abraham P.; Bachman, Mark G.
2004-08-24
A magnetohydrodynamic fluidic system includes a reagent source containing a reagent fluid and a sample source containing a sample fluid that includes a constituent. A reactor is operatively connected to the supply reagent source and the sample source. MHD pumps utilize a magnetohydrodynamic drive to move the reagent fluid and the sample fluid in a flow such that the reagent fluid and the sample fluid form an interface causing the constituent to be separated from the sample fluid.
Simulation-based optimal Bayesian experimental design for nonlinear systems
Huan, Xun
2013-01-01
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters.Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. © 2012 Elsevier Inc.
Multifluid magnetohydrodynamic turbulent decay
Downes, Turlough P
2011-01-01
It is generally believed that turbulence has a significant impact on the dynamics and evolution of molecular clouds and the star formation which occurs within them. Non-ideal magnetohydrodynamic effects are known to influence the nature of this turbulence. We present the results of a suite of 512-cubed resolution simulations of the decay of initially super-Alfvenic and supersonic fully multifluid MHD turbulence. We find that ambipolar diffusion increases the rate of decay of the turbulence while the Hall effect has virtually no impact. The decay of the kinetic energy can be fitted as a power-law in time and the exponent is found to be -1.34 for fully multifluid MHD turbulence. The power spectra of density, velocity and magnetic field are all steepened significantly by the inclusion of non-ideal terms. The dominant reason for this steepening is ambipolar diffusion with the Hall effect again playing a minimal role except at short length scales where it creates extra structure in the magnetic field. Interestingl...
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
Non-linear PIC simulation in a penning trap
Energy Technology Data Exchange (ETDEWEB)
Delzanno, G. L. (Gian L.); Lapenta, G. M. (Giovanni M.); Finn, J. M. (John M.)
2001-01-01
We study the non-linear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column. A new cylindrical PIC code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as it is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a reference Eulerian fluid code. We compare the dynamics of three different models: a model with compression effects, the standard Euler model and a geophysical fluid dynamics model. The results of our investigation prove that Penning traps can really be used to simulate geophysical fluids.
Energy Technology Data Exchange (ETDEWEB)
Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.
Magnetohydrodynamic mechanism for pedestal formation.
Guazzotto, L; Betti, R
2011-09-16
Time-dependent two-dimensional magnetohydrodynamic simulations are carried out for tokamak plasmas with edge poloidal flow. Differently from conventional equilibrium theory, a density pedestal all around the edge is obtained when the poloidal velocity exceeds the poloidal sound speed. The outboard pedestal is induced by the transonic discontinuity, the inboard one by mass redistribution. The density pedestal follows the formation of a highly sheared flow at the transonic surface. These results may be relevant to the L-H transition and pedestal formation in high performance tokamak plasmas.
Implicit Methods for the Magnetohydrodynamic Description of Magnetically Confined Plasmas
Energy Technology Data Exchange (ETDEWEB)
Jardin, S C
2010-09-28
Implicit algorithms are essential for predicting the slow growth and saturation of global instabilities in today’s magnetically confined fusion plasma experiments. Present day algorithms for obtaining implicit solutions to the magnetohydrodynamic (MHD) equations for highly magnetized plasma have their roots in algorithms used in the 1960s and 1970s. However, today’s computers and modern linear and non-linear solver techniques make practical much more comprehensive implicit algorithms than were previously possible. Combining these advanced implicit algorithms with highly accurate spatial representations of the vector fields describing the plasma flow and magnetic fields and with improved methods of calculating anisotropic thermal conduction now makes possible simulations of fusion experiments using realistic values of plasma parameters and actual configuration geometry.
Nonuniversality and Finite Dissipation in Decaying Magnetohydrodynamic Turbulence.
Linkmann, M F; Berera, A; McComb, W D; McKay, M E
2015-06-12
A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cϵ=Cϵ,∞+C/R-+O(1/R-(2)), where R- is a generalized Reynolds number. The constant Cϵ,∞ describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of Cϵ,∞ is not universal. Direct numerical simulations were conducted on up to 2048(3) grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems.
Large scale instabilities in two-dimensional magnetohydrodynamics
Boffetta; Celani; Prandi
2000-04-01
The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state describing a motionless fluid and a layered magnetic field, becomes unstable with respect to large scale perturbations. The exact expressions for eddy-viscosity and eddy-resistivity are derived in the nearby of the critical point where the instability sets in. In this marginally unstable case the nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics characterized by coalescence of magnetic islands leading to a final new equilibrium state. High resolution numerical simulations confirm quantitatively the predictions of multiscale analysis.
Stability of an impulsively accelerated density interface in magnetohydrodynamics.
Wheatley, V; Pullin, D I; Samtaney, R
2005-09-16
In the framework of ideal incompressible magnetohydrodynamics, we examine the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This is accomplished by analytically solving the linearized initial value problem, which is a model for the Richtmyer-Meshkov instability. We find that the initial growth rate of the interface is unaffected by the presence of a magnetic field, but for a finite magnetic field the interface amplitude asymptotes to a constant value. Thus the instability of the interface is suppressed. The interface behavior from the analytical solution is compared to the results of both linearized and nonlinear compressible numerical simulations.
Magnetohydrodynamically generated velocities in confined plasma
Morales, Jorge A.; Bos, Wouter J. T.; Schneider, Kai; Montgomery, David C.
2015-04-01
We investigate by numerical simulation the rotational flows in a toroid confining a conducting magnetofluid in which a current is driven by the application of externally supported electric and magnetic fields. The computation involves no microscopic instabilities and is purely magnetohydrodynamic (MHD). We show how the properties and intensity of the rotations are regulated by dimensionless numbers (Lundquist and viscous Lundquist) that contain the resistivity and viscosity of the magnetofluid. At the magnetohydrodynamic level (uniform mass density and incompressible magnetofluids), rotational flows appear in toroidal, driven MHD. The evolution of these flows with the transport coefficients, geometry, and safety factor are described.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Hoelzl, M.; Huijsmans, G. T. A.; Merkel, P.; Atanasiu, C.; Lackner, K.; Nardon, E.; Aleynikova, K.; Liu, F.; Strumberger, E.; McAdams, R.; Chapman, I.; Fil, A.
2014-11-01
The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.
Nonlinear polarization of ionic liquids: theory, simulations, experiments
Kornyshev, Alexei
2010-03-01
Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.
Mahanthesh, B.; Gireesha, B. J.; Gorla, R. S. Reddy; Abbasi, F. M.; Shehzad, S. A.
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases.
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Hardee, Philip E
2010-01-01
We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the Current-Driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations the CD kink instability is excited by a small initial velocity perturbation and develops turbulent structure inside the hot plasma column. We demonstrate that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter \\sigma, the ratio of the Poynting to the kinetic energy flux, declines from an initial value of 0.3 to about 0.01 when the CD kink instability saturates. Our simulations demonstrate that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae do not contradict the natural assumption that the magnetic energy flux still remains a good frac...
Gan, Zhaoming; Li, Hui; Li, Shengtai; Yuan, Feng
2017-04-01
The distinctive morphology of head-tail radio galaxies reveals strong interactions between the radio jets and their intra-cluster environment, the general consensus on the morphology origin of head-tail sources is that radio jets are bent by violent intra-cluster weather. We demonstrate in this paper that such strong interactions provide a great opportunity to study the jet properties and also the dynamics of the intra-cluster medium (ICM). By three-dimensional magnetohydrodynamical simulations, we analyze the detailed bending process of a magnetically dominated jet, based on the magnetic tower jet model. We use stratified atmospheres modulated by wind/shock to mimic the violent intra-cluster weather. Core sloshing is found to be inevitable during the wind-cluster core interaction, which induces significant shear motion and could finally drive ICM turbulence around the jet, making it difficult for the jet to survive. We perform a detailed comparison between the behavior of pure hydrodynamical jets and the magnetic tower jet and find that the jet-lobe morphology could not survive against the violent disruption in all of our pure hydrodynamical jet models. On the other hand, the head-tail morphology is well reproduced by using a magnetic tower jet model bent by wind, in which hydrodynamical instabilities are naturally suppressed and the jet could always keep its integrity under the protection of its internal magnetic fields. Finally, we also check the possibility for jet bending by shock only. We find that shock could not bend the jet significantly, and thus could not be expected to explain the observed long tails in head-tail radio galaxies.
Energy Technology Data Exchange (ETDEWEB)
Savani, N. P. [University Corporation for Atmospheric Research (UCAR), Boulder, CO 80307 (United States); Shiota, D. [Computational Astrophysics Laboratory, Advanced Science Institute, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Kusano, K. [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya 464-8601 (Japan); Vourlidas, A. [Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352 (United States); Lugaz, N., E-mail: neel.savani02@imperial.ac.uk [Experimental Space Plasma Group, University of New Hampshire, Durham, NH 03824 (United States)
2012-11-10
We perform four numerical magnetohydrodynamic simulations in 2.5 dimensions (2.5D) of fast coronal mass ejections (CMEs) and their associated shock fronts between 10 Rs and 300 Rs. We investigate the relative change in the shock standoff distance, {Delta}, as a fraction of the CME radial half-width, D {sub OB} (i.e., {Delta}/D {sub OB}). Previous hydrodynamic studies have related the shock standoff distance for Earth's magnetosphere to the density compression ratio (DR; {rho} {sub u}/{rho} {sub d}) measured across the bow shock. The DR coefficient, k {sub dr}, which is the proportionality constant between the relative standoff distance ({Delta}/D {sub OB}) and the compression ratio, was semi-empirically estimated as 1.1. For CMEs, we show that this value varies linearly as a function of heliocentric distance and changes significantly for different radii of curvature of the CME's leading edge. We find that a value of 0.8 {+-} 0.1 is more appropriate for small heliocentric distances (<30 Rs) which corresponds to the spherical geometry of a magnetosphere presented by Seiff. As the CME propagates its cross section becomes more oblate and the k {sub dr} value increases linearly with heliocentric distance, such that k {sub dr} = 1.1 is most appropriate at a heliocentric distance of about 80 Rs. For terrestrial distances (215 Rs) we estimate k {sub dr} = 1.8 {+-} 0.3, which also indicates that the CME cross-sectional structure is generally more oblate than that of Earth's magnetosphere. These alterations to the proportionality coefficients may serve to improve investigations into the estimates of the magnetic field in the corona upstream of a CME as well as the aspect ratio of CMEs as measured in situ.
Robust large-scale parallel nonlinear solvers for simulations.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any
Angular spectrum approach for fast simulation of pulsed non-linear ultrasound fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
The paper presents an Angular Spectrum Approach (ASA) for simulating pulsed non-linear ultrasound fields. The source of the ASA is generated by Field II, which can simulate array transducers of any arbitrary geometry and focusing. The non-linear ultrasound simulation program - Abersim, is used...... the fundamental and keep the second harmonic field, since Abersim simulates non-linear fields with all harmonic components. ASA and Abersim are compared for the pulsed fundamental and second harmonic fields in the time domain at depths of 30 mm, 40 mm (focal depth) and 60 mm. Full widths at -6 dB (FWHM) are f0...
Current-sheet formation in incompressible electron magnetohydrodynamics
DEFF Research Database (Denmark)
Ruban, Victor P.
2002-01-01
The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonl......The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local...
Transient, nonlinear rheology of reversible colloidal gels by dynamic simulation
Landrum, Benjamin; Russel, William; Zia, Roseanna
2014-11-01
We study the nonlinear rheology of reversible colloidal gels via dynamic simulation as they undergo age- and flow-induced structural evolution, with a view toward understanding and predicting transient behaviors such as multi-step and delayed yield. The gel is formed from 750,000 Brownian spheres interacting via hard-sphere repulsion and O(kT) short-range attraction, where thermal fluctuations are strong enough to allow continued structural rearrangement in the absence of flow. During startup of imposed strain rate, the transition to steady state is characterized by one or more ``overshoots'' in the stress which suggest initial yield, formation of a stronger gel, and subsequent yield of the new gel. When subjected to step-shear stress, the microstructure undergoes limited creep, followed by viscous flow. This macroscopic ``delayed flow'' is consistent with previously proposed models of competition between breakage and formation of particle bonds among static load-bearing structures. Our findings suggest, however, that the load-bearing structures evolve, and that the gel's resistance to delayed failure depends upon this structural evolution and reinforcement. We put forth a micro-mechanical model of stress gradient-driven particle transport that captures this macroscopic behavior.
Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Jørgen Arendt
2013-01-01
. The accuracy of the nonlinear ASA is compared to the non-linear simulation program – Abersim, which is a numerical solution to the Burgers equation based on the OSM. Simulations are performed for a linear array transducer with 64 active elements, focus at 40 mm, and excitation by a 2-cycle sine wave......A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly...... increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated...
El-Alaoui, M.; Richard, R. L.; Ashour-Abdalla, M.; Walker, R. J.; Goldstein, M. L.
2012-01-01
We report the results of MHD simulations of Earth's magnetosphere for idealized steady solar wind plasma and interplanetary magnetic field (IMF) conditions. The simulations feature purely northward and southward magnetic fields and were designed to study turbulence in the magnetotail plasma sheet. We found that the power spectral densities (PSDs) for both northward and southward IMF had the characteristics of turbulent flow. In both cases, the PSDs showed the three scale ranges expected from theory: the energy-containing scale, the inertial range, and the dissipative range. The results were generally consistent with in-situ observations and theoretical predictions. While the two cases studied, northward and southward IMF, had some similar characteristics, there were significant differences as well. For southward IMF, localized reconnection was the main energy source for the turbulence. For northward IMF, remnant reconnection contributed to driving the turbulence. Boundary waves may also have contributed. In both cases, the PSD slopes had spatial distributions in the dissipative range that reflected the pattern of resistive dissipation. For southward IMF there was a trend toward steeper slopes in the dissipative range with distance down the tail. For northward IMF there was a marked dusk-dawn asymmetry with steeper slopes on the dusk side of the tail. The inertial scale PSDs had a dusk-dawn symmetry during the northward IMF interval with steeper slopes on the dawn side. This asymmetry was not found in the distribution of inertial range slopes for southward IMF. The inertial range PSD slopes were clustered around values close to the theoretical expectation for both northward and southward IMF. In the dissipative range, however, the slopes were broadly distributed and the median values were significantly different, consistent with a different distribution of resistivity.
Huarte-Espinosa, Martin; Alexander, Paul
2011-01-01
Radio observations of Fanaroff-Riley class II sources often show correlations between the synchrotron emission and the linear-polarimetric distributions. Magnetic position vectors seem to align with the projected emission of both the radio jets and the sources' edges. Using statistics we study such relation as well as its unknown time evolution via synthetic polarisation maps of model FR II sources formed in 3D-MHD numerical simulations of bipolar, hypersonic and weakly magnetised jets. The magnetic field is initially random with a Kolmogorov power spectrum, everywhere. We investigate the structure and evolution of magnetic fields in the sources as a function of the power of jets and the observational viewing angle. Our synthetic polarisation maps agree with observations, showing B-field vectors which are predominantly aligned with the jet axis, and show that magnetic fields inside sources are shaped by the jets' backflow. Polarimetry is found to correlate with time, the viewing angle and the jet-to-ambient d...
Simulations of the Ocean Response to a Hurricane: Nonlinear Processes
Zedler, Sarah E.
2009-10-01
Superinertial internal waves generated by a tropical cyclone can propagate vertically and laterally away from their local generation site and break, contributing to turbulent vertical mixing in the deep ocean and maintenance of the stratification of the main thermocline. In this paper, the results of a modeling study are reported to investigate the mechanism by which superinertial fluctuations are generated in the deep ocean. The general properties of the superinertial wave wake were also characterized as a function of storm speed and central latitude. The Massachusetts Institute of Technology (MIT) Ocean General Circulation Model (OGCM) was used to simulate the open ocean response to realistic westward-tracking hurricane-type surface wind stress and heat and net freshwater buoyancy forcing for regions representative of midlatitudes in the Atlantic, the Caribbean, and low latitudes in the eastern Pacific. The model had high horizontal [Δ(x, y) = 1/6°] and vertical (Δz = 5 m in top 100 m) resolution and employed a parameterization for vertical mixing induced by shear instability. In the horizontal momentum equation, the relative size of the nonlinear advection terms, which had a dominant frequency near twice the inertial, was large only in the upper 200 m of water. Below 200 m, the linear momentum equations obeyed a linear balance to 2%. Fluctuations at nearly twice the inertial frequency (2f) were prevalent throughout the depth of the water column, indicating that these nonlinear advection terms in the upper 200 m forced a linear mode below at nearly twice the inertial frequency via vorticity conservation. Maximum variance at 2f in horizontal velocity occurred on the south side of the track. This was in response to vertical advection of northward momentum, which in the north momentum equation is an oscillatory positive definite term that constituted a net force to the south at a frequency near 2f. The ratio of this term to the Coriolis force was larger on the
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint
Energy Technology Data Exchange (ETDEWEB)
Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan
2016-01-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
Equivalent circuit simulation of HPEM-induced transient responses at nonlinear loads
Directory of Open Access Journals (Sweden)
M. Kotzev
2017-09-01
Full Text Available In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.
Nonlinear excitation of low-n harmonics in reduced MHD simulations of edge-localized modes
Krebs, Isabel; Lackner, Karl; Guenter, Sibylle
2013-01-01
Nonlinear simulations of the early ELMphase based on a typical type-I ELMy ASDEX Upgrade discharge have been carried out using the reduced MHD code JOREK. The analysis is focused on the evolution of the toroidal Fourier spectrum. It is found that during the nonlinear evolution, linearly subdominant low-n Fourier components, in particular the n = 1, grow to energies comparable with linearly dominant harmonics. A simple model is developed, based on the idea that energy is transferred among the toroidal harmonics via second order nonlinear interaction. The simple model reproduces and explains very well the early nonlinear evolution of the toroidal spectrum in the JOREK simulations. Furthermore, it is shown for the n = 1 harmonic, that its spatial structure changes significantly during the transition from linear to nonlinearly driven growth. The rigidly growing structure of the linearly barely unstable n = 1 reaches far into the plasma core. In contrast, the nonlinearly driven n = 1 has a rigidly growing structur...
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Magnetohydrodynamics on Heterogeneous architectures: a performance comparison
Pang, Bijia; Perrone, Michael
2010-01-01
We present magneto-hydrodynamic simulation results for heterogeneous systems. Heterogeneous architectures combine high floating point performance many-core units hosted in conventional server nodes. Examples include Graphics Processing Units (GPU's) and Cell. They have potentially large gains in performance, at modest power and monetary cost. We implemented a magneto-hydrodynamic (MHD) simulation code on a variety of heterogeneous and multi-core architectures --- multi-core x86, Cell, Nvidia and ATI GPU --- in different languages, FORTRAN, C, Cell, CUDA and OpenCL. We present initial performance results for these systems. To our knowledge, this is the widest comparison of heterogeneous systems for MHD simulations. We review the different challenges faced in each architecture, and potential bottlenecks. We conclude that substantial gains in performance over traditional systems are possible, and in particular that is possible to extract a greater percentage of peak theoretical performance from some systems when...
Colombeau, J. F.
2007-01-01
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is to invite the readers in applying these techniques in their own work without significant prerequisites by presenting their use on a sample of elementary applications from engineering. Pure mathematicians can read it easily since the numerical techniques are ...
Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics
Reynolds, Daniel R.
2012-01-01
We apply the automatic differentiation tool OpenAD toward constructing a preconditioner for fully implicit simulations of mapped grid visco-resistive magnetohydrodynamics (MHD), used in modeling tokamak fusion devices. Our simulation framework employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner, which typically requires knowledge of the Jacobian of the nonlinear residual function. However, due to significant nonlinearity within our PDE system, our mapped spatial discretization, and stencil adaptivity at physical boundaries, analytical derivation of these Jacobian entries is highly nontrivial. This paper therefore focuses on Jacobian construction using automatic differentiation. In particular, we discuss applying OpenAD to the case of a spatially-adaptive stencil patch that automatically handles differences between the domain interior and boundary, and configuring AD for reduced stencil approximations to the Jacobian. We investigate both scalar and vector tangent mode differentiation, along with simple finite difference approaches, to compare the resulting accuracy and efficiency of Jacobian construction in this application. © 2012 Springer-Verlag.
Simulation of Nonlinear Gain Saturation in Active Photonic Crystal Waveguides
DEFF Research Database (Denmark)
Chen, Yaohui; Mørk, Jesper
2012-01-01
In this paper we present a theoretical analysis of slowlight enhanced traveling wave amplification in an active semiconductor Photonic crystal waveguides. The impact of group index on nonlinear modal gain saturation is investigated.......In this paper we present a theoretical analysis of slowlight enhanced traveling wave amplification in an active semiconductor Photonic crystal waveguides. The impact of group index on nonlinear modal gain saturation is investigated....
Energy Technology Data Exchange (ETDEWEB)
Hillstrom, K. E.
1976-02-01
A simulation test technique was developed to evaluate and compare unconstrained nonlinear optimization computer algorithms. Descriptions of the test technique, test problems, computer algorithms tested, and test results are provided. (auth)
Magnetohydrodynamics of the sun
Priest, Eric
2014-01-01
Magnetohydrodynamics of the Sun is a completely new up-to-date rewrite from scratch of the 1982 book Solar Magnetohydrodynamics, taking account of enormous advances in understanding since that date. It describes the subtle and complex interaction between the Sun's plasma atmosphere and its magnetic field, which is responsible for many fascinating dynamic phenomena. Chapters cover the generation of the Sun's magnetic field by dynamo action, magnetoconvection and the nature of photospheric flux tubes such as sunspots, the heating of the outer atmosphere by waves or reconnection, the structure of prominences, the nature of eruptive instability and magnetic reconnection in solar flares and coronal mass ejections, and the acceleration of the solar wind by reconnection or wave-turbulence. It is essential reading for graduate students and researchers in solar physics and related fields of astronomy, plasma physics and fluid dynamics. Problem sets and other resources are available at www.cambridge.org/9780521854719.
Thermoacoustic magnetohydrodynamic electrical generator
Wheatley, John C.; Swift, Gregory W.; Migliori, Albert
1986-01-01
A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1,000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.
Lectures on magnetohydrodynamical drives
Loigom, Villem
The paper deals with nonconventional types of electrical machines and drives - magnetohydrodynamical (MHD) machines and drives. In cardinal it is based on the research conducted with participation of the author in Tallinn Technical University at the Institute of Electrical Drives and Power Electronics, where the use of magnetohydrodynamical motors and drives in the metallurgical and casting industries have been studied for a long time. Major research interests include the qualities and applications of the induction MHD-drives for set in the motion (pumping, turning, dosing, mixing, etc.) non-ferrous molten metals like Al, Mg, Sn, Pb, Na, K, and their alloys. The first part of the paper describes induction MHD motors and their electrohydraulical qualities. In the second part energy conversion problems are described. Also, on the basis of the analogy between electromechanical and electrohydraulical phenomenas, static and dynamic qualities of MHD drives with induction MHD machines are discussed.
Decay rates of the magnetohydrodynamic model for quantum plasmas
Pu, Xueke; Xu, Xiuli
2017-02-01
In this paper, we consider the quantum magnetohydrodynamic model for quantum plasmas. We prove the optimal decay rates for the solution to the constant state in the whole space in the Lp-norm with 2≤ p≤ 6 and its first derivatives in L2-norm. The proof is based on the optimal decay of the linearized equation and nonlinear energy estimates.
Parallel magnetohydrodynamics on the Cray T3D
Meijer, P. M.; Poedts, S.; Goedbloed, J. P.
1996-01-01
The equations of magnetohydrodynamics (MHD) are discussed in the framework of parallel computing. Both linear and nonlinear MHD models are addressed. Special attention is given to the parallellisation of the kernels of the existing sequential MHD codes. These kernels involve matrix-vector multiplica
Dynamic Simulations of Nonlinear Multi-Domain Systems Based on Genetic Programming and Bond Graphs
Institute of Scientific and Technical Information of China (English)
DI Wenhui; SUN Bo; XU Lixin
2009-01-01
A dynamic simulation method for non-linear systems based on genetic programming (GP) and bond graphs (BG) was developed to improve the design of nonlinear multi-domain energy conversion sys-tems. The genetic operators enable the embryo bond graph to evolve towards the target graph according to the fitness function. Better simulation requires analysis of the optimization of the eigenvalue and the filter circuit evolution. The open topological design and space search ability of this method not only gives a more optimized convergence for the operation, but also reduces the generation time for the new circuit graph for the design of nonlinear multi-domain systems.
Magnetohydrodynamic Turbulence and the Geodynamo
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Vortex disruption by magnetohydrodynamic feedback
Mak, Julian; Hughes, D W
2016-01-01
In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to form strong current sheets on their edges. Associated with these current sheets are magnetic stresses, which are subsequently released through reconnection, leading to vortex disruption, and possibly even destruction. This disruption phenomenon is investigated here in the context of two-dimensional, homogeneous, incompressible magnetohydrodynamics. We derive a simple order of magnitude estimate for the magnetic stresses --- and thus the degree of disruption --- that depends on the strength of the background magnetic field (measured by the parameter $M$, a ratio between the Alfv\\'en speed and a typical flow speed) and on the magnetic diffusivity (measured by the magnetic Reynolds number $\\mbox{Rm}$). The resulting estimate suggests that significant disruption occurs when $M^{2}\\mbox{Rm} = O(1)$. To test our prediction, we analyse direct numerical simulations of vortices generated by the breakup of unstable shear flo...
Scale locality of magnetohydrodynamic turbulence.
Aluie, Hussein; Eyink, Gregory L
2010-02-26
We investigate the scale locality of cascades of conserved invariants at high kinetic and magnetic Reynold's numbers in the "inertial-inductive range" of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross helicity-or, equivalently, fluxes of Elsässer energies-are dominated by the contributions of local triads. Flux of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term may also be dominated by nonlocal triads, but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion nonlocally between disparate scales. We present supporting data from a 1024{3} simulation of forced MHD turbulence.
Spectrum of weak magnetohydrodynamic turbulence.
Boldyrev, Stanislav; Perez, Jean Carlos
2009-11-27
Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or nonbalanced, in that the energies of Alfvén waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy E(v) - E(b) at small field-parallel wave numbers. As a result, the energy spectra of Alfvén waves are generally not scale invariant in an inertial interval of limited extent. In the limit of an infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling E(k) proportional to k(perpendicular)(-2). The generation of a condensate is apparently related to the breakdown of mirror symmetry in nonbalanced turbulence.
Higher-order nonlinear Schrodinger equations for simulations of surface wavetrains
Slunyaev, Alexey
2016-04-01
Numerous recent results of numerical and laboratory simulations of waves on the water surface claim that solutions of the weakly nonlinear theory for weakly modulated waves in many cases allow a smooth generalization to the conditions of strong nonlinearity and dispersion, even when the 'envelope' is difficult to determine. The conditionally 'strongly nonlinear' high-order asymptotic equations still imply the smallness of the parameter employed in the asymptotic series. Thus at some (unknown a priori) level of nonlinearity and / or dispersion the asymptotic theory breaks down; then the higher-order corrections become useless and may even make the description worse. In this paper we use the higher-order nonlinear Schrodinger (NLS) equation, derived in [1] (the fifth-order NLS equation, or next-order beyond the classic Dysthe equation [2]), for simulations of modulated deep-water wave trains, which attain very large steepness (below or beyond the breaking limit) due to the Benjamin - Feir instability. The results are compared with fully nonlinear simulations of the potential Euler equations as well as with the weakly nonlinear theories represented by the nonlinear Schrodinger equation and the classic Dysthe equation with full linear dispersion [2]. We show that the next-order Dysthe equation can significantly improve the description of strongly nonlinear wave dynamics compared with the lower-order asymptotic models. [1] A.V. Slunyaev, A high-order nonlinear envelope equation for gravity waves in finite-depth water. JETP 101, 926-941 (2005). [2] K. Trulsen, K.B. Dysthe, A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281-289 (1996).
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Future of Magnetohydrodynamic Ship Propulsion,
1983-08-16
83 FOREIGN TECHNOLOGY DIVISION FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION by A.P. Baranov DTIQ ~E tJ Approved for public release; 0.. distribution...MAGNETOHYDRODYNAMIC SHIP PROPULSION By: A.P. Baranov -,English pages: 10 Source: Sudostroyeniye, Nr. 12, December 1966, pp. 3-6 . Country of origin: USSR X...equations, etc. merged into this translation were extracted from the best quality copy available. FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION A. P
Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
Carrillo, José A.
2016-09-22
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient flow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this property with various examples in spatial dimension one and two.
三维磁流体强化超燃冲压发动机数值模拟%Simulation of three-dimensional magnetohydrodynamic enhanced scramjet
Institute of Scientific and Technical Information of China (English)
郑小梅; 杨兴宇
2012-01-01
Simulation model of the three-dimensional magnetohydrodynamic(MHD) enhanced scramjet viscous inner flow field was established.Geometry of a scramjet applied both MHD controlled inlet and MHD energy bypass was designed at Ma=6.Numerical simulation was performed,and three-dimensional flow field structure,distribution pattern of the electric parameters,and characteristics of energy transformation were analyzed.The results show when flight Ma=8,MHD controlled inlet can be used to draw the compressive shock waves back to the cowl lip,the separation zone disappears,and the flow field of the inner inlet recovers to the design condition.The MHD energy bypass can decrease Ma of the flow before combustor efficiently,so as to improve engine performance.In the MHD generator,distributions of flow and electric parameters are comparatively ideal to make efficient effect,while the MHD accelerator needs large amount of energy input to make a significant acceleration.In the MHD accelerator,Joule heating dissipation is severe near the electrodes,which results in local high temperature,flow field complication and performance deterioration of the MHD accelerator.%建立了三维磁流体强化超燃冲压发动机内部黏性流场的求解模型.针对马赫数为6设计了联合应用磁控进气道和磁流体能量旁路的磁流体强化超燃冲压发动机模型.针对该模型进行了数值模拟研究，分析其中的三维流场结构、电参数分布规律以及能量转换特性.结果表明：当飞行马赫数为8时，磁控进气道的应用能够使头部压缩激波回到唇口，使分离区消失，内进气道中的流动恢复到设计状态.磁流体能量旁路可有效降低燃烧室入口处的马赫数，从而改善发动机性能.其中发生器中的流动参数和电参数的分布比较理想，效果显著；而加速器要取得显著的加速效果则需要人量的能量输入.在加速器中，电极附近焦耳耗散严重，导致局部高温
Current-sheet formation in incompressible electron magnetohydrodynamics.
Ruban, V P
2002-04-01
The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia.
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Bhatia, Tanayveer Singh
2016-01-01
The emergence of turbulence in shear flows is a well-investigated field. Yet, one of major issues is the apparent contradiction between linear stability analysis quoting a flow to be stable and results from experiments and simulations proving it to be otherwise. There is some success, in particular in astrophysical systems, based on Magneto-Rotational Instability (MRI). However, MRI requires the system to be weakly magnetized, which is not a feature of general magnetohydrodynamic (MHD) flows. Nevertheless, linear perturbations of such flows are nonnormal in nature which argues for an origin of nonlinearity therein. The idea is, nonnormal perturbations could produce huge transient energy growth (TEG), which may lead to non-linearity and further turbulence. However, so far, nonnormal effects in shear flows have not been explored much in the presence of magnetic fields. Here, we consider the perturbed visco-resistive incompressible MHD shear flows with rotation in general. Basically we consider the magnetized ve...
Interactions between two magnetohydrodynamic Kelvin-Helmholtz instabilities.
Lai, S H; Ip, W-H
2011-10-01
Kelvin-Helmholtz instability (KHI) driven by velocity shear is a generator of waves found away from the vicinity of the velocity-shear layers since the fast-mode waves radiated from the surface perturbation can propagate away from the transition layer. Thus the nonlinear evolution associated with KHI is not confined near the velocity-shear layer. To understand the physical processes in multiple velocity-shear layers, the interactions between two KHIs at a pair of tangential discontinuities are studied by two-dimensional magnetohydrodynamic simulations. It is shown that the interactions between two neighboring velocity-shear layers are dominated by the propagation of the fast-mode waves radiated from KHIs in a nonuniform medium. That is, the fast-mode Mach number of the surface waves M(Fy), a key factor of the nonlinear evolution of KHI, will vary with the nonuniform background plasma velocity due to the existence of two neighboring velocity-shear layers. As long as the M(Fy) observed in the plasma rest frame across the neighboring velocity-shear layer is larger than one, newly formed fast-mode Mach-cone-like (MCL) plane waves generated by the fast-mode waves can be found in this region. As results of the interactions of two KHIs, reflection and distortion of the MCL plane waves generate the turbulence and increase the plasma temperature, which provide possible mechanisms of heating and accelerating local plasma between two neighboring velocity-shear layers.
Institute of Scientific and Technical Information of China (English)
张洪生; 洪广文; 丁平兴; 曹振轶
2001-01-01
In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.
Magnetohydrodynamics of Chiral Relativistic Fluids
Boyarsky, Alexey; Ruchayskiy, Oleg
2015-01-01
We study the dynamics of a plasma of charged relativistic fermions at very high temperature $T\\gg m$, where $m$ is the fermion mass, coupled to the electromagnetic field. In particular, we derive a magneto-hydrodynamical description of the evolution of such a plasma. We show that, as compared to conventional MHD for a plasma of non-relativistic particles, the hydrodynamical description of the relativistic plasma involves new degrees of freedom described by a pseudo-scalar field originating in a local asymmetry in the densities of left-handed and right-handed fermions. This field can be interpreted as an effective axion field. Taking into account the chiral anomaly we present dynamical equations for the evolution of this field, as well as of other fields appearing in the MHD description of the plasma. Due to its non-linear coupling to helical magnetic fields, the axion field significantly affects the dynamics of a magnetized plasma and can give rise to a novel type of inverse cascade.
Intense DC beam nonlinear transport-analysis & simulation
Institute of Scientific and Technical Information of China (English)
L(U) Jian-Qin; ZHAO Xiao-Song
2009-01-01
The intense dc beam nonlinear transport was analyzed with the Lie algebraic method,and the particle trajectories of the second order approximation were obtained.Based on the theoretical analysis a computer code was designed.To get self-consistent solutions,iteration procedures were used in the code.As an example,we calculated a beam line(drift-electrostatic quadrupole doublet-drift).The results agree to the results calculated by using the PIC method.
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.
Institute of Scientific and Technical Information of China (English)
WU; Shaoping(吴少平); YI; Fan(易帆)
2002-01-01
By using FICE scheme, a numerical simulation of nonlinear propagation of gravity wave packet in three-dimension compressible atmosphere is presented. The whole nonlinear propagation process of the gravity wave packet is shown; the basic characteristics of nonlinear propagation and the influence of the ambient winds on the propagation are analyzed. The results show that FICE scheme can be extended in three-dimension by which the calculation is steady and kept for a long time; the increase of wave amplitude is faster than the exponential increase according to the linear gravity theory; nonlinear propagation makes the horizontal perturbation velocity increase greatly which can lead to enhancement of the local ambient winds; the propagation path and the propagation velocity of energy are different from the results expected by the linear gravity waves theory, the nonlinearity causes the change in propagation characteristics of gravity wave; the ambient winds alter the propagation path and group velocity of gravity wave.
Two-dimensional simulations of nonlinear beam-plasma interaction in isotropic and magnetized plasmas
Timofeev, I V
2012-01-01
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroying the BGK--type nonlinear wave are identified. In the weak magnetic field, the energy of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction goes predominantly to the short-wavelength upper-hybrid waves propagating parallel to the magnetic field, whereas in the strong magnetic field the spectral energy is transferred to the electrostatic whistlers with oblique propagation.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Solitary vortexes in magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Vainshtein, S.I.
1985-12-01
Stationary configurations in magnetohydrodynamics are investigated for the following two particular cases: (1) there is no motion, which corresponds to a state of magnetostatic equilibrium; and (2) the magnetic field intensity becomes zero, i.e., hydrodynamic vortexes are involved. It is shown that in certain cases the line-of-force topology must be sufficiently simple in order before a stationary or equilibrium state can be achieved. It is also shown that in the two-dimensional case, the magnetic surfaces of an equilibrium configuration represent coaxial cylindrical surfaces. 12 references.
Conservation of Circulation in Magnetohydrodynamics
Bekenstein, J D; Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We demonstrate, both at the Newtonian and (general) relativistic levels, theexistence of a generalization of Kelvin's circulation theorem (for pure fluids)which is applicable to perfect magnetohydrodynamics. The argument is based onthe least action principle for magnetohydrodynamic flow. Examples of the newconservation law are furnished. The new theorem should be helpful inidentifying new kinds of vortex phenomena distinct from magnetic ropes or fluidvortices.
Direct Evidence of the Transition from Weak to Strong Magnetohydrodynamic Turbulence.
Meyrand, Romain; Galtier, Sébastien; Kiyani, Khurom H
2016-03-11
One of the most important predictions in magnetohydrodynamics is that in the presence of a uniform magnetic field b_{0}e[over ^]_{∥} a transition from weak to strong wave turbulence should occur when going from large to small perpendicular scales. This transition is believed to be a universal property of several anisotropic turbulent systems. We present, for the first time, direct evidence of such a transition using a decaying three-dimensional direct numerical simulation of incompressible balanced magnetohydrodynamic turbulence with a grid resolution of 3072^{2}×256. From large to small scales, the change of regime is characterized by (i) a change of slope in the energy spectrum going from approximately -2 to -3/2, (ii) an increase of the ratio between the wave and nonlinear times, with a critical ratio of χ_{c}∼1/3, (iii) a modification of the isocontours of energy revealing a transition from a purely perpendicular cascade to a cascade compatible with the critical-balance-type phenomenology, and (iv) an absence followed by a dramatic increase of the communication between Alfvén modes. The changes happen at approximately the same transition scale and can be seen as manifest signatures of the transition from weak to strong wave turbulence. Furthermore, we observe a significant nonlocal three-wave coupling between strongly and weakly nonlinear modes resulting in an inverse transfer of energy from small to large scales.
A magnetic betelgeuse? Numerical simulations of non-linear dynamo action
DEFF Research Database (Denmark)
Dorch, S. B. F.
2004-01-01
question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible...... and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action....
Wei, Jingsong; Wang, Rui; Yan, Hui; Fan, Yongtao
2014-04-07
This study explores how interference manipulation breaks through the diffraction limit and induces super-resolution nano-optical hot spots through the nonlinear Fabry-Perot cavity structure. The theoretical analytical model is established, and the numerical simulation results show that when the thickness of the nonlinear thin film inside the nonlinear Fabry-Perot cavity structure is adjusted to centain value, the constructive interference effect can be formed in the central point of the spot, which causes the nanoscale optical hot spot in the central region to be produced. The simulation results also tell us that the hot spot size is sensitive to nonlinear thin film thickness, and the accuracy is required to be up to nanometer or even subnanometer scale, which is very large challenging for thin film deposition technique, however, slightly changing the incident laser power can compensate for drawbacks of low thickness accuracy of nonlinear thin films. Taking As(2)S(3) as the nonlinear thin film, the central hot spot with a size of 40nm is obtained at suitable nonlinear thin film thickness and incident laser power. The central hot spot size is only about λ/16, which is very useful in super-high density optical recording, nanolithography, and high-resolving optical surface imaging.
Magnetohydrodynamic process in solar activity
Directory of Open Access Journals (Sweden)
Jingxiu Wang
2014-01-01
Full Text Available Magnetohydrodynamics is one of the major disciplines in solar physics. Vigorous magnetohydrodynamic process is taking place in the solar convection zone and atmosphere. It controls the generating and structuring of the solar magnetic fields, causes the accumulation of magnetic non-potential energy in the solar atmosphere and triggers the explosive magnetic energy release, manifested as violent solar flares and coronal mass ejections. Nowadays detailed observations in solar astrophysics from space and on the ground urge a great need for the studies of magnetohydrodynamics and plasma physics to achieve better understanding of the mechanism or mechanisms of solar activity. On the other hand, the spectacular solar activity always serves as a great laboratory of magnetohydrodynamics. In this article, we reviewed a few key unresolved problems in solar activity studies and discussed the relevant issues in solar magnetohydrodynamics.
Simulation of financial market via nonlinear Ising model
Ko, Bonggyun; Song, Jae Wook; Chang, Woojin
2016-09-01
In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.
Protostellar outflows with Smoothed Particle Magnetohydrodynamics (SPMHD)
Bürzle, Florian; Stasyszyn, Federico; Dolag, Klaus; Klessen, Ralf S
2011-01-01
The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D AMR/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the Smoothed Particle Hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show, that Smoothed Particle Magnetohydrodynamics (SPMHD) is a...
Nonlinear Site Response Due to Large Ground Acceleration: Observation and Computer Simulation
Noguchi, S.; Furumura, T.; Sasatani, T.
2009-12-01
We studied nonlinear site response due to large ground acceleration during the 2003 off-Miyagi Earthquake (Mw7.0) in Japan by means of horizontal-to-vertical spectral ratio analysis of S-wave motion. The results were then confirmed by finite-difference method (FDM) simulation of nonlinear seismic wave propagation. A nonlinear site response is often observed at soft sediment sites, and even at hard bedrock sites which are covered by thin soil layers. Nonlinear site response can be induced by strong ground motion whose peak ground acceleration (PGA) exceeds about 100 cm/s/s, and seriously affects the amplification of high frequency ground motion and PGA. Noguchi and Sasatani (2008) developed an efficient technique for quantitative evaluation of nonlinear site response using the horizontal-to-vertical spectral ratio of S-wave (S-H/V) derived from strong ground motion records, based on Wen et al. (2006). We applied this technique to perform a detailed analysis of the properties of nonlinear site response based on a large amount of data recorded at 132 K-NET and KiK-net strong motion stations in Northern Japan during the off-Miyagi Earthquake. We succeeded in demonstrating a relationship between ground motion level, nonlinear site response and surface soil characteristics. For example, the seismic data recorded at KiK-net IWTH26 showed obvious characteristics of nonlinear site response when the PGA exceeded 100 cm/s/s. As the ground motion level increased, the dominant peak of S-H/V shifted to lower frequency, the high frequency level of S-H/V dropped, and PGA amplification decreased. On the other hand, the records at MYGH03 seemed not to be affected by nonlinear site response even for high ground motion levels in which PGA exceeds 800 cm/s/s. The characteristics of such nonlinear site amplification can be modeled by evaluating Murnaghan constants (e.g. McCall, 1994), which are the third-order elastic constants. In order to explain the observed characteristics of
Modeling and Simulation of Nonlinear Micro-electromechanical Circular Plate
Directory of Open Access Journals (Sweden)
Chin-Chia Liu
2013-09-01
Full Text Available In the present study, the hybrid differential transformation and finite difference method is applied to analyze the dynamic behavior of the nonlinear micro-electromechanical circular plate actuated by combined DC / AC loading schemes. The analysis takes account of the axial residual stress and hydrostatic pressure acting on micro circular plate upper surface. The dynamic response of the plate as a function of the magnitude of the AC driving voltage is explored. Moreover, the effect of the initial gap height on the pull-in voltage of the plate is systematically explored.
Magnetohydrodynamics of blood flow.
Keltner, J R; Roos, M S; Brakeman, P R; Budinger, T F
1990-10-01
The changes in hydrostatic pressure and electrical potentials across vessels in the human vasculature in the presence of a large static magnetic field are estimated to determine the feasibility of in vivo NMR spectroscopy at fields as high as 10 T.A 10-T magnetic field changes the vascular pressure in a model of the human vasculature by less than 0.2%. An exact solution to the magnetohydrodynamic equations describing a conducting fluid flowing transverse to a static magnetic field in a nonconducting, straight, circular tube is used. This solution is compared to an approximate solution that assumes that no magnetic fields are induced in the fluid and that has led previous investigators to predict significant biological effects from static magnetic fields. Experimental results show that the exact solution accurately predicts the magnetohydrodynamic slowing of 15% NaCl flowing transverse to 2.3- and 4.7-T magnetic fields for fluxes below 0.5 liter/min while the approximate solution predicts a much more retarded flow.
2-D Composite Model for Numerical Simulations of Nonlinear Waves
Institute of Scientific and Technical Information of China (English)
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
Inoue, S; Magara, T; Choe, G S; Park, Y D
2015-01-01
We clarify a relationship of the dynamics of a solar flare and a growing Coronal Mass Ejection (CME) by investigating the dynamics of magnetic fields during the X2.2-class flare taking place in the solar active region 11158 on 2011 February 15, based on simulation results obtained from Inoue et al. 2014. We found that the strongly twisted lines formed through the tether-cutting reconnection in the twisted lines of a nonlinear force-free field (NLFFF) can break the force balance within the magnetic field, resulting in their launch from the solar surface. We further discover that a large-scale flux tube is formed during the eruption as a result of the tether-cutting reconnection between the eruptive strongly twisted lines and these ambient weakly twisted lines. Then the newly formed large flux tube exceeds the critical height of the torus instability. The tether-cutting reconnection thus plays an important role in the triggering a CME. Furthermore, we found that the tangential fields at the solar surface illust...
Simulations and model of the nonlinear Richtmyer-Meshkov instability (U)
Energy Technology Data Exchange (ETDEWEB)
Dimonte, Guy [Los Alamos National Laboratory
2009-01-01
The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two-dimensions (20). The purpose of the simulations is to develop a nonlinear model of the RM instability that is accurate to the regime of inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and initial amplitude kh{sub o} (k {triple_bond} wavenumber) of the perturbation. The FLASH code is first validated by obtaining excellent agreement with RM experiments well into the nonlinear regime. The results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A and kh{sub o} but not for the values characteristic of ICF and ejecta formation. As a result, a new nonlinear model is developed that captures the simulation results consistent with potential flow and for a broader range of A and kh{sub o}.
Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
National Research Council Canada - National Science Library
Kumbhakar, Dharmadas
2012-01-01
.... The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories...
Interactive Classroom Graphics--Simulating Non-Linear Arrhenius Plots.
Ben-Zion, M.; Hoz, S.
1980-01-01
Describes two simulation programs using an interactive graphic display terminal that were developed for a course in physical organic chemistry. Demonstrates the energetic conditions that give rise to deviations from linearity in the Arrhenius equation. (CS)
DEFF Research Database (Denmark)
Du, Yigang; Fan, Rui; Li, Yong
2016-01-01
An ultrasound imaging framework modeled with the first order nonlinear pressure–velocity relations (NPVR) based simulation and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound...... propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework......, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA...
Hieber, Simone E.; Koumoutsakos, Petros
2008-11-01
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress-strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.
Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing
Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng
2017-05-01
Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.
THE SIGNATURE OF INITIAL CONDITIONS ON MAGNETOHYDRODYNAMIC TURBULENCE
Energy Technology Data Exchange (ETDEWEB)
Dallas, V.; Alexakis, A., E-mail: vdallas@lps.ens.fr, E-mail: alexakis@lps.ens.fr [Laboratoire de Physique Statistique, École Normale Supérieure, Université Pierre et Marié Curie, Université Paris Diderot, CNRS, 24 rue Lhomond, F-75005 Paris (France)
2014-06-20
We demonstrate that the initial correlation between velocity and current density fluctuations can lead to the formation of enormous current sheets in freely evolving magnetohydrodynamic (MHD) turbulence. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all of the nonlinear interactions during the formation of turbulence. The size of these structures spans our computational domain, dominating the scaling of the energy spectrum, which follows a E∝k {sup –2} power law. As the Reynolds number increases, the curling of the current sheets due to Kelvin-Helmholtz-type instabilities and reconnection modifies the scaling of the energy spectrum from k {sup –2} toward k {sup –5/3}. This transition occurs due to the decorrelation of the velocity and the current density which is proportional to Re{sub λ}{sup −3/2}. Finite Reynolds number behavior is observed without reaching a finite asymptote for the energy dissipation rate even for a simulation of Re{sub λ} ≅ 440 with 2048{sup 3} grid points. This behavior demonstrates that even state-of-the-art numerical simulations of the highest Reynolds numbers can be influenced by the choice of initial conditions and consequently they are inadequate to deduce unequivocally the fate of universality in MHD turbulence. Implications for astrophysical observations are discussed.
Simulations of Energetic Particles Interacting with Nonlinear Anisotropic Dynamical Turbulence
Heusen, Martin
2016-01-01
We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bend...
On the spatio-temporal behavior of magnetohydrodynamic turbulence in a magnetized plasma
Lugones, R; Mininni, P D; Wan, M; Matthaeus, W H
2016-01-01
Using direct numerical simulations of three-dimensional magnetohydrodynamic (MHD) turbulence the spatio-temporal behavior of magnetic field fluctuations is analyzed. Cases with relatively small, medium and large values of a mean background magnetic field are considered. The (wavenumber) scale dependent time correlation function is directly computed for different simulations, varying the mean magnetic field value. From this correlation function the time decorrelation is computed and compared with different theoretical times, namely, the local non-linear time, the random sweeping time, and the Alfv\\'enic time, the latter being a wave effect. It is observed that time decorrelations are dominated by sweeping effects, and only at large values of the mean magnetic field and for wave vectors mainly aligned with this field time decorrelations are controlled by Alfv\\'enic effects.
Computational Methods for Ideal Magnetohydrodynamics
Kercher, Andrew D.
Numerical schemes for the ideal magnetohydrodynamics (MHD) are widely used for modeling space weather and astrophysical flows. They are designed to resolve the different waves that propagate through a magnetohydro fluid, namely, the fast, Alfven, slow, and entropy waves. Numerical schemes for ideal magnetohydrodynamics that are based on the standard finite volume (FV) discretization exhibit pseudo-convergence in which non-regular waves no longer exist only after heavy grid refinement. A method is described for obtaining solutions for coplanar and near coplanar cases that consist of only regular waves, independent of grid refinement. The method, referred to as Compound Wave Modification (CWM), involves removing the flux associated with non-regular structures and can be used for simulations in two- and three-dimensions because it does not require explicitly tracking an Alfven wave. For a near coplanar case, and for grids with 213 points or less, we find root-mean-square-errors (RMSEs) that are as much as 6 times smaller. For the coplanar case, in which non-regular structures will exist at all levels of grid refinement for standard FV schemes, the RMSE is as much as 25 times smaller. A multidimensional ideal MHD code has been implemented for simulations on graphics processing units (GPUs). Performance measurements were conducted for both the NVIDIA GeForce GTX Titan and Intel Xeon E5645 processor. The GPU is shown to perform one to two orders of magnitude greater than the CPU when using a single core, and two to three times greater than when run in parallel with OpenMP. Performance comparisons are made for two methods of storing data on the GPU. The first approach stores data as an Array of Structures (AoS), e.g., a point coordinate array of size 3 x n is iterated over. The second approach stores data as a Structure of Arrays (SoA), e.g. three separate arrays of size n are iterated over simultaneously. For an AoS, coalescing does not occur, reducing memory efficiency
A practical nonlinear robust control approach of electro-hydraulic load simulator
Institute of Scientific and Technical Information of China (English)
Wang Chengwen; Jiao Zongxia; Wu Shuai; Shang Yaoxing
2014-01-01
This paper studies a nonlinear robust control algorithm of the electro-hydraulic load simulator (EHLS). The tracking performance of the EHLS is mainly limited by the actuator’s motion disturbance, flow nonlinearity, and friction, etc. The developed controller is developed based on the nonlinear motion loading model. The problems of the actuator’s disturbance and flow nonlinearity are considered. To address the friction problem, the friction model of the loading motor is identified experimentally. The friction disturbance is compensated using the obtained friction model. Therefore, this paper considers the main three factors comprehensively. The devel-oped algorithm is easy to apply since the controller can be obtained just with one step back-stepping design. The stability of the developed algorithm is proven via Lyapunov analysis. Both co-simula-tion and experiments are performed to verify the effectiveness of this method.
Introduction to magnetohydrodynamics
Thompson, Ian
2016-01-01
Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.
Magnetohydrodynamic inertial reference system
Eckelkamp-Baker, Dan; Sebesta, Henry R.; Burkhard, Kevin
2000-07-01
Optical platforms increasingly require attitude knowledge and optical instrument pointing at sub-microradian accuracy. No low-cost commercial system exists to provide this level of accuracy for guidance, navigation, and control. The need for small, inexpensive inertial sensors, which may be employed in pointing control systems that are required to satisfy angular line-of-sight stabilization jitter error budgets to levels of 1-3 microradian rms and less, has existed for at least two decades. Innovations and evolutions in small, low-noise inertial angular motion sensor technology and advances in the applications of the global positioning system have converged to allow improvement in acquisition, tracking and pointing solutions for a wide variety of payloads. We are developing a small, inexpensive, and high-performance inertial attitude reference system that uses our innovative magnetohydrodynamic angular rate sensor technology.
Magnetohydrodynamic Shearing Waves
Johnson, B M
2006-01-01
I consider the nonaxisymmetric linear theory of an isothermal magnetohydrodynamic (MHD) shear flow. The analysis is performed in the shearing box, a local model appropriate for a thin disk geometry. Linear perturbations in this model can be decomposed in terms of shearing waves (shwaves), which appear spatially as plane waves in a frame comoving with the shear. The time dependence of these waves cannot in general be expressed in terms of a frequency eigenvalue as in a normal mode decomposition, and numerical integration of a set of first-order amplitude equations is required for a complete characterization of their behavior. Their generic time dependence, however, is oscillatory with slowly-varying frequency and amplitude, and one can construct accurate analytic solutions by applying the Wentzel-Kramers-Brillouin method to the full set of amplitude equations. For the bulk of wavenumber space, therefore, the shwaves are well-approximated as modes with time-dependent frequencies and amplitudes. The incompressiv...
Astrophysical Weighted Particle Magnetohydrodynamics
Gaburov, Evghenii
2010-01-01
This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD schem...
Introduction to modern magnetohydrodynamics
Galtier, Sébastien
2016-01-01
Ninety-nine percent of ordinary matter in the Universe is in the form of ionized fluids, or plasmas. The study of the magnetic properties of such electrically conducting fluids, magnetohydrodynamics (MHD), has become a central theory in astrophysics, as well as in areas such as engineering and geophysics. This textbook offers a comprehensive introduction to MHD and its recent applications, in nature and in laboratory plasmas; from the machinery of the Sun and galaxies, to the cooling of nuclear reactors and the geodynamo. It exposes advanced undergraduate and graduate students to both classical and modern concepts, making them aware of current research and the ever-widening scope of MHD. Rigorous derivations within the text, supplemented by over 100 illustrations and followed by exercises and worked solutions at the end of each chapter, provide an engaging and practical introduction to the subject and an accessible route into this wide-ranging field.
2015-08-27
The high voltage diodes D5 to D10 are used to protect the HV switch against negative back swing voltage, while D4 diode for reverse current ...AFRL-AFOSR-CL-TR-2015-0001 STUDY OF HV DIELECTRICS FOR HIGH FREQUENCY OPERATION IN LINEAR & NONLINEAR TRANSMISSION LINES & SIMULATION & DEVELOPMENT...AFOSR Final Performance Report Study of HV Dielectrics for High Frequency Operation in Linear and Nonlinear Transmission Lines and Simulation
2010-03-31
comprised linear structural dynamics (e.g. [7.2]), vibro-acoustics, aeroelasticity (e.g. [7.1]), rotordynamics [7.7] (including the joint simulation...2006. [7.7] Murthy, R., Mignolet, M.P., and El-Shafei, A., "Nonparametric Stochastic Modeling of Structural Uncertainty in Rotordynamic
Non-linear simulations of ELMs in ASDEX Upgrade including diamagnetic drift effects
Energy Technology Data Exchange (ETDEWEB)
Lessig, Alexander; Hoelzl, Matthias; Krebs, Isabel; Franck, Emmanuel; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstrasse 2, 85748 Garching (Germany); Orain, Francois; Morales, Jorge; Becoulet, Marina [CEA-IRFM, Cadarache, 13108 Saint-Paul-Lez-Durance (France); Huysmans, Guido [ITER Organization, 13067 Saint-Paul-Lez-Durance (France)
2015-05-01
Large edge localized modes (ELMs) are a severe concern for ITER due to high transient heat loads on divertor targets and wall structures. Using the non-linear MHD code JOREK, we have performed ELM simulations for ASDEX Upgrade (AUG) including diamagnetic drift effects. The influence of diamagnetic terms onto the evolution of the toroidal mode spectrum for different AUG equilibria and the non-linear interaction of the toroidal harmonics are investigated. In particular, we confirm the diamagnetic stabilization of high mode numbers and present new features of a previously introduced quadratic mode coupling model for the early non-linear evolution of the mode structure. Preliminary comparisons of full ELM crashes with experimental observations are shown aiming at code validation and the understanding of different ELM types. Work is ongoing to include toroidal and neoclassical poloidal rotation in our simulations.
Numerical Simulations on Nonlinear Dynamics in Lasers as Related High Energy Physics Phenomena
Directory of Open Access Journals (Sweden)
Andreea Rodica Sterian
2013-01-01
Full Text Available This paper aims to present some results on nonlinear dynamics in active nanostructures as lasers with quantum wells and erbium doped laser systems using mathematical models, methods, and numerical simulations for some related high energy physics phenomena. We discuss nonlinear dynamics of laser with quantum wells and of fiber optics laser and soliton interactions. The results presented have important implications in particle detection and postdetection processing of information as well as in soliton generation and amplification or in the case that these simulations are thought to be useful in the experiments concerning the high energy particles. The soliton behaviour as particle offers the possibility to use solitons for better understanding of real particles in this field. The developed numerical models concerning nonlinear dynamics in nanostructured lasers, erbium doped laser systems, the soliton interactions, and the obtained results are consistent with the existing data in the literature.
Nonlinear genetic-based simulation of soil shear strength parameters
Indian Academy of Sciences (India)
Seyyed Mohammad Mousavi; Amir Hossein Alavi; Amir Hossein Gandomi; Ali Mollahasani
2011-12-01
New nonlinear solutions were developed to estimate the soil shear strength parameters utilizing linear genetic programming (LGP). The soil cohesion intercept () and angle of shearing resistance () were formulated in terms of the basic soil physical properties. The best models were selected after developing and controlling several models with different combinations of influencing parameters. Comprehensive experimental database used for developing the models was established upon a series of unconsolidated, undrained, and unsaturated triaxial tests conducted in this study. Further, sensitivity and parametric analyses were carried out. and were found to be mostly influenced by the soil unit weight and liquid limit. In order to benchmark the proposed models, a multiple least squares regression (MLSR) analysis was performed. The validity of the models was proved on portions of laboratory results that were not included in the modelling process. The developed models are able to effectively learn the complex relationship between the soil strength parameters and their contributing factors. The LGP models provide a significantly better prediction performance than the regression models.
Nonlinear Simulation of Plasma Response to the NSTX Error Field
Breslau, J. A.; Park, J. K.; Boozer, A. H.; Park, W.
2008-11-01
In order to better understand the effects of the time-varying error field in NSTX on rotation braking, which impedes RWM stabilization, we model the plasma response to an applied low-n external field perturbation using the resistive MHD model in the M3D code. As an initial benchmark, we apply an m=2, n=1 perturbation to the flux at the boundary of a non-rotating model equilibrium and compare the resulting steady-state island sizes with those predicted by the ideal linear code IPEC. For sufficiently small perturbations, the codes agree; for larger perturbations, the nonlinear correction yields an upper limit on the island width beyond which stochasticity sets in. We also present results of scaling studies showing the effects of finite resistivity on island size in NSTX, and of time-dependent studies of the interaction between these islands and plasma rotation. The M3D-C1 code is also being evaluated as a tool for this analysis; first results will be shown. J.E. Menard, et al., Nucl. Fus. 47, S645 (2007). W. Park, et al., Phys. Plasmas 6, 1796 (1999). J.K. Park, et al., Phys. Plasmas 14, 052110 (2007). S.C. Jardin, et al., J. Comp. Phys. 226, 2146 (2007).
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.
Electron magnetohydrodynamics: dynamics and turbulence.
Lyutikov, Maxim
2013-11-01
We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector k(1)=k(2) do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade [proportionality]k(-2). The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.
Simulating nonlinear cosmological structure formation with massive neutrinos
Banerjee, Arka
2016-01-01
We present a new method for simulating cosmologies that contain massive particles with thermal free streaming motion, such as massive neutrinos or warm/hot dark matter. This method combines particle and fluid descriptions of the thermal species to eliminate the shot noise known to plague conventional N-body simulations. We describe this method in detail, along with results for a number of test cases to validate our method, and check its range of applicability. Using this method, we demonstrate that massive neutrinos can produce a significant scale-dependence in the large-scale biasing of deep voids in the matter field. We show that this scale-dependence may be quantitatively understood using an extremely simple spherical expansion model which reproduces the behavior of the void bias for different neutrino parameters.
Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX
Belova, E. V.; Gorelenkov, N. N.; Crocker, N. A.; Lestz, J. B.; Fredrickson, E. D.; Tang, S.; Tritz, K.
2017-04-01
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n =4 -9 , and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.
Nonlinear simulation of arch dam cracking with mixed finite element method
Directory of Open Access Journals (Sweden)
Ren Hao
2008-06-01
Full Text Available This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts: external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.
Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment
Citrin, J.; Jenko, F.; Mantica, P.; Told, D.; Bourdelle, C.; Dumont, R.; Garcia, J.; Haverkort, J. W.; Hogeweij, G. M. D.; Johnson, T.; Pueschel, M. J.
2014-01-01
Recent experimental observations at JET show evidence of reduced ion temperature profile stiffness. An extensive set of nonlinear gyrokinetic simulations are performed based on the experimental discharges, investigating the physical mechanism behind the observations. The impact on the ion heat flux
Review of magnetohydrodynamic pump applications
National Research Council Canada - National Science Library
Al-Habahbeh, O.M; Al-Saqqa, M; Safi, M; Abo Khater, T
2016-01-01
Magneto-hydrodynamic (MHD) principle is an important interdisciplinary field. One of the most important applications of this effect is pumping of materials that are hard to pump using conventional pumps...
Simulation of Novel Tunable Nonlinear Chirped Fiber Bragg Grating
Institute of Scientific and Technical Information of China (English)
LIU Yu-min; YU Zhong-yuan; ZHANG Xiao-guang; YU Li; YANG Bo-jun
2003-01-01
A novel tunable chirped fiber Bragg grating technology is proposed and simulated numerically by Matlab. If we adhere a uniform fiber grating with super magnetostrictive film and expose them in a non-uniform magnetic field, the period of the grating can be changed with the strain imposed on it by the magnetostrictive effect .The chirped characteristics can be tuned by changing the magnetic filed which is very flexible in designing.
Conservation of Circulation in Magnetohydrodynamics
Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We demonstrate, both at the Newtonian and (general) relativistic levels, the existence of a generalization of Kelvin's circulation theorem (for pure fluids) which is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
Conservation of circulation in magnetohydrodynamics
Bekenstein; Oron
2000-10-01
We demonstrate at both the Newtonian and (general) relativistic levels the existence of a generalization of Kelvin's circulation theorem (for pure fluids) that is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
A new lattice Boltzmann model for incompressible magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
Chen Xing-Wang; Shi Bao-Chang
2005-01-01
Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.
Trautmann, L.; Rabenstein, R.
2004-12-01
The functional transformation method (FTM) is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Magnetohydrodynamic Augmented Propulsion Experiment
Litchford, Ron J.; Cole, John; Lineberry, John; Chapman, Jim; Schmidt, Harold; Cook, Stephen (Technical Monitor)
2002-01-01
A fundamental obstacle to routine space access is the specific energy limitations associated with chemical fuels. In the case of vertical take-off, the high thrust needed for vertical liftoff and acceleration to orbit translates into power levels in the 10 GW range. Furthermore, useful payload mass fractions are possible only if the exhaust particle energy (i.e., exhaust velocity) is much greater than that available with traditional chemical propulsion. The electronic binding energy released by the best chemical reactions (e.g., LOX/LH2 for example, is less than 2 eV per product molecule (approx. 1.8 eV per H2O molecule), which translates into particle velocities less than 5 km/s. Useful payload fractions, however, will require exhaust velocities exceeding 15 km/s (i.e., particle energies greater than 20 eV). As an added challenge, the envisioned hypothetical RLV (reusable launch vehicle) should accomplish these amazing performance feats while providing relatively low acceleration levels to orbit (2-3g maximum). From such fundamental considerations, it is painfully obvious that planned and current RLV solutions based on chemical fuels alone represent only a temporary solution and can only result in minor gains, at best. What is truly needed is a revolutionary approach that will dramatically reduce the amount of fuel and size of the launch vehicle. This implies the need for new compact high-power energy sources as well as advanced accelerator technologies for increasing engine exhaust velocity. Electromagnetic acceleration techniques are of immense interest since they can be used to circumvent the thermal limits associated with conventional propulsion systems. This paper describes the Magnetohydrodynamic Augmented Propulsion Experiment (MAPX) being undertaken at NASA Marshall Space Flight Center (MSFC). In this experiment, a 1-MW arc heater is being used as a feeder for a 1-MW magnetohydrodynamic (MHD) accelerator. The purpose of the experiment is to demonstrate
Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qi
2003-01-01
A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, ...
Energy Technology Data Exchange (ETDEWEB)
Brett, Walter
2014-07-21
In the presented work the Kelvin-Helmholtz-Instability in magnetohydrodynamic flows is analyzed with the methods of Multiple Scales. The concerned fluids are incompressible or have a varying density perpendicular to the vortex sheet, which is taken into account using a Boussinesq-Approximation and constant Brunt-Vaeisaelae-Frequencies. The Multiple Scale Analysis leads to nonlinear evolution equations for the amplitude of the perturbations. Special solutions to these equations are presented and the effects of the magnetic fields are discussed.
Current-sheet formation in 3D ideal incompressible magnetohydrodynamics
Grauer; Marliani
2000-05-22
The evolution of current density and vorticity in the ideal, inviscid incompressible magnetohydrodynamic equations in three dimensions is studied numerically. Highly effective resolutions are obtained by adaptive structured mesh refinement techniques. We report on results for three different initial conditions showing similar behavior: in the early stage of the evolution a fast increase in vorticity and current density is observed. Thereafter, the evolution towards nearly two-dimensional current sheets results in a depletion of nonlinearity.
The Simulation Analysis of Nonlinear for a Power Amplifier with Memory Effects
Directory of Open Access Journals (Sweden)
Lv. Jinqiu
2014-09-01
Full Text Available For the nonlinear distortion problem of current power amplifiers (PAs with memory effects, we use goal programming to present a memoryless predistorter matrix model based on limiting baseband predistortion technique, and the normalized mean squared error (NMSE is limited in a satisfactory range while the output power is maximum. Then we propose a nonlinear power amplifier with memory effects based on back propagation neural network (BPNN with three tapped delay nodes and six single hidden layer nodes, which is single input - dual output. Simulation results show that the method proposed in this paper makes the experimental precision higher. Further, the linearization effect of power amplifiers becomes better.
Directory of Open Access Journals (Sweden)
MANFREDI, P.
2014-11-01
Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.
Directory of Open Access Journals (Sweden)
Hong Qin
2000-08-01
Full Text Available Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1% in axial momentum of the beam particles.
Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment
Citrin, J; Haverkort, J W; Hogeweij, G M D; Jenko, F; Mantica, P; Pueschel, M J; Told, D; contributors, JET-EFDA
2013-01-01
Recent experimental observations at JET show evidence of reduced ion temperature profile stiffness at low magnetic shear (s) in the presence of flow shear. Non-linear gyrokinetic simulations are performed, aiming to investigate the physical mechanism behind the observations. The sensitivity of profile stiffness to the variations of plasma parameters experimentally observed when transitioning to the low-stiffness regime is assessed. It is found that non-linear electromagnetic effects, even at low beta_e, can significantly reduce the profile stiffness, although not by a degree sufficient to explain the experimental observations. The effect of toroidal flow shear itself is not predicted by the simulations to lead to a significant reduction in flux due to significant parallel gradient velocity destabilisation. For the majority of discharges studied, the simulated and experimental ion heat flux values do agree within reasonable variations of input parameters around the experimental uncertainties. However, no such ...
Intrinsic rotation of toroidally confined magnetohydrodynamics.
Morales, Jorge A; Bos, Wouter J T; Schneider, Kai; Montgomery, David C
2012-10-26
The spatiotemporal self-organization of viscoresistive magnetohydrodynamics in a toroidal geometry is studied. Curl-free toroidal magnetic and electric fields are imposed. It is observed in our simulations that a flow is generated, which evolves from dominantly poloidal to toroidal when the Lundquist numbers are increased. It is shown that this toroidal organization of the flow is consistent with the tendency of the velocity field to align with the magnetic field. Up-down asymmetry of the geometry causes the generation of a nonzero toroidal angular momentum.
MHD数值模拟中清除伪磁场散度方法%Spurious Magnetic Field Divergence Cleaning in Magnetohydrodynamic Simulation
Institute of Scientific and Technical Information of China (English)
田正雨; 张康平; 丁国昊; 李桦
2009-01-01
针对全MHD(Magnetohydrodynamics)数值模拟中存在伪磁场散度的问题,发展了如下计算方法:基本格式基于八波对称形式方程组,补充相关源项以保持方程组守恒性,并采用投影方法辅助清除伪散度.投影方法中,基于有限体积方法求解三维Poisson方程.算例显示,对于光滑解析磁场,伪磁场散度得到有效清除;对于带激波高超声速MHD流动,全局投影下自由来流区域误差增大.提出一种局部投影方法,在高磁场散度区域进行投影.结果表明,最终流场收敛稳定,高磁场散度得到有效清除,而低散度区域散度不受影响.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
Del Zanna, L; Landi, S; Bugli, M; Bucciantini, N
2016-01-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retriev...
Stabilization of numerical interchange in spectral-element magnetohydrodynamics
Sovinec, C. R.
2016-08-01
Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code Sovinec et al. [17], provided that the projections introduce numerical dissipation.
Tang, H. T.; Hofmann, R.; Yee, G.; Vaughan, D. K.
1980-01-01
Transient, nonlinear soil-structure interaction simulations of an Electric Power Research Institute, SIMQUAKE experiment were performed using the large strain, time domain STEALTH 2D code and a cyclic, kinematically hardening cap soil model. Results from the STEALTH simulations were compared to identical simulations performed with the TRANAL code and indicate relatively good agreement between all the STEALTH and TRANAL calculations. The differences that are seen can probably be attributed to: (1) large (STEALTH) vs. small (TRANAL) strain formulation and/or (2) grid discretization differences.
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Dobigeon, Nicolas; Somers, Ben; Altmann, Yoann; Coppin, Pol
2013-01-01
Spectral unmixing is a crucial processing step when analyzing hyperspectral data. In such analysis, most of the work in the literature relies on the widely acknowledged linear mixing model to describe the observed pixels. Unfortunately, this model has been shown to be of limited interest for specific scenes, in particular when acquired over vegetated areas. Consequently, in the past few years, several nonlinear mixing models have been introduced to take nonlinear effects into account. These models have been proposed empirically, however without any thorough validation. In this paper, the authors take advantage of two sets of real and physical-based simulated data to validate the accuracy of various nonlinear models in vegetated areas. These physics-based and analysis models, and their corresponding unmixing algorithms, are evaluated with respect to their ability of fitting the measured spectra and of providing an accurate estimation of the abundance coefficients, considered as the spatial distribution of the ...
All-optical random number generation using highly nonlinear fibers by numerical simulation
Wang, Juanfen; Liang, Junqiang; Li, Pu; Yang, Lingzhen; Wang, Yuncai
2014-06-01
A new scheme of all-optical random number generation based on the nonlinear effects in highly nonlinear fibers (HNLF) is proposed. The scheme is comprised of ultra-wide band chaotic entropy source, all-optical sampler, all-optical comparator and all-optical exclusive-or (XOR), which are mainly realized by four-wave mixing (FWM) and cross-phase modulation (XPM) in highly nonlinear fibers. And we achieve 10 Gbit/s random numbers through numerically simulating all the processes. The entire operations are completed in the all-optical domain, which may overcome the bottleneck problem of electronic devices, and apply directly in high-speed all-optical communication network.
Research of nonlinear simulation on sweep voltage of streak tube imaging lidar
Zhai, Qian; Han, Shao-kun; Zhai, Yu; Lei, Jie-yu; Yao, Jian-feng
2016-10-01
In order to study the influence of nonlinear sweep voltage on the range accuracy of streak tube imaging lidar, a nonlinear distance model of streak tube is proposed. The model of the parallel-plate deflection system is studied, and the mathematical relation between the sweep voltage and the position of the image point on the screen is obtained based on the movement rule of phoelectron. And the mathematical model of the sweep voltage is established on the basis of its principle. The simulation of streak image is carried out for the selected staircase target, the range image of the target can be reconstructed by extremum method. Comparing reconstruction result and actual target, the range accuracy caused by the nonlinear sweep voltage is obtained. The curve of the errors varying with target ranges is also obtained. And the range accuracy of the system is analyzed by the means of changing the parameter relate to sweep time.
Kaneko, Yuta
2014-01-01
Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated.
Center for Extended Magnetohydrodynamics Modeling - Final Technical Report
Energy Technology Data Exchange (ETDEWEB)
Parker, Scott [Univ. of Colorado, Boulder, CO (United States)
2016-02-14
This project funding supported approximately 74 percent of a Ph.D. graduate student, not including costs of travel and supplies. We had a highly successful research project including the development of a second-order implicit electromagnetic kinetic ion hybrid model [Cheng 2013, Sturdevant 2016], direct comparisons with the extended MHD NIMROD code and kinetic simulation [Schnack 2013], modeling of slab tearing modes using the fully kinetic ion hybrid model and finally, modeling global tearing modes in cylindrical geometry using gyrokinetic simulation [Chen 2015, Chen 2016]. We developed an electromagnetic second-order implicit kinetic ion fluid electron hybrid model [Cheng 2013]. As a first step, we assumed isothermal electrons, but have included drift-kinetic electrons in similar models [Chen 2011]. We used this simulation to study the nonlinear evolution of the tearing mode in slab geometry, including nonlinear evolution and saturation [Cheng 2013]. Later, we compared this model directly to extended MHD calculations using the NIMROD code [Schnack 2013]. In this study, we investigated the ion-temperature-gradient instability with an extended MHD code for the first time and got reasonable agreement with the kinetic calculation in terms of linear frequency, growth rate and mode structure. We then extended this model to include orbit averaging and sub-cycling of the ions and compared directly to gyrokinetic theory [Sturdevant 2016]. This work was highlighted in an Invited Talk at the International Conference on the Numerical Simulation of Plasmas in 2015. The orbit averaging sub-cycling multi-scale algorithm is amenable to hybrid architectures with GPUS or math co-processors. Additionally, our participation in the Center for Extend Magnetohydrodynamics motivated our research on developing the capability for gyrokinetic simulation to model a global tearing mode. We did this in cylindrical geometry where the results could be benchmarked with existing eigenmode
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
Extended inertial range phenomenology of magnetohydrodynamic turbulence
Matthaeus, William H.; Zhou, YE
1989-01-01
A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan (1965). The role of Alfven wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22-1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented 'golden rules' for relating the spectral transfer time scale to the Alfven and eddy-turnover time scales.
Anomalous magnetohydrodynamics in the extreme relativistic domain
Giovannini, Massimo
2016-01-01
The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost-invariant and with vanishing four-acceleration the corresponding evolution equations are explicitly integrated so that the various physic...
Integrable version of Burgers equation in magnetohydrodynamics.
Olesen, P
2003-07-01
It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields v(y)(y,t) and Bx(y,t), one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the propagation of the nonlinear effects is governed by the initial velocity (as in Burgers case) as well as by the initial Alfvén velocity. Many results previously obtained for the Burgers equation can be transferred to the MHD case. We also discuss equipartition v(y)=+/-Bx. It is shown that an initial localized small scale magnetic field will end up in fields moving to the left and the right, thus transporting energy from smaller to larger distances.
Taylor, Z A; Cheng, M; Ourselin, S
2008-05-01
The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16,000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.
Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A
2003-06-01
Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
Kanjilal, Oindrila; Manohar, C. S.
2017-07-01
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.
Shen, Yanfeng; Cesnik, Carlos E. S.
2016-04-01
This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
Del Zanna, L.; Papini, E.; Landi, S.; Bugli, M.; Bucciantini, N.
2016-08-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula; hence, its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two-dimensional numerical simulations, the linear phase and the subsequent non-linear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics (MHD), as appropriate in situations where the Alfvén velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S-1/3 are considered, the so-called ideal tearing regime is retrieved, with modes growing independently of S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfvén velocity. In the fully non-linear stage, we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfvén speed from the X-point, and a fast reconnection rate at the predicted value {R}˜ (ln S)^{-1}.
A magnetic betelgeuse? Numerical simulations of non-linear dynamo action
DEFF Research Database (Denmark)
Dorch, S. B. F.
2004-01-01
Betelgeuse is an example of a cool super-giant displaying brightness fluctuations and irregular surface structures. Simulations by Freytag et al. (2002) of the convective envelope of the star have shown that the fluctuations in the star's luminosity may be caused by giant cell convection. A related...... question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible...... and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action....
Simulation of non-linear rf losses derived from characteristic Nb topography
Energy Technology Data Exchange (ETDEWEB)
Reece, Charles E. [JLAB; Xu, Chen; Kelley, Michael [W& M. JLAB
2013-09-01
A simplified model has been developed to simulate non-linear RF losses on Nb surfaces exclusively due to topographical enhancement of surface magnetic fields. If local sharp edges are small enough, at locations where local surface fields exceed Hc, small volumes of material may become normal conducting without thermal leading to quench. These small volumes of normal material yield increases in the effective surface resistance of the Nb. Using topographic data from typical BCP?d and EP?d fine grain niobium surfaces, we have simulated field-dependent losses and found that when extrapolated to resulting cavity performance, these losses correspond well to characteristic BCP/EP high field Q0 performance differences for fine grain Nb. We describe the structure of the model, its limitations, and the effects of this type of non-linear loss contribution on SRF cavities.
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
Numerical simulation of nonlinear long waves interacting with arrays of emergent cylinders
Zainali, Amir; Weiss, Robert; Irish, Jennifer L; Yang, Yongqian
2016-01-01
We presented numerical simulation of long waves, interacting with arrays of emergent cylinders inside regularly spaced patches, representing discontinues patchy coastal vegetation. We employed the fully nonlinear and weakly dispersive Serre-Green-Naghdi equations (SGN) until the breaking process starts, while we changed the governing equations to nonlinear shallow water equations (NSW) at the vicinity of the breaking-wave peak and during the runup stage. We modeled the cylinders as physical boundaries rather than approximating them as macro-roughness friction. We showed that the cylinders provide protection for the areas behind them. However they might also cause amplification in local water depth in those areas. The presented results are extensively validated against the existing numerical and experimental data. Our results demonstrate the capability and reliability of our model in simulating wave interaction with emergent cylinders.
Vuori, Kaarina; Strandén, Ismo; Sevón-Aimonen, Marja-Liisa; Mäntysaari, Esa A
2006-01-01
A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.
NUMERICAL SIMULATION OF TRAVELING WAVE CONVECTION IN A WEAKLY NONLINEAR REGIME
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper presents a simulational result on a blinking traveling wave (BTW) state in binary fluid convection in a rectangular cell. The numerical simulations were made using the two-dimensional perturbation equations of full hydrodynamic equations. We found for the first time that the BTW or sloshing traveling wave state is a type of modulated traveling wave (MTW) generated by the motion of a source defect which originates from the reflection effect at the end walls and depends on the reduced Rayleigh number r. Comparison with the localized traveling wave (LTW) shows that the BTW is convective patterns on a weakly nonlinear branch with a small amplitude and the LTW is those on a full nonlinear branch whth a large amplitude. They have different dynamical behaviour. A discontinuous jump from the BTW branch to the stable LTW branch takes place as the oscillatory period lengthens and the amplitude grows above the upper critical value of the BTW.
Magnetohydrodynamic Modeling of the Jovian Magnetosphere
Walker, Raymond
2005-01-01
Under this grant we have undertaken a series of magnetohydrodynamic (MHD) simulation and data analysis studies to help better understand the configuration and dynamics of Jupiter's magnetosphere. We approached our studies of Jupiter's magnetosphere in two ways. First we carried out a number of studies using our existing MHD code. We carried out simulation studies of Jupiter s magnetospheric boundaries and their dependence on solar wind parameters, we studied the current systems which give the Jovian magnetosphere its unique configuration and we modeled the dynamics of Jupiter s magnetosphere following a northward turning of the interplanetary magnetic field (IMF). Second we worked to develop a new simulation code for studies of outer planet magnetospheres.
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
Three dimensional full-wave nonlinear acoustic simulations: Applications to ultrasound imaging
Energy Technology Data Exchange (ETDEWEB)
Pinton, Gianmarco [Joint Department of Biomedical Engineering, University of North Carolina - North Carolina State University, 348 Taylor Hall, Chapel Hill, NC 27599, USA gfp@unc.edu (United States)
2015-10-28
Characterization of acoustic waves that propagate nonlinearly in an inhomogeneous medium has significant applications to diagnostic and therapeutic ultrasound. The generation of an ultrasound image of human tissue is based on the complex physics of acoustic wave propagation: diffraction, reflection, scattering, frequency dependent attenuation, and nonlinearity. The nonlinearity of wave propagation is used to the advantage of diagnostic scanners that use the harmonic components of the ultrasonic signal to improve the resolution and penetration of clinical scanners. One approach to simulating ultrasound images is to make approximations that can reduce the physics to systems that have a low computational cost. Here a maximalist approach is taken and the full three dimensional wave physics is simulated with finite differences. This paper demonstrates how finite difference simulations for the nonlinear acoustic wave equation can be used to generate physically realistic two and three dimensional ultrasound images anywhere in the body. A specific intercostal liver imaging scenario for two cases: with the ribs in place, and with the ribs removed. This configuration provides an imaging scenario that cannot be performed in vivo but that can test the influence of the ribs on image quality. Several imaging properties are studied, in particular the beamplots, the spatial coherence at the transducer surface, the distributed phase aberration, and the lesion detectability for imaging at the fundamental and harmonic frequencies. The results indicate, counterintuitively, that at the fundamental frequency the beamplot improves due to the apodization effect of the ribs but at the same time there is more degradation from reverberation clutter. At the harmonic frequency there is significantly less improvement in the beamplot and also significantly less degradation from reverberation. It is shown that even though simulating the full propagation physics is computationally challenging it
Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan
2017-01-01
The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.
Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano
Falaize, Antoine; Hélie, Thomas
2017-03-01
This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.
Faster Simulation Methods for the Non-Stationary Random Vibrations of Non-Linear MDOF Systems
DEFF Research Database (Denmark)
Askar, A.; Köylüoglu, H. U.; Nielsen, Søren R. K.;
In this paper semi-analytical forward-difference Monte Carlo simulation procedures are proposed for the determination of the lower order statistics and the Joint Probability Density Function (JPDF) of the stochastic response of geometrically nonlinear multi-degree-of-freedom structural systems....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...
Nonlinear kinetic modeling and simulations of Raman scattering in a two-dimensional geometry
Directory of Open Access Journals (Sweden)
Bénisti Didier
2013-11-01
Full Text Available In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering (SRS by the means of envelope equations, whose coefficients have been derived using a mixture of perturbative and adiabatic calculations. First examples of the numerical resolution of these envelope equations in a two-dimensional homogeneous plasma are given, and the results are compared against those of particle-in-cell (PIC simulations. These preliminary comparisons are encouraging since our envelope code provides threshold intensities consistent with those of PIC simulations while requiring computational resources reduced by 4 to 5 orders of magnitude compared to full-kinetic codes.
Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator
Directory of Open Access Journals (Sweden)
Han Songshan
2015-02-01
Full Text Available A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion simulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simulators. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decomposition of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the controller theoretically can guarantee asymptotic tracking performance in the presence of the above uncertainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.
Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator
Institute of Scientific and Technical Information of China (English)
Han Songshan; Jiao Zongxia; Wang Chengwen; Shang Yaoxing
2015-01-01
A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion sim-ulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simula-tors. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO) fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decom-position of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the control-ler theoretically can guarantee asymptotic tracking performance in the presence of the above uncer-tainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.
Energy Technology Data Exchange (ETDEWEB)
Biedron, S. G.; Freund, H. P.; Li, Y.; Milton, S. V.
2000-07-05
A single-pass, high-gain free-electron laser (FEL) x-ray amplifier was simulated using the 3D, polychromatic simulation code MEDUSA. The seed for the system is a table-top, soft x-ray laser. The simulated fundamental and nonlinear harmonic x-ray output wavelengths are discussed.
Liang, Fayun; Chen, Haibing; Huang, Maosong
2017-07-01
To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.
Directory of Open Access Journals (Sweden)
ARIF A. EBRAHEEM AL-QASSAR
2008-12-01
Full Text Available The design of the re-entry space vehicles and high-speed aircrafts requires special attention to the nonlinear thermoelastic and aerodynamic instabilities of their structural components. The thermal effects are important since temperature environment influences significantly the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes. To contribute to the understanding of dynamic behavior of these “hot” structures, a double-wedge lifting surface with combined freeplay and cubic stiffening structural nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes has been analyzed. A third order Piston Theory Aerodynamics is used to evaluate the applied nonlinear unsteady aerodynamic loads. The loss of torsional stiffness that may be incurred by lifting surfaces subjected to axial stresses induced by aerodynamic heating is also considered. The aerodynamic heating effect is estimated based on the adiabatic wall temperature due to high speed airstreams. Modelling issues as well as simulation results have been presented and pertinent conclusions outlined. It is highlighted that a serious loss of torsional stiffness may induce the dynamic instability of the lifting surfaces. The influence of various parameters such as flight condition, thickness ratio, freeplays and pitching stiffness nonlinearity are also discussed.
Spectral analysis in magnetohydrodynamic equilibria
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Galindo, Felix [Departamento de Analisis Matematico, Universidad de Valladolid, Valladolid (Spain)
1998-12-11
It has been universally assumed that the spectrum of the magnetohydrodynamics equations, linearized around an equilibrium state, provides enough information on the short-term evolution of the plasma to study certain stability properties. We show that this is true if one takes into account viscous and resistive effects and the equilibrium satisfies certain regularity conditions. (author)
MAGNETOHYDRODYNAMIC MODELING FOR FUSION PLASMAS
Keppens, R.; Goedbloed, J. P.; Blokland, J. W. S.
2010-01-01
The magnetohydrodynamic model for fusion plasma dynamics governs the large-scale equilibrium properties, and sets the most stringent constraints on the parameter space accessible without violent disruptions. In conjunction with linear stability analysis in the complex tokamak geometry, the MHD parad
Magnetohydrodynamic stability of tokamaks
Zohm, Hartmut
2014-01-01
This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong lin
Quadratic solid-shell elements for nonlinear structural analysis and sheet metal forming simulation
Wang, Peng; Chalal, Hocine; Abed-Meraim, Farid
2017-01-01
In this paper, two quadratic solid-shell (SHB) elements are proposed for the three-dimensional modeling of thin structures. These consist of a 20-node hexahedral solid-shell element, denoted SHB20, and its 15-node prismatic counterpart, denoted SHB15. The formulation of these elements is extended in this work to include geometric and material nonlinearities, for application to problems involving large displacements and rotations as well as plasticity. For this purpose, the SHB elements are coupled with large-strain anisotropic elasto-plastic constitutive equations for metallic materials. Although based on a purely three-dimensional approach, several modifications are introduced in the formulation of these elements to provide them with interesting shell features. In particular, a special direction is chosen to represent the thickness, along which a user-defined number of integration points are located. Furthermore, for efficiency requirements and for alleviating locking phenomena, an in-plane reduced-integration scheme is adopted. The resulting formulations are implemented into the finite element software ABAQUS/Standard and, to assess their performance, a variety of nonlinear benchmark problems are investigated. Attention is then focused on the simulation of various complex sheet metal forming processes, involving large strain, anisotropic plasticity, and double-sided contact. From all simulation results, it appears that the SHB elements represent an interesting alternative to traditional shell and solid elements, due to their versatility and capability of accurately modeling selective nonlinear benchmark problems as well as complex sheet metal forming processes.
Fast Simulation of Nonlinear Circuits with an Algorithm of Partial Matrix Elimination (PME)
Institute of Scientific and Technical Information of China (English)
CAI Xingjian; MAO Junfa; YANG Xiaoping; LI Zhengfan
2001-01-01
In this paper a theorem is proven thatthe contribution of any linear circuit elements to theadmittance matrix [Y] in the modified nodal admit-tance (MNA) equation of circuit analysis is invariantwith time.Based on this theorem a fast time-domainalgorithm of partial matrix elimination (PME) is de-veloped for simulation of high-speed nonlinear circuitswith interconnects.In PME the matrix [Y] is ar-ranged to consist of two submatrices.The lower sub-matrix that contains entries from only linear circuit el-ements is partially triangulated by Gauss eliminationfor the first-time-step transient analysis.At the fol-lowing time steps of transient analysis,Gauss elimina-tion is needed only for the upper submatrix containingcontributions of nonlinear circuit devices.Efficiencyanalysis of PME is given in detail,showing that it canaccelerate circuit simulation by a factor of at least 2.5for linear or lightly nonlinear circuits without employ-ing any numerical approximation.Moreover,PME isuseful for circuits debugging.
Quadratic solid-shell elements for nonlinear structural analysis and sheet metal forming simulation
Wang, Peng; Chalal, Hocine; Abed-Meraim, Farid
2016-10-01
In this paper, two quadratic solid-shell (SHB) elements are proposed for the three-dimensional modeling of thin structures. These consist of a 20-node hexahedral solid-shell element, denoted SHB20, and its 15-node prismatic counterpart, denoted SHB15. The formulation of these elements is extended in this work to include geometric and material nonlinearities, for application to problems involving large displacements and rotations as well as plasticity. For this purpose, the SHB elements are coupled with large-strain anisotropic elasto-plastic constitutive equations for metallic materials. Although based on a purely three-dimensional approach, several modifications are introduced in the formulation of these elements to provide them with interesting shell features. In particular, a special direction is chosen to represent the thickness, along which a user-defined number of integration points are located. Furthermore, for efficiency requirements and for alleviating locking phenomena, an in-plane reduced-integration scheme is adopted. The resulting formulations are implemented into the finite element software ABAQUS/Standard and, to assess their performance, a variety of nonlinear benchmark problems are investigated. Attention is then focused on the simulation of various complex sheet metal forming processes, involving large strain, anisotropic plasticity, and double-sided contact. From all simulation results, it appears that the SHB elements represent an interesting alternative to traditional shell and solid elements, due to their versatility and capability of accurately modeling selective nonlinear benchmark problems as well as complex sheet metal forming processes.
Magnetohydrodynamic Origin of Jets from Accretion Disks
Lovelace, R V E; Koldoba, A V
1999-01-01
A review is made of recent magnetohydrodynamic (MHD) theory and simulations of origin of jets from accretion disks. Many compact astrophysical objects emit powerful, highly-collimated, oppositely directed jets. Included are the extra galactic radio jets of active galaxies and quasars, and old compact stars in binaries, and emission line jets in young stellar objects. It is widely thought that these different jets arise from rotating, conducting accretion disks threaded by an ordered magnetic field. The twisting of the magnetic field by the rotation of the disk drives the jets by magnetically extracting matter, angular momentum, and energy from the accretion disk. Two main regimes have been discussed theoretically, hydromagnetic winds which have a significant mass flux, and Poynting flux jets where the mass flux is negligible. Over the past several years, exciting new developments on models of jets have come from progress in MHD simulations which now allow the study of the origin - the acceleration and collima...
Strumik, Marek
2016-01-01
We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of ...
Xiao, Jianyuan; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-01-01
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and cur...
Green, P. L.
2015-02-01
This work details the Bayesian identification of a nonlinear dynamical system using a novel MCMC algorithm: 'Data Annealing'. Data Annealing is similar to Simulated Annealing in that it allows the Markov chain to easily clear 'local traps' in the target distribution. To achieve this, training data is fed into the likelihood such that its influence over the posterior is introduced gradually - this allows the annealing procedure to be conducted with reduced computational expense. Additionally, Data Annealing uses a proposal distribution which allows it to conduct a local search accompanied by occasional long jumps, reducing the chance that it will become stuck in local traps. Here it is used to identify an experimental nonlinear system. The resulting Markov chains are used to approximate the covariance matrices of the parameters in a set of competing models before the issue of model selection is tackled using the Deviance Information Criterion.
Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2010-12-15
Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.
Statistical analysis of nonlinear wave interactions in simulated Langmuir turbulence data
Directory of Open Access Journals (Sweden)
J. Soucek
Full Text Available We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identify two and three wave processes in the data, and the Volterra model was furthermore employed to evaluate the direction and magnitude of energy transfer between the wave modes in the case of Langmuir wave decay. We demonstrate that these methods allow one to determine the relative importance of strongly and weakly turbulent processes. The statistical validity of the results was thoroughly tested using surrogated data set analysis.
Key words. Space plasma physics (wave-wave interactions; experimental and mathematical techniques; nonlinear phenomena
Simulation of "Tsunami Waves" Propagating along Non-Linear Transmission Lines
Directory of Open Access Journals (Sweden)
J. Valsa
2005-09-01
Full Text Available The paper compares three methods for computer simulation oftransients on transmission lines with losses and nonlinear behavior,namely distributed LC model, FDTD (Finite-Difference Time-Domainmethod, and a new and very effective Method of Slices. The losses areresponsible for attenuation and shape changes of the waves as functionof time and distance from the source. Special behavior of the line dueto voltage-dependent capacitance of the line is considered in detail.The non-linear nature of the line causes that the higher is the voltagethe higher is the velocity of propagation. Then, the waves tend to tiltover so that their top moves faster than their base. As a result"tsunami waves" are created on the line. Fundamental algorithms arepresented in Matlab language. Several typical situations are solved asan illustration of individual methods.
Directory of Open Access Journals (Sweden)
R. Rabenstein
2004-06-01
Full Text Available The functional transformation method (FTM is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Lack of universality in decaying magnetohydrodynamic turbulence.
Lee, E; Brachet, M E; Pouquet, A; Mininni, P D; Rosenberg, D
2010-01-01
Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed uniform magnetic field, we show that three different inertial ranges for the energy spectrum may emerge for three different initial magnetic fields, the selecting parameter being the ratio of nonlinear eddy to Alfvén time. Equivalent computational grids range from 128(3) to 2048(3) points with a unit magnetic Prandtl number and a Taylor Reynolds number of up to 1500 at the peak of dissipation. We also show a convergence of our results with Reynolds number. Our study is consistent with previous findings of a variety of energy spectra in MHD turbulence by studies performed in the presence of both a forcing term with a given correlation time and a strong, uniform magnetic field. However, in contrast to the previous studies, here the ratio of characteristic time scales can only be ascribed to the intrinsic nonlinear dynamics of the paradigmatic flows under study.
Martínez-Sykora, Juan; De Pontieu, Bart; Carlsson, Mats; Hansteen, Viggo H.; Nóbrega-Siverio, Daniel; Gudiksen, Boris V.
2017-09-01
We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion–neutral interaction effects using the generalized Ohm’s law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible.
NUMERICAL SIMULATIONS OF HIGHLY NONLINEAR STEADY AND UNSTEADY FREE SURFACE FLOWS
Institute of Scientific and Technical Information of China (English)
YANG Chi; HUANG Fuxin; WANG Lijue; WAN De-cheng
2011-01-01
A numerical simulation model based on an open source Computational Fluid Dynamics (CFD) package-Open Field Operation and Manipulation (OpenFOAM) has been developed to study highly nonlinear steady and unsteady free surface flows.A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid (VOF) method.The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells.Both steady and unsteady free surface flows are simulated,which include:(1) a submerged NACA0012 2-D hydrofoil moving at a constant speed,(2) the Wigley hull moving at a constant speed,(3) numerical wave tank,(4) green water overtopping a fixed 2-D deck,(5) green water impact on a fixed 3-D body without or with a vertical wall on the deck.The numerical results obtained have been compared with the experimental measurements and other CFD results,and the agreements are satisfactory.The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.
Nonlinear evolution of mirror instability in the Earth's magnetosheath in pic simulations
Ahmadi, Narges
Mirror modes are large amplitude non-propagating structures frequently observed in the magnetosheath and they are generated in space plasma environments with proton temperature anisotropy of larger than one. The proton temperature anisotropy also drives the proton cyclotron instability which has larger linear growth rate than that of the mirror instability. Linear dispersion theory predicts that electron temperature anisotropy can enhance the mirror instability growth rate while leaving the proton cyclotron instability largely unaffected. Contrary to the hypothesis, electron temperature anisotropy leads to excitement of the electron whistler instability. Our results show that the electron whistler instability grows much faster than the mirror instability and quickly consumes the electron free energy, so that there is not enough electron temperature anisotropy left to significantly impact the evolution of the mirror instability. Observational studies have shown that the shape of mirror structures is related to local plasma parameters and distance to the mirror instability threshold. Mirror structures in the form of magnetic holes are observed when plasma is mirror stable or marginally mirror unstable and magnetic peaks are observed when plasma is mirror unstable. Mirror structures are created downstream of the quasi-perpendicular bow shock and they are convected toward the magnetopause. In the middle magnetosheath, where plasma is mirror unstable, mirror structures are dominated by magnetic peaks. Close to the magnetopause, plasma expansion makes the region mirror stable and magnetic peaks evolve to magnetic holes. We investigate the nonlinear evolution of mirror instability using expanding box Particle-in-Cell simulations. We change the plasma conditions by artificially enlarging the simulation box over time to make the plasma mirror stable and investigate the final nonlinear state of the mirror structures. We show that the direct nonlinear evolution of the mirror
Neurosurgery Simulation Using Non-linear Finite Element Modeling and Haptic Interaction.
Lee, Huai-Ping; Audette, Michel; Joldes, Grand Roman; Enquobahrie, Andinet
2012-02-23
Real-time surgical simulation is becoming an important component of surgical training. To meet the real-time requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
Neurosurgery simulation using non-linear finite element modeling and haptic interaction
Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet
2012-02-01
Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
Rapid decay of nonlinear whistler waves in two dimensions: Full particle simulation
Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro
2017-05-01
The decay of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave is investigated by utilizing a two-dimensional (2D) fully relativistic electromagnetic particle-in-cell code. The simulation is performed under a low-beta condition in which the plasma pressure is much lower than the magnetic pressure. It has been shown that the nonlinear (large-amplitude) parent whistler wave decays through the parametric instability in a one-dimensional (1D) system. The present study shows that there is another channel for the decay of the parent whistler wave in 2D, which is much faster than in the timescale of the parametric decay in 1D. The parent whistler wave decays into two sideband daughter whistlers propagating obliquely with respect to the ambient magnetic field with a frequency close to the parent wave and two quasi-perpendicular electromagnetic modes with a frequency close to zero via a 2D decay instability. The two sideband daughter oblique whistlers also enhance a nonlinear longitudinal electrostatic wave via a three-wave interaction as a secondary process.
Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative
Mokem Fokou, I. S.; Buckjohn, C. Nono Dueyou; Siewe Siewe, M.; Tchawoua, C.
2017-08-01
In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping (μb). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μb play an important role in the response of the system.
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, K. [Kinki Univ Osaka (Japan)
1997-08-05
Space structure engineering comes under the combination of different engineering fields. Role of numerical analysis and simulation is large in space structure engineering. Considering space structure engineering as an application of non-linear mechanical simulation, constrains with simulation technology and analysis examples are explained in this paper. Following important points are confirmed by simulating the motion of membrane under external force acting on inner and outer surfaces at a particular point of square satellite model which rotates in tension membrane. When the external force is removed, each material point and membrane centre move with vibration, however centre of gravity of satellite moves very rapidly along the vertical direction of membrane centre. Further external disturbance (which develops on material points) propagates at all material points and membrane centre as a twisted wave. Maximum relative displacement between inner surface and outer surface decreases with the increment of initial angular velocity but not on the points of upper membrane. Fluctuation of position motion of satellite resulted from external disturbance is become small as initial rotation angular velocity increases. 10 refs., 6 figs., 2 tabs.
Variational Integrators for Reduced Magnetohydrodynamics
Kraus, Michael; Grasso, Daniela
2015-01-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws are described both at the continuous and discrete level. We verify...
Dynamic multiscaling in magnetohydrodynamic turbulence
Ray, Samriddhi Sankar; Pandit, Rahul
2016-01-01
We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Dynamic multiscaling in magnetohydrodynamic turbulence.
Ray, Samriddhi Sankar; Sahoo, Ganapati; Pandit, Rahul
2016-11-01
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Test particle acceleration in explosive magnetohydrodynamic reconnection
Ripperda, Bart; Xia, Chun; Keppens, Rony
2016-01-01
Magnetic reconnection is the mechanism behind many violent phenomena in the universe. We demonstrate that energy released during reconnection can lead to non-thermal particle distribution functions. We use a method in which we combine resistive magnetohydrodynamics (MHD) with relativistic test particle dynamics. Using our open-source grid-adaptive MPI-AMRVAC software, we simulate global MHD evolution combined with test particle treatments in MHD snapshots. This approach is used to evaluate particle acceleration in explosive reconnection. The reconnection is triggered by an ideal tilt instability in two-and-a-half dimensional (2.5D) scenarios and by a combination of ideal tilt and kink instabilities in three-dimensional (3D) scenarios. These instabilities occur in a system with two parallel, adjacent, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and a separation on Alfv\\'enic t...
Classes of hydrodynamic and magnetohydrodynamic turbulent decay
Brandenburg, Axel
2016-01-01
We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, and not by the initial conditions, as is widely assumed. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k^4). All of our self-similar solutions have an intrinsic subinertial range close to k^4$.
Acceleration of particles in imbalanced magnetohydrodynamic turbulence.
Teaca, Bogdan; Weidl, Martin S; Jenko, Frank; Schlickeiser, Reinhard
2014-08-01
The present work investigates the acceleration of test particles, relevant to the solar-wind problem, in balanced and imbalanced magnetohydrodynamic turbulence (terms referring here to turbulent states possessing zero and nonzero cross helicity, respectively). These turbulent states, obtained numerically by prescribing the injection rates for the ideal invariants, are evolved dynamically with the particles. While the energy spectrum for balanced and imbalanced states is known, the impact made on particle heating is a matter of debate, with different considerations giving different results. By performing direct numerical simulations, resonant and nonresonant particle accelerations are automatically considered and the correct turbulent phases are taken into account. For imbalanced turbulence, it is found that the acceleration rate of charged particles is reduced and the heating rate diminished. This behavior is independent of the particle gyroradius, although particles that have a stronger adiabatic motion (smaller gyroradius) tend to experience a larger heating.
Magnetohydrodynamic stability of broad line region clouds
Krause, Martin; Burkert, Andreas
2012-01-01
Hydrodynamic stability has been a longstanding issue for the cloud model of the broad line region in active galactic nuclei. We argue that the clouds may be gravitationally bound to the supermassive black hole. If true, stabilisation by thermal pressure alone becomes even more difficult. We further argue that if magnetic fields should be present in such clouds at a level that could affect the stability properties, they need to be strong enough to compete with the radiation pressure on the cloud. This would imply magnetic field values of a few Gauss for a sample of Active Galactic Nuclei we draw from the literature. We then investigate the effect of several magnetic configurations on cloud stability in axi-symmetric magnetohydrodynamic simulations. For a purely azimuthal magnetic field which provides the dominant pressure support, the cloud first gets compressed by the opposing radiative and gravitational forces. The pressure inside the cloud then increases, and it expands vertically. Kelvin-Helmholtz and colu...
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
Mohseni, F; Succi, S; Herrmann, H J
2015-01-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...
Energy interactions in homogeneously sheared magnetohydrodynamic flows
Collard, Diane; Praturi, Divya Sri; Girimaji, Sharath
2016-11-01
We investigate the behavior of homogeneously sheared magnetohydrodynamic (MHD) flows subject to perturbations in various directions. We perform rapid distortion theory (RDT) analysis and direct numerical simulations (DNS) to examine the interplay between magnetic, kinetic, and internal energies. For perturbation wavevectors oriented along the spanwise direction, RDT analysis shows that the magnetic and velocity fields are decoupled. In the case of streamwise wavevectors, the magnetic and velocity fields are tightly coupled. The coupling is "harmonic" in nature. DNS is then used to confirm the RDT findings. Computations of spanwise perturbations indeed exhibit behavior that is impervious to the magnetic field. Computed streamwise perturbations exhibit oscillatory evolution of kinetic and magnetic energies for low magnetic field strength. As the strength of magnetic field increases, the oscillatory behavior intensifies even as the energy magnitude decays, indicating strong stabilization.
Hooper, E. B.; Sovinec, C. R.
2016-10-01
An instability observed in whole-device, resistive magnetohydrodynamic simulations of the driven phase of coaxial helicity injection in the National Spherical Torus eXperiment is identified as a current-driven resistive mode in an unusual geometry that transiently generates a current sheet. The mode consists of plasma flow velocity and magnetic field eddies in a tube aligned with the magnetic field at the surface of the injected magnetic flux. At low plasma temperatures (˜10-20 eV), the mode is benign, but at high temperatures (˜100 eV) its amplitude undergoes relaxation oscillations, broadening the layer of injected current and flow at the surface of the injected toroidal flux and background plasma. The poloidal-field structure is affected and the magnetic surface closure is generally prevented while the mode undergoes relaxation oscillations during injection. This study describes the mode and uses linearized numerical computations and an analytic slab model to identify the unstable mode.
Bierwage, Andreas; Spong, Donald A.
2009-05-01
Hybrid-MHD-Gyrokinetic Code (HMGC) [1] and the gyrofluid code TAEFL [2,3] are used for nonlinear simulation of Alfven Eigenmodes in Tokamak plasma. We compare results obtained in two cases: (I) a case designed for cross-code benchmark of TAE excitation; (II) a case based on a dedicated DIII-D shot #132707 where RSAE and TAE activity is observed. Differences between the numerical simulation results are discussed and future directions are outlined. [1] S. Briguglio, G. Vlad, F. Zonca and C. Kar, Phys. Plasmas 2 (1995) 3711. [2] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Fluids B4 (1992) 3316. [3] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Plasmas 1 (1994) 1503.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
-numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...... of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
Local conservative regularizations of compressible magnetohydrodynamic and neutral flows
Krishnaswami, Govind S.; Sachdev, Sonakshi; Thyagaraja, A.
2016-02-01
Ideal systems like magnetohydrodynamics (MHD) and Euler flow may develop singularities in vorticity ( w =∇×v ). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper, we propose a minimal, local, conservative, nonlinear, dispersive regularization of compressible flow and ideal MHD, in analogy with the KdV regularization of the 1D kinematic wave equation. This work extends and significantly generalizes earlier work on incompressible Euler and ideal MHD. It involves a micro-scale cutoff length λ which is a function of density, unlike in the incompressible case. In MHD, it can be taken to be of order the electron collisionless skin depth c/ωpe. Our regularization preserves the symmetries of the original systems and, with appropriate boundary conditions, leads to associated conservation laws. Energy and enstrophy are subject to a priori bounds determined by initial data in contrast to the unregularized systems. A Hamiltonian and Poisson bracket formulation is developed and applied to generalize the constitutive relation to bound higher moments of vorticity. A "swirl" velocity field is identified, and shown to transport w/ρ and B/ρ, generalizing the Kelvin-Helmholtz and Alfvén theorems. The steady regularized equations are used to model a rotating vortex, MHD pinch, and a plane vortex sheet. The proposed regularization could facilitate numerical simulations of fluid/MHD equations and provide a consistent statistical mechanics of vortices/current filaments in 3D, without blowup of enstrophy. Implications for detailed analyses of fluid and plasma dynamic systems arising from our work are briefly discussed.
Analytical model and MD simulation of nonlinear Richtmyer-Meshkov instability
Nishihara, Katsunobu; Abe, Motomi; Fukuda, Yuko; Zhakhovskii, Vasilii; Matsuoka, Chihiro
2001-10-01
We present two topics, an analytical model and moelrcular dynamic (MD) simulations of the Richtmyer-Meshokov instability (RMI). We have developled a selfconsistent analytical model that describes a nonlinear evolution of a vortex sheet in the two-dimensional RMI. The model consists of two kinematic boundary conditions, a modified Birkhoff-Rott equation and an equation for time evolution of circulation at the interface with a finite Atwood number. It is shown that the created vortcity on the interface has strong inhomogeneity, that causes locally streching and compression of the sheet. We discuss the dependence of the Atwood number on the nonlinear dynamics of the sheet. MD approache has been applied for converging shocks and RMI in a dense Lennard-Jones fluid in cylindrical geometry. MD method has fundamental advantages over hydrodymanic simulations such as no limitation of resolution in turbulent state. The appearance of Mach stems in the rippled shocks and turbulent mixing in RMI have been observed when the reflected shock passes through the unstable surface again. We discuss the mode number and Mach number dependence on the mixing.
Directory of Open Access Journals (Sweden)
Mäntysaari Esa A
2006-06-01
Full Text Available Abstract A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.
Study of non-linear deformation of vocal folds in simulations of human phonation
Saurabh, Shakti; Bodony, Daniel
2014-11-01
Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).
NUMERICAL SIMULATIONS OF NONLINEAR WAVE TRANSFORMATION AROUND WAVE-PERMEABLE STRUCTURE
Institute of Scientific and Technical Information of China (English)
Li Xi; YAN Yi-xin
2005-01-01
The problem of wave partial/full reflection and transmission by wave-permeable structure is approached by solving the shape-related function with focus on the understanding of wave attenuation.2D depth-averaged Boussinesq type wave equations are given with new damping item in simulating the nonlinear wave transmission through wave-permeable structure.1D wave equation is examined to give the analytical expression of the absorbing coefficient, and is compared with laboratory data in flume to calibrate the coefficients, and the expression is applied directly in modified Boussinesq type equations.Compared with wave basin data for various incident wave conditions,the accurate predictions of combined diffraction-refraction effects in simulating nonlinear wave going through wave-permeable breakwater in the engineering application can be obtained.It shows that wave-permeable breakwaters with proper absorbing effects can be used as an effective alternative to massive gravity breakwaters in reduction of wave transmission in shallow water.
On the Global Regularity for the 3D Magnetohydrodynamics Equations Involving Partial Components
Qian, Chenyin
2017-01-01
In this paper, we study the regularity criteria of the three-dimensional magnetohydrodynamics system in terms of some components of the velocity field and the magnetic field. With a decomposition of the four nonlinear terms of the system, this result gives an improvement of some corresponding previous works (Yamazaki in J Math Fluid Mech 16: 551-570, 2014; Jia and Zhou in Nonlinear Anal Real World Appl 13: 410-418, 2012).
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Ferraro, N. M.; Jardin, S. C.
2009-11-01
M3D- C1 is an implicit, high-order finite element code for the solution of the time-dependent nonlinear two-fluid magnetohydrodynamic equations [S.C. Jardin, J. Breslau, N. Ferraro, A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions, J. Comp. Phys. 226 (2) (2007) 2146-2174]. This code has now been extended to allow computations in toroidal geometry. Improvements to the spatial integration and time-stepping algorithms are discussed. Steady-states of a resistive two-fluid model, self-consistently including flows, anisotropic viscosity (including gyroviscosity) and heat flux, are calculated for diverted plasmas in geometries typical of the National Spherical Torus Experiment (NSTX) [M. Ono et al., Exploration of spherical torus physics in the NSTX device, Nucl. Fusion 40 (3Y) (2000) 557-561]. These states are found by time-integrating the dynamical equations until the steady-state is reached, and are therefore stationary or statistically steady on both magnetohydrodynamic and transport time-scales. Resistively driven cross-surface flows are found to be in close agreement with Pfirsch-Schlüter theory. Poloidally varying toroidal flows are in agreement with comparable calculations [A.Y. Aydemir, Shear flows at the tokamak edge and their interaction with edge-localized modes, Phys. Plasmas 14]. New effects on core toroidal rotation due to gyroviscosity and a local particle source are observed.
Energy transfers in shell models for magnetohydrodynamics turbulence.
Lessinnes, Thomas; Carati, Daniele; Verma, Mahendra K
2009-06-01
A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes.
Pan, Shuokai; Elliott, Stephen J; Teal, Paul D; Lineton, Ben
2015-06-01
Nonlinear models of the cochlea are best implemented in the time domain, but their computational demands usually limit the duration of the simulations that can reasonably be performed. This letter presents a modified state space method and its application to an example nonlinear one-dimensional transmission-line cochlear model. The sparsity pattern of the individual matrices for this alternative formulation allows the use of significantly faster numerical algorithms. Combined with a more efficient implementation of the saturating nonlinearity, the computational speed of this modified state space method is more than 40 times faster than that of the original formulation.
Energy Technology Data Exchange (ETDEWEB)
Jakobi, A.
2007-07-01
Air flow around airship configurations is highly complex and is governed by 3D aerodynamic effects. Detailed knowledge of this nonlinear aerodynamics is important especially in airship design. The author describes the relevant physical effects governing flow and shows how they are taken account of in the method of calculation he presents. A panel boundary layer method is described in detail which calculates frictionless external flow in a 3D panel method coupled with a 3D integral method for laminar or turbulent boundary layers. The method calculates the tensor of the virtual mass of any given airship takes account of desplacement by the boundary layer, and simulates the effects of propellers. The modelling of free vortex layers in the context of potential theory is described in detail, and the results are discussed. A new panel with two-dimensional vortex distribution is derived. (orig.)
Edge localized mode rotation and the nonlinear dynamics of filaments
Energy Technology Data Exchange (ETDEWEB)
Morales, J. A.; Bécoulet, M.; Garbet, X.; Dif-Pradalier, G.; Huijsmans, G. T. A.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G. [CEA, IRFM, 13108 St. Paul-Lez-Durance (France); Orain, F.; Hoelzl, M. [Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Pamela, S. [CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Cahyna, P. [Institute of Plasma Physics ASCR, Za Slovankou 1782/3, 182 00 Prague 8 (Czech Republic)
2016-04-15
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Edge localized mode rotation and the nonlinear dynamics of filaments
Morales, J. A.; Bécoulet, M.; Garbet, X.; Orain, F.; Dif-Pradalier, G.; Hoelzl, M.; Pamela, S.; Huijsmans, G. T. A.; Cahyna, P.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G.
2016-04-01
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations
Lalanne, Benjamin; Abi Chebel, Nicolas; Vejražka, Jiří; Tanguy, Sébastien; Masbernat, Olivier; Risso, Frédéric
2015-12-01
This paper focuses on shape-oscillations of a gas bubble or a liquid drop rising in another liquid. The bubble/drop is initially attached to a capillary and is released by a sudden motion of that capillary, resulting in the rise of the bubble/drop along with the oscillations of its shape. Such experimental conditions make difficult the interpretation of the oscillation dynamics with regard to the standard linear theory of oscillation because (i) amplitude of deformation is large enough to induce nonlinearities, (ii) the rising motion may be coupled with the oscillation dynamics, and (iii) clean conditions without residual surfactants may not be achieved. These differences with the theory are addressed by comparing experimental observation with numerical simulation. Simulations are carried out using Level-Set and Ghost-Fluid methods with clean interfaces. The effect of the rising motion is investigated by performing simulations under different gravity conditions. Using a decomposition of the bubble/drop shape into a series of spherical harmonics, experimental and numerical time evolutions of their amplitudes are compared. Due to large oscillation amplitude, non-linear couplings between the modes are evidenced from both experimental and numerical signals; modes of lower frequency influence modes of higher frequency, whereas the reverse is not observed. Nevertheless, the dominant frequency and overall damping rate of the first five modes are in good agreement with the linear theory. Effect of the rising motion on the oscillations is globally negligible, provided the mean shape of the oscillation remains close to a sphere. In the drop case, despite the residual interface contamination evidenced by a reduction in the terminal velocity, the oscillation dynamics is shown to be unaltered compared to that of a clean drop.
Hoelzl, M; Merkel, P; Atanasiu, C; Lackner, K; Nardon, E; Aleynikova, K; Liu, F; Strumberger, E; McAdams, R; Chapman, I; Fil, A
2014-01-01
The dynamics of large scale plasma instabilities can strongly be influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realist...
Structures in magnetohydrodynamic turbulence: detection and scaling.
Uritsky, V M; Pouquet, A; Rosenberg, D; Mininni, P D; Donovan, E F
2010-11-01
We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536³ points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic-field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with magnetohydrodynamics. We suggest that this range can be governed by turbulence dynamics as opposed to criticality and propose an interpretation of intermittency in terms of propagation of local instabilities.
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Energy Technology Data Exchange (ETDEWEB)
Akiyama, Yasunobu; Imaishi, Nobuyuki [Kyushu University, Fukuoka (Japan)
1999-06-05
The simulation algorithm of step/hole coverage shape which could be applied at the Chemical Vapor Deposition (CVD) system with the nonlinear surface reaction speed was devised. By combining with the conventional simple Monte Carlo calculation technique, the code which could simulate the coverage shape at high speed was made. It was quantitatively explainable in respect of raw material density dependence (fluoridation tungsten (6); WF{sub 6}) of the coverage shape, when this code was applied to the thermal CVD of tungsten (W) with nonlinear surface reaction. (translated by NEDO)
Nonlinear Dynamic Modeling and Simulation of a Passively Cooled Small Modular Reactor
Arda, Samet Egemen
A nonlinear dynamic model for a passively cooled small modular reactor (SMR) is developed. The nuclear steam supply system (NSSS) model includes representations for reactor core, steam generator, pressurizer, hot leg riser and downcomer. The reactor core is modeled with the combination of: (1) neutronics, using point kinetics equations for reactor power and a single combined neutron group, and (2) thermal-hydraulics, describing the heat transfer from fuel to coolant by an overall heat transfer resistance and single-phase natural circulation. For the helical-coil once-through steam generator, a single tube depiction with time-varying boundaries and three regions, i.e., subcooled, boiling, and superheated, is adopted. The pressurizer model is developed based upon the conservation of fluid mass, volume, and energy. Hot leg riser and downcomer are treated as first-order lags. The NSSS model is incorporated with a turbine model which permits observing the power with given steam flow, pressure, and enthalpy as input. The overall nonlinear system is implemented in the Simulink dynamic environment. Simulations for typical perturbations, e.g., control rod withdrawal and increase in steam demand, are run. A detailed analysis of the results show that the steady-state values for full power are in good agreement with design data and the model is capable of predicting the dynamics of the SMR. Finally, steady-state control programs for reactor power and pressurizer pressure are also implemented and their effect on the important system variables are discussed.
Nonlinear dynamics modeling and simulation of two-wheeled self-balancing vehicle
Directory of Open Access Journals (Sweden)
Yunping Liu
2016-11-01
Full Text Available Two-wheeled self-balancing vehicle system is a kind of naturally unstable underactuated system with high-rank unstable multivariable strongly coupling complicated dynamic nonlinear property. Nonlinear dynamics modeling and simulation, as a basis of two-wheeled self-balancing vehicle dynamics research, has the guiding effect for system design of the project demonstration and design phase. Dynamics model of the two-wheeled self-balancing vehicle is established by importing a TSi ProPac package to the Mathematica software (version 8.0, which analyzes the stability and calculates the Lyapunov exponents of the system. The relationship between external force and stability of the system is analyzed by the phase trajectory. Proportional–integral–derivative control is added to the system in order to improve the stability of the two-wheeled self-balancing vehicle. From the research, Lyapunov exponent can be used to research the stability of hyperchaos system. The stability of the two-wheeled self-balancing vehicle is better by inputting the proportional–integral–derivative control. The Lyapunov exponent and phase trajectory can help us analyze the stability of a system better and lay the foundation for the analysis and control of the two-wheeled self-balancing vehicle system.
Exponents of non-linear clustering in scale-free one dimensional cosmological simulations
Benhaiem, David; Sicard, François
2012-01-01
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \\gamma depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter \\kappa controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which \\gamma depends strongly on both n and \\kappa and where it agrees very well with a simple general...
Blind Equalization of a Nonlinear Satellite System Using MCMC Simulation Methods
Directory of Open Access Journals (Sweden)
Sénécal Stéphane
2002-01-01
Full Text Available This paper proposes the use of Markov Chain Monte-Carlo (MCMC simulation methods for equalizing a satellite communication system. The main difficulties encountered are the nonlinear distorsions caused by the amplifier stage in the satellite. Several processing methods manage to take into account the nonlinearity of the system but they require the knowledge of a training/learning input sequence for updating the parameters of the equalizer. Blind equalization methods also exist but they require a Volterra modelization of the system. The aim of the paper is also to blindly restore the emitted message. To reach the goal, we adopt a Bayesian point of view. We jointly use the prior knowledge on the emitted symbols, and the information available from the received signal. This is done by considering the posterior distribution of the input sequence and the parameters of the model. Such a distribution is very difficult to study and thus motivates the implementation of MCMC methods. The presentation of the method is cut into two parts. The first part solves the problem for a simplified model; the second part deals with the complete model, and a part of the solution uses the algorithm developed for the simplified model. The algorithms are illustrated and their performance is evaluated using bit error rate versus signal-to-noise ratio curves.
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
Energy Technology Data Exchange (ETDEWEB)
Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Non-linear simulations of combustion instabilities with a quasi-1D Navier-Stokes code
Haugen, Nils Erland L; Sannan, Sigurd
2010-01-01
As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities with high accuracy. The inherent non-linearities in combustion instabilities can be of crucial importance, and we here propose an approach in which the one-dimensional Navier-Stokes and scalar transport equations are solved for geometries of variable cross-section. The focus is on attached flames, and for this purpose a new phenomenological model for the unsteady heat release from a flame front is introduced. In the attached flame method (AFM) the heat release occurs over the full length of the flame. The non-linear code with the use of the AFM approach is validated against results from an experimental study of thermoacoustic instabilities in oxy-fuel flames by Ditaranto and Hals [Combustion and Flame, 146, 493-512 (2006)]. The numerical simulations are in accordance with the...
Simulations of heart valves by thin shells with non-linear material properties
Borazjani, Iman; Asgharzadeh, Hafez; Hedayat, Mohammadali
2016-11-01
The primary function of a heart valve is to allow blood to flow in only one direction through the heart. Triangular thin-shell finite element formulation is implemented, which considers only translational degrees of freedom, in three-dimensional domain to simulate heart valves undergoing large deformations. The formulation is based on the nonlinear Kirchhoff thin-shell theory. The developed method is intensively validated against numerical and analytical benchmarks. This method is added to previously developed membrane method to obtain more realistic results since ignoring bending forces can results in unrealistic wrinkling of heart valves. A nonlinear Fung-type constitutive relation, based on experimentally measured biaxial loading tests, is used to model the material properties for response of the in-plane motion in heart valves. Furthermore, the experimentally measured liner constitutive relation is used to model the material properties to capture the flexural motion of heart valves. The Fluid structure interaction solver adopts a strongly coupled partitioned approach that is stabilized with under-relaxation and the Aitken acceleration technique. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.
Pinton, Gianmarco F; Trahey, Gregg E; Dahl, Jeremy J
2011-04-01
A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-andsum beamforming is used to generate point spread functions (PSF) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is reverberation from near-field structures. Reverberation clutter in the harmonic PSF is 26 dB higher than the fundamental PSF. An artificial medium with uniform velocity but unchanged impedance characteristics indicates that for the fundamental PSF, the primary source of degradation is phase aberration. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beamforming algorithm to generate images. These beamformed images are compared with images obtained from convolution of the PSF with a scatterer field to demonstrate that a very large portion of the PSF must be used to accurately represent the clutter observed in conventional imaging. © 2011 IEEE
Plasma Relaxation in Hall Magnetohydrodynamics
Shivamoggi, B K
2011-01-01
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics.
Fundamental fluid mechanics and magnetohydrodynamics
Hosking, Roger J
2016-01-01
This book is primarily intended to enable postgraduate research students to enhance their understanding and expertise in Fluid Mechanics and Magnetohydrodynamics (MHD), subjects no longer treated in isolation. The exercises throughout the book often serve to provide additional and quite significant knowledge or to develop selected mathematical skills, and may also fill in certain details or enhance readers’ understanding of essential concepts. A previous background or some preliminary reading in either of the two core subjects would be advantageous, and prior knowledge of multivariate calculus and differential equations is expected.
Bañón Navarro, A.; Bardóczi, L.; Carter, T. A.; Jenko, F.; Rhodes, T. L.
2017-03-01
Neoclassical tearing modes have deleterious effects on plasma confinement and, if they grow large enough, they can lead to discharge termination. Therefore, they impose a major barrier in the development of operating scenarios of present-day tokamaks. Gyrokinetics offers a path toward studying multi-scale interactions with turbulence and the effect on plasma confinement. As a first step toward this goal, we have implemented static magnetic islands in nonlinear gyrokinetic simulations with the GENE code. We investigate the effect of the islands on profiles, flows, turbulence and transport and the scaling of these effects with respect to island size. We find a clear threshold island width, below which the islands have little or no effect while beyond this point the islands significantly perturb flows, increase turbulence and transport. Additionally, we study the effect of radially asymmetric islands on shear flows for the first time. We find that island induced shear flows can regulate turbulent fluctuation levels in the vicinity of the island separatrices. Throughout this work, we focus on experimentally relevant quantities, such as rms levels of density and electron temperature fluctuations, as well as amplitude and phasing of turbulence modulation. These simulations aim to provide guidelines for interpreting experimental results by comparing qualitative trends in the simulations with those obtained in tokamak experiments.
Nonlinear simulation of free surfaces and atomization in pressure swirl atomizers
Park, Hongbok; Heister, Stephen D.
2006-05-01
A fully nonlinear boundary element method (BEM) model has been developed to simulate the pressure swirl or simplex atomizer. The free surface inside the vortex chamber and within the hollow-cone/primary atomization zone is simulated with a fourth order scheme thereby permitting investigation of highly distorted surfaces up to the point where atomization occurs. For the axisymmetric calculations, annular rings of fluid are pinched from the main liquid domain. Swirling flow is simulated via a superposition of a potential vortex with the base axial flow emanating from the nozzle in a BEM formulation. Results show good comparison to film thicknesses from test data as well as from linear one-dimensional theory. Parametric studies are conducted to assess the influence of injector geometry and flow characteristics on film thickness and spray angle produced by the atomizer. Limited results are also provided to compare droplet sizes with experimental data. In this regard, the linear stability analysis of Ponstein is used to predict the number of droplets created from each ring of fluid shed by the axisymmetric calculation.
A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.
Delsanto, P P; Gliozzi, A S; Hirsekorn, M; Nobili, M
2006-07-01
A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.
Matda, Y.; Crawford, F. W.
1974-01-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described.
Furtmaier, Oliver
2016-01-01
Inspired by the idea of mimicking the measurement on a quantum system through a decoherence process to target specific eigenstates based on Born's law instead of the hierarchy of eigenvalues, we transform a Lindblad equation for the reduced density operator into a nonlinear Schr\\"odinger equation to obtain a computationally feasible simulation of the decoherent dynamics in the open quantum system. The method shows an exponential convergence and its computational costs scale linear for sparse matrix representations of the involved Hermitian operators. Symmetries of the problem can be incorporated either in the initial state of the dynamics or explicitly using the symmetry operators in the evolution equation. As an application of the method we discuss \\textit{eigenstate towing}, which relies on the perturbation theory to follow the progression of an arbitrary subset of eigenstates along a sum of perturbation operators with the intention to explore for instance the effect of interactions on these eigenstates.
LEADS-DC: A computer code for intense dc beam nonlinear transport simulation
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ~13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously,the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.
3D Nonlinear Numerical Simulation of Intact and Debonded Reinforced Concrete Beams
Institute of Scientific and Technical Information of China (English)
Chen Quan(陈权); Marcus L.
2004-01-01
To study the behaviour of reinforced concrete (RC) structures with sections of concrete removed and the reinforcement exposed, 3D nonlinear numerical analysis was performed upon both intact and debonded RC beams by using finite element techniques. The deformational characteristics and the ultimate loads were obtained through numerical models, as well as crack and stress distributions. The failure modes can also be deduced from computational results. Compared with intact beams, the normal assumptions of plane section behaviour is not hold true and the patterns of stress and strain are different in debonded RC beams. The numerical results show good consistency with experimental data. This kind of numerical simulation is a supplement to existing codes.
Nonlinear magnetic field transport in opening switch plasmas
Mason, R. J.; Auer, P. L.; Sudan, R. N.; Oliver, B. V.; Seyler, C. E.; Greenly, J. B.
1993-04-01
The nonlinear transport of magnetic field in collisionless plasmas, as present in the plasma opening switch (POS), using the implicit multifluid simulation code anthem [J. Comput. Phys. 71, 429 (1987)] is studied. The focus is on early time behavior in the electron-magnetohydrodynamic (EMHD) limit, with the ions fixed, and the electrons streaming as a fluid under the influence of ve×B Hall forces. Through simulation, magnetic penetration and magnetic exclusion waves are characterized, due to the Hall effect in the presence of transverse density gradients, and the interaction of these Hall waves with nonlinear diffusive disturbances from electron velocity advection, (veṡ∇)ve, is studied. It is shown how these mechanisms give rise to the anode magnetic insulation layer, central diffusion, and cathode potential hill structures seen in earlier opening switch plasmas studies.
Damping of nonlinear standing kink oscillations: a numerical study
Magyar, N
2016-01-01
We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in particular to the development of the Kelvin-Helmholtz instability (KHI). We run idea, high-resolution three-dimensional (3D) magnetohydrodynamics (MHD) simulations, studying the influence of the initial velocity amplitude and the inhomogeneous layer thickness. We model the coronal loop as a straight, homogeneous magnetic flux tube with an outer inhomogeneous layer, embedded in a straight, homogeneous magnetic field. We find that, for low amplitudes which do not allow for the KHI to develop during the simulated time, the damping time agrees with the theory of resonant absorption. However, for higher amplitudes, the presence of KHI around the oscillating loop can alter the loop's evolution, resulting in a significantly faster damping than predicted by the linear theory in so...
Anomalous k⊥(-8/3) spectrum in electron magnetohydrodynamic turbulence.
Meyrand, Romain; Galtier, Sébastien
2013-12-27
Electron magnetohydrodynamic turbulence is investigated under the presence of a relatively strong external magnetic field b0e∥ and through three-dimensional direct numerical simulations. Our study reveals the emergence of a k⊥(-8/3) scaling for the magnetic energy spectrum at scales k∥(D)≤k⊥≤k⊥(D), where k∥(D) and k⊥(D) are, respectively, the typical largest dissipative scales along and transverse to the b0 direction. Unlike standard magnetohydrodynamic, this turbulence regime is characterized by filaments of electric currents parallel to b0. The anomalous scaling is in agreement with a heuristic model in which the transfer in the parallel direction is negligible. Implications for solar wind turbulence are discussed.
Intermittency in Hall-magnetohydrodynamics with a strong guide field
Imazio, P Rodriguez; Dmitruk, P; Mininni, P D
2013-01-01
We present a detailed study of intermittency in the velocity and magnetic field fluctuations of compressible Hall-magnetohydrodynamic turbulence with an external guide field. To solve the equations numerically, a reduced model valid when a strong guide field is present is used. Different values for the ion skin depth are considered in the simulations. The resulting data is analyzed computing field increments in several directions perpendicular to the guide field, and building structure functions and probability density functions. In the magnetohydrodynamic limit we recover the usual results with the magnetic field being more intermittent than the velocity field. In the presence of the Hall effect, field fluctuations at scales smaller than the ion skin depth show a substantial decrease in the level of intermittency, with close to monofractal scaling.
Institute of Scientific and Technical Information of China (English)
张向洪; 伍贻兆; 王江峰
2012-01-01
采用基于电子束电离的磁流体力学（MHD）控制系统,对高超声速流场附面层,以及非设计状态下的高超声速进气道流场的磁流体控制进行了深入研究.控制方程为低磁雷诺数Navier-Stokes方程,采用等离子体动力学模型与电子束模型模拟空气电离过程.研究结果表明：①电子束电离能有效提高流场的电导率,增强磁场对流场的控制效率;②基于电子束诱导电离的MHD控制系统能有效地控制高超声速流场的附面层,但其控制效率跟电子束能量大小相关;③基于电子束诱导电离的MHD控制系统能有效地改变非设计状态下高超声速飞行器的斜激波结构,使进气道重新满足Shock-on-lip（SOL）条件,但进气道的总压恢复系数以及流量将会降低.%The magnetohydrodynamic （MHD） controlling of hypersonic boundary layer and hypersonic inlets in off-design conditions were studied by magnetohydrodynamie control system based on electron beam ionization. The governing equations were low magnetic Reynolds number Navier-Stokes （N-S） equations, and the plasma kinetics model coupled with electron beam model was developed to simulate air ionization. Results indicate. （1） The electron beam ionization can improve the conductivity of flow and the control efficiency of magnetic field. （2） The MHD system can effectively control the hypersonic boundary lay- er and the control efficiency closely related with the electron beam energy. （3） The MHD system can bring oblique shock in off-design conditions back to the location of shock-on-lip （SOL） condition, and the total pressure recovery coefficient and flow mass of inlets would be reduced.
Variational integrators for reduced magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Kraus, Michael, E-mail: michael.kraus@ipp.mpg.de [Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching (Germany); Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, 85748 Garching (Germany); Tassi, Emanuele, E-mail: tassi@cpt.univ-mrs.fr [Aix-Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 163 avenue de Luminy, case 907, 13288 cedex 9 Marseille (France); Grasso, Daniela, E-mail: daniela.grasso@infm.polito.it [ISC-CNR and Politecnico di Torino, Dipartimento Energia, C.so Duca degli Abruzzi 24, 10129 Torino (Italy)
2016-09-15
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Variational integrators for reduced magnetohydrodynamics
Kraus, Michael; Tassi, Emanuele; Grasso, Daniela
2016-09-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Magnetic reversals in a modified shell model for magnetohydrodynamics turbulence.
Nigro, Giuseppina; Carbone, Vincenzo
2010-07-01
The aim of the paper is the study of dynamo action using a simple nonlinear model in the framework of magnetohydrodynamic turbulence. The nonlinear behavior of the system is described by using a shell model for velocity field and magnetic field fluctuations, modified for the magnetic field at the largest scale by a term describing a supercritical pitchfork bifurcation. Turbulent fluctuations generate a dynamical situation where the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field. Despite its simplicity, the model has the capability to describe a long time series of reversals from which we infer results about the statistics of persistence times and scaling laws of cancellations between opposite polarities for different magnetic diffusivity coefficients. These properties of the model are compared with real paleomagnetic data, thus revealing the origin of long-range correlations in the process.
MHD (Magnetohydrodynamic) Simulation of a Comet Magnetosphere.
1984-04-12
University Code 2628 (20 copies) New York, New York 10027 DTIC (2 copies) ATTN: R. Taussig R.A. Cross University of Alaska Geophysical Institute...Technology Croup Temerin, Michael Space Science Dept. Space Science Lab. Building 1-1, Room 1170 University of California One Space Park Berkeley...Minneapolis, MN 55455 Schulz, Michael Aerospace Corp. A6/2451, P.O. lox 92957 Los Angeles, California 90009 Shavhan, Stanley Dept. of Physics
2015-09-30
1 A multiscale nested modeling framework to simulate the interaction of surface gravity waves with nonlinear internal gravity waves...Minnesota LONG-TERM GOALS Our long-term goal is to develop a multiscale nested modeling framework that simulates, with the finest resolution...frameworks such as the proposed HYCOM-LZSNFS-SUNTANS-LES nested model are crucial for understanding multiscale processes that are unresolved, and hence
Domenech, Arnau Pons
2016-01-01
Many new nonlinear effects become relevant when the quantized nature of the quantum electrodynamics (QED) vacuum is taken into account. We derive an algorithm for simulating these effects in up to 3 spatial dimensions and verify its validity against known 1D analytic results. Finally we use the algorithm to explore systems in which analytic methods are inefficient.
van den Berg, Stéphanie Martine
2009-01-01
Modeling both genetic and cultural transmission in parent-offspring data in the presence of phenotypic assortment requires the imposition of nonlinear constraints. This article reports a simulation study that determined how well the structural equation modeling software package Mx and the
Berg, van den Stephanie M.
2009-01-01
Modeling both genetic and cultural transmission in parent-offspring data in the presence of phenotypic assortment requires the imposition of nonlinear constraints. This article reports a simulation study that determined how well the structural equation modeling software package Mx and the Bayesian-o
Directory of Open Access Journals (Sweden)
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
Nonlinear compensation research and simulation of bandlimited QPSK digital satellite channels
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Presents a phase compensation against the signal distortion mainly caused by TWTA to solve the problem of compensation and modelling of a nonlinear QPSK satellite channel assumed to be bandlimited and exhibit both ampli tude and phase nonlinearities, and to lower the bit error probability of nonlinear channel, and concludes with simula tion results that the compensation against phase distortion of TWTA can significantly improve the nonlinear performance of the channel.
Non-linear friction in reciprocating hydraulic rod seals: Simulation and measurement
Bullock, A. K.; Tilley, D. G.; Johnston, D. N.; Bowen, C. R.; Keogh, P. S.
2009-08-01
Non-linear seal friction can impede the performance of hydraulic actuation systems designed for high precision positioning with favourable dynamic response. Methods for predicting seal friction are required to help develop sealing systems for this type of application. Recent simulation techniques have claimed progress, although have yet to be validated experimentally. A conventional reciprocating rod seal is analysed using established elastohydrodynamic theory and the mixed lubrication Greenwood-Williamson-average Reynolds model. A test rig was used to assess the accuracy of the simulation results for both instroke and outstroke. Inverse hydrodynamic theory is shown to predict a U0.5 power law between rod speed and friction. Comparison with experimental data shows the theory to be qualitatively inaccurate and to predict friction levels an order of magnitude lower than those measured. It was not possible to model the regions very close to the inlet and outlet due to the high pressure gradients at the edges of the contact. The mixed lubrication model produces friction levels within the correct order of magnitude, although incorrectly predicts higher friction during instroke than outstroke. Previous experiments have reported higher friction during instroke than outstroke for rectangular seals, suggesting that the mixed lubrication model used could possibly be suitable for symmetric seals, although not for seal tribology in general.
Nonlinear 3-D simulation of high-intensity focused ultrasound therapy in the kidney
Suomi, Visa; Treeby, Bradley; Cleveland, Robin
2016-01-01
Kidney cancer is a severe disease which can be treated non-invasively using high-intensity focused ultrasound (HIFU) therapy. However, tissue in front of the transducer and the deep location of kidney can cause significant losses to the efficiency of the treatment. The effect of attenuation, refraction and reflection due to different tissue types on HIFU therapy of the kidney was studied using a nonlinear ultrasound simulation model. The geometry of the tissue was derived from a computed tomography (CT) dataset of a patient which had been segmented for water, bone, soft tissue, fat and kidney. The combined effect of inhomogeneous attenuation and sound-speed was found to result in an 11.0 dB drop in spatial peak-temporal average (SPTA) intensity in the kidney compared to pure water. The simulation without refraction effects showed a 6.3 dB decrease indicating that both attenuation and refraction contribute to the loss in focal intensity. The losses due to reflections at soft tissue interfaces were less than 0....
Low-frequency 1/f fluctuations in hydrodynamic and magnetohydrodynamic turbulence.
Dmitruk, Pablo; Matthaeus, W H
2007-09-01
We investigate the occurrence of 1/f spectra of low-frequency fluctuations in numerical simulations of three-dimensional hydrodynamic and magnetohydrodynamic turbulence driven by a random forcing with a controlled correlation time. A range of one decade of 1/f spectrum is observed when a strong background magnetic field is present. The frequency spectra of individual Fourier modes is also analyzed and it is observed that the 1/f range is present in the largest available wavelength mode for the magnetohydrodynamic simulations with and without a background magnetic field and it is not observed (or is less clear) for the hydrodynamic case. The presence of 1/f spectra of low-frequency fluctuations is also analyzed for two-dimensional magnetohydrodynamic and hydrodynamic turbulence simulations and it is observed in both cases. The origin of these long period fluctuations is discussed.
A Magnetohydrodynamic Boost for Relativistic Jets
Mizuno, Yosuke; Hardee, Philip; Hartmann, Dieter H.; Nishikawa, Ken-Ichi; Zhang, Bing
2007-01-01
We performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. Simulation results show that the presence of a magnetic field changes the properties of the shock interface between the tenuous, overpressured jet (V^z j) flowing tangentially to a dense external medium. We find that magnetic fields can lead to more efficient acceleration of the jet, in comparison to the pure-hydrodynamic case. A "poloidal" magnetic field (B^z), tangent to the interface and parallel to the jet flow, produces both a stronger outward moving shock and a stronger inward moving rarefaction wave. This leads to a large velocity component normal to the interface in addition to acceleration tangent to the interface, and the jet is thus accelerated to larger Lorentz factors than those obtained in the pure-hydrodynamic case. Likewise, a strong "toroidal" magnetic field (B^y), tangent to the interface but perpendicular to the jet flow, also leads to stronger acceleration tangent to the shock interface relative to the pure-hydrodynamic case. Thus. the presence and relative orientation of a magnetic field in relativistic jets can significant modify the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Dissipation and reconnection in boundary-driven reduced magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Wan, Minping; Rappazzo, Antonio Franco; Matthaeus, William H. [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States); Servidio, Sergio [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Oughton, Sean [Department of Mathematics, University of Waikato, Hamilton 3240 (New Zealand)
2014-12-10
We study the statistics of coherent current sheets, the population of X-type critical points, and reconnection rates in a coronal loop geometry, via numerical simulations of reduced magnetohydrodynamic turbulence. Current sheets and sites of reconnection (magnetic X-points) are identified in two-dimensional planes of the three-dimensional simulation domain. The geometry of the identified current sheets—including area, length, and width—and the magnetic dissipation occurring in the current sheets are statistically characterized. We also examine the role of magnetic reconnection, by computing the reconnection rates at the identified X-points and investigating their association with current sheets.
Directory of Open Access Journals (Sweden)
Ramoni Marco F
2007-05-01
Full Text Available Abstract Background Reverse engineering cellular networks is currently one of the most challenging problems in systems biology. Dynamic Bayesian networks (DBNs seem to be particularly suitable for inferring relationships between cellular variables from the analysis of time series measurements of mRNA or protein concentrations. As evaluating inference results on a real dataset is controversial, the use of simulated data has been proposed. However, DBN approaches that use continuous variables, thus avoiding the information loss associated with discretization, have not yet been extensively assessed, and most of the proposed approaches have dealt with linear Gaussian models. Results We propose a generalization of dynamic Gaussian networks to accommodate nonlinear dependencies between variables. As a benchmark dataset to test the new approach, we used data from a mathematical model of cell cycle control in budding yeast that realistically reproduces the complexity of a cellular system. We evaluated the ability of the networks to describe the dynamics of cellular systems and their precision in reconstructing the true underlying causal relationships between variables. We also tested the robustness of the results by analyzing the effect of noise on the data, and the impact of a different sampling time. Conclusion The results confirmed that DBNs with Gaussian models can be effectively exploited for a first level analysis of data from complex cellular systems. The inferred models are parsimonious and have a satisfying goodness of fit. Furthermore, the networks not only offer a phenomenological description of the dynamics of cellular systems, but are also able to suggest hypotheses concerning the causal interactions between variables. The proposed nonlinear generalization of Gaussian models yielded models characterized by a slightly lower goodness of fit than the linear model, but a better ability to recover the true underlying connections between
Simulation of the oscillation regimes of bowed bars: a non-linear modal approach
Inácio, Octávio; Henrique, Luís.; Antunes, José
2003-06-01
It is still a challenge to properly simulate the complex stick-slip behavior of multi-degree-of-freedom systems. In the present paper we investigate the self-excited non-linear responses of bowed bars, using a time-domain modal approach, coupled with an explicit model for the frictional forces, which is able to emulate stick-slip behavior. This computational approach can provide very detailed simulations and is well suited to deal with systems presenting a dispersive behavior. The effects of the bar supporting fixture are included in the model, as well as a velocity-dependent friction coefficient. We present the results of numerical simulations, for representative ranges of the bowing velocity and normal force. Computations have been performed for constant-section aluminum bars, as well as for real vibraphone bars, which display a central undercutting, intended to help tuning the first modes. Our results show limiting values for the normal force FN and bowing velocity ẏbow for which the "musical" self-sustained solutions exist. Beyond this "playability space", double period and even chaotic regimes were found for specific ranges of the input parameters FN and ẏbow. As also displayed by bowed strings, the vibration amplitudes of bowed bars also increase with the bow velocity. However, in contrast to string instruments, bowed bars "slip" during most of the motion cycle. Another important difference is that, in bowed bars, the self-excited motions are dominated by the system's first mode. Our numerical results are qualitatively supported by preliminary experimental results.
Influence of nonlinear waves on sandbar migrations using Monte Carlo simulations
Abreu, Tiago; Figueiredo, Fábio; Silva, Paulo A.
2014-05-01
Coastal systems typically involve a variety of natural processes working together. Understanding the interaction between waves and currents and its influence on long-term geomorphological evolution of coastlines and sandbar features is of great importance for coastal managers and policy makers. Our knowledge and understanding of these processes has undergone significant developments in the last decades but this issue still remains a challenge to researchers. The modelling of the sea bed topography changes in the coastal zone can be obtained from numerical simulation of hydrodynamic and sediment transport processes. In the present work, one adopts a morphodynamic model that considers an intra-wave approach. The sediment transport processes are resolved for each individual wave cycle in conjunction with a sediment continuity equation, enabling to calculate morphological changes through time. In this work, we investigate the performance of the morphodynamic model to simulate sandbar migration. The numerical results are compared against the observed beach profile evolutions obtained during the European project "Large Installations Plan" (LIP) (Arcilla et al., 1994). The LIP 1B case is investigated, corresponding to an erosive case, typical of storm events, where a breaker bar in the surf zone migrates offshore. The large-scale laboratory experiments were performed in the Delta flume of Deltares, resulting into a two-dimensional analysis (2D). Consequently, this work contributes to the cross-shore transport problem, particularly, for the modelling of nearshore sandbars. The ability of practical sediment transport models, recognized to capture the interaction between non-linear waves and undertow currents, is assessed (e.g., Hoefel and Elgar, 2003; Silva et al., 2006; Nielsen, 2006; Abreu et al., 2013). Local values for the non-linear parameters (wave asymmetry and skewness) are computed in the model according to Ruessink et al. (2012). In particular, this study
Kinetic approach to Kaluza's magnetohydrodynamics
Sandoval-Villalbazo, A.; Garcia-Colin, L. S.
2011-11-01
Ten years ago we presented a formalism by means of which the basic tenets of relativistic magnetohydrodynamics were derived using Kaluza's ideas about unifying fields in terms of the corresponding space time curvature for a given metric. In this work we present an attempt to obtain the thermodynamic properties of a charged fluid using using Boltzmann's equation for a dilute system adapted to kaluza's formalism. The main results that we obtain are analytical expressions for the main currents and corresponding forces, within the formalism of linear irreversible thermodynamics. We also indicate how transport coefficients can be calculated. Other relevant results are also mentioned. A. Sandoval-Villalbazo and L.S. Garcia-Colin; Phys. of Plasmas 7, 4823 (2000).
Shell Models of Magnetohydrodynamic Turbulence
Plunian, Franck; Frick, Peter
2012-01-01
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accu...
Method for manufacturing magnetohydrodynamic electrodes
Killpatrick, Don H.; Thresh, Henry R.
1982-01-01
A method of manufacturing electrodes for use in a magnetohydrodynamic (MHD) generator comprising the steps of preparing a billet having a core 10 of a first metal, a tubular sleeve 12 of a second metal, and an outer sheath 14, 16, 18 of an extrusile metal; evacuating the space between the parts of the assembled billet; extruding the billet; and removing the outer jacket 14. The extruded bar may be made into electrodes by cutting and bending to the shape required for an MDH channel frame. The method forms a bond between the first metal of the core 10 and the second metal of the sleeve 12 strong enough to withstand a hot and corrosive environment.
Micromachined magnetohydrodynamic actuators and sensors
Lee, Abraham P.; Lemoff, Asuncion V.
2000-01-01
A magnetohydrodynamic (MHD) micropump and microsensor which utilizes micromachining to integrate the electrodes with microchannels and includes a magnet for producing magnetic fields perpendicular to both the electrical current direction and the fluid flow direction. The magnet can also be micromachined and integrated with the micropump using existing technology. The MHD micropump, for example, can generate continuous, reversible flow, with readily controllable flow rates. The flow can be reversed by either reversing the electrical current flow or reversing the magnetic field. By mismatching the electrodes, a swirling vortex flow can be generated for potential mixing applications. No moving parts are necessary and the dead volume is minimal. The micropumps can be placed at any position in a fluidic circuit and a combination of micropumps can generate fluidic plugs and valves.
Magnetohydrodynamic turbulence: Observation and experiment
Energy Technology Data Exchange (ETDEWEB)
Brown, M. R.; Schaffner, D. A.; Weck, P. J. [Department of Physics and Astronomy, Swarthmore College, 500 College Avenue, Swarthmore, Pennsylvania 19081 (United States)
2015-05-15
We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations E{sub B}(f). We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.
Introduction to Magneto-Hydrodynamics
Pelletier, Guy
Magneto-Hydrodynamics (hereafter MHD) describes plasmas on large scales and more generally electrically conducting fluids. This description does not discriminate between the various fluids that constitute the medium. In laboratory, it allows to globally describe a plasma machine, for instance a toroidal nuclear fusion reactor like a Tokamak. In astrophysics it plays an essential role in the description of cosmic objects and their environments, as well as the media, such as the interstellar or the intergalactic medium. A set of phenomena are specific to MHD description. Some of them will be presented in this lecture such as the tension effect, confinement, magnetic diffusivity, magnetic field freezing, Alfvén waves, magneto-sonic waves, reconnection. A celebrated phenomenon of MHD will not be introduced in this brief lecture, namely the dynamo effect.
van den Berg, Stéphanie M
2009-01-01
Modeling both genetic and cultural transmission in parent-offspring data in the presence of phenotypic assortment requires the imposition of nonlinear constraints. This article reports a simulation study that determined how well the structural equation modeling software package Mx and the Bayesian-oriented BUGS software package can handle such nonlinear constraints under various conditions. Results generally showed good and comparable results for Mx and BUGS, although BUGS was much slower than Mx. However, since BUGS uses Markov-chain Monte Carlo estimation it could be used for parent-offspring models with non-normal data and/or item-response theory models.
Annenkov, Sergei; Shrira, Victor
2016-04-01
We study numerically the long-term evolution of water wave spectra without wind forcing, using three different models, aiming at understanding the role of different sets of assumptions. The first model is the classical Hasselmann kinetic equation (KE). We employ the WRT code kindly provided by G. van Vledder. Two other models are new. As the second model, we use the generalised kinetic equation (gKE), derived without the assumption of quasi-stationarity. Thus, unlike the KE, the gKE is valid in the cases when a wave spectrum is changing rapidly (e.g. at the initial stage of evolution of a narrow spectrum). However, the gKE employs the same statistical closure as the KE. The third model is based on the Zakharov integrodifferential equation for water waves and does not depend on any statistical assumptions. Since the Zakharov equation plays the role of the primitive equation of the theory of wave turbulence, we refer to this model as direct numerical simulation of spectral evolution (DNS-ZE). For initial conditions, we choose two narrow-banded spectra with the same frequency distribution (a JONSWAP spectrum with high peakedness γ = 6) and different degrees of directionality. These spectra are from the set of observations collected in a directional wave tank by Onorato et al (2009). Spectrum A is very narrow in angle (corresponding to N = 840 in the cosN directional model). Spectrum B is initially wider in angle (corresponds to N = 24). Short-term evolution of both spectra (O(102) wave periods) has been studied numerically by Xiao et al (2013) using two other approaches (broad-band modified nonlinear Schrödinger equation and direct numerical simulation based on the high-order spectral method). We use these results to verify the initial stage of our DNS-ZE simulations. However, the advantage of the DNS-ZE method is that it allows to study long-term spectral evolution (up to O(104) periods), which was previously possible only with the KE. In the short-term evolution
Institute of Scientific and Technical Information of China (English)
孙亚琴; 叶剑雄; 牟晓佳; 滕虎; 冯恩民; 曾安平; 修志龙
2012-01-01
Glycerol may be converted to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae under anaerobic conditions and glycerol dismutation involves two parallel pathways controlled by the dha regulon. In this study, a fourteen-dimensional nonlinear dynamic system is presented to describe the continuous culture and multiplicity analysis, in which two regulated negative-feedback mechanisms of repression and enzyme inhibition are investigated. The model describing the expression of gene-mRNA-enzyme-product was established according to the repression of the dha regulon by 3-hydroxypropionaldehy (3-HPA). Comparisons between simulated and experimental results indicate that the model can be used to describe the production of 1,3-PD under continuous fermentation. The new model is translated into the corresponding S-system version. The robustness of this model is discussed by using the S-system model and the sensitivity analysis shows that the model is sufficiently robust. The influences of initial glycerol concentration and dilution rate on the biosynthesis of 1,3-PD and the stability of the dha regulon model are investigated. The intracellular concentrations of glycerol, 1,3-PD, 3-HPA, repressor mRNA, repressor, mRNA and protein levels of glycerol dehydratase (GDHt) and 1,3-PD oxydoreductase (PDOR) can be predicted for continuous cultivation. The results of simulation and analysis indicate that 3-HPA accumulation will repress the expression of the dha regulon at the transcriptional level. This model gives new insights into the regulation of glycerol metabolism in K. pneumoniae and explain some of the experimental observations.
Evolution of Accretion Discs around a Kerr Black Hole using Extended Magnetohydrodynamics
Foucart, Francois; Gammie, Charles F; Quataert, Eliot
2015-01-01
Black holes accreting well below the Eddington rate are believed to have geometrically thick, optically thin, rotationally supported accretion discs in which the Coulomb mean free path is large compared to $GM/c^2$. In such an environment, the disc evolution may differ significantly from ideal magnetohydrodynamic predictions. We present non-ideal global axisymmetric simulations of geometrically thick discs around a rotating black hole. The simulations are carried out using a new code ${\\rm\\it grim}$, which evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines, and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. We find that the pressure anisotropy grows to match the ...
Grossmann, Cristian; Langel, Christian; Mazzotti, Marco; Morari, Manfred; Morbidelli, Massimo
2010-03-26
In order to better exploit the economic potential of the simulated moving bed chromatography a 'cycle to cycle' controller which only requires the information about the linear adsorption behavior and the overall average porosity of the columns has been proposed. Recently, an automated on-line HPLC monitoring system which determines the concentrations in the two product streams averaged over one cycle, and returns them as feedback information to the controller was implemented. The new system allows for an accurate determination of the average concentration of the product streams even if the plant is operated at high concentrations. This paper presents the experimental implementation of the 'cycle to cycle' control concept to the separation of guaifenesin enantiomers under nonlinear chromatographic conditions, i.e. at high feed concentrations. Different case studies have been carried out to challenge the controller under realistic operation conditions, e.g. introducing pump disturbances and changing the feed concentration during the operation. The experimental results clearly demonstrate that the controller can indeed deliver the specified purities and improve the process performance.
Fully Nonlinear Simulation for Fluid/Structure Impact:A Review
Institute of Scientific and Technical Information of China (English)
Shili Sun; Guoxiong Wu
2014-01-01
This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method (BEM). Fully nonlinear boundary conditions are imposed on the unknown free surface and the wetted surface of the moving body. The review includes (1) vertical and oblique water entry of a body at constant or a prescribed varying speed, as well as free fall motion, (2) liquid droplets or column impact as well as wave impact on a body, (3) similarity solution of an expanding body. It covers two dimensional (2D), axisymmetric and three dimensional (3D) cases. Key techniques used in the numerical simulation are outlined, including mesh generation on the multivalued free surface, the stretched coordinate system for expanding domain, the auxiliary function method for decoupling the mutual dependence of the pressure and the body motion, and treatment for the jet or the thin liquid film developed during impact.
Owolabi, Kolade M.
2017-03-01
In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 < α < 2. Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 < α < 1) and super-diffusive (1 < α < 2) scenarios. It is observed that computer simulations of SFORDE give enough evidence that pattern formation in fractional medium at certain parameter value is practically the same as in the standard reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.