Unconditionally energy stable numerical schemes for phase-field vesicle membrane model
Guillén-González, F.; Tierra, G.
2018-02-01
Numerical schemes to simulate the deformation of vesicles membranes via minimizing the bending energy have been widely studied in recent times due to its connection with many biological motivated problems. In this work we propose a new unconditionally energy stable numerical scheme for a vesicle membrane model that satisfies exactly the conservation of volume constraint and penalizes the surface area constraint. Moreover, we extend these ideas to present an unconditionally energy stable splitting scheme decoupling the interaction of the vesicle with a surrounding fluid. Finally, the well behavior of the proposed schemes are illustrated through several computational experiments.
The numerical viscosity of entropy stable schemes for systems of conservation laws. I
Tadmor, Eitan
1987-01-01
Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison.To this end, conservative schemes which are also entropy-conservative are constructed. These entropy-conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise-linear finite-element methods, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.
The numerical viscosity of entropy stable schemes for systems of conservation laws
Tadmor, E.
1985-01-01
Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes, is quantified and related to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones.
Numerical viscosity of entropy stable schemes for systems of conservation laws. Final Report
International Nuclear Information System (INIS)
Tadmor, E.
1985-11-01
Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones
DEFF Research Database (Denmark)
Hyun, Jaeyub; Kook, Junghwan; Wang, Semyung
2015-01-01
and basis vectors for use according to the target system. The proposed model reduction scheme is applied to the numerical simulation of the simple mass-damping-spring system and the acoustic metamaterial systems (i.e., acoustic lens and acoustic cloaking device) for the first time. Through these numerical...
Numerical schemes for explosion hazards
International Nuclear Information System (INIS)
Therme, Nicolas
2015-01-01
In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. Blast waves resulting from explosions are modeled by the system of Euler equations for compressible flows, whereas Navier-Stokes equations with reactive source terms and level set techniques are used to simulate the propagation of flame front during the deflagration phase. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations, then the buildup of reliable schemes for the front propagation. In both cases, explicit in time schemes are used, but we also introduce a pressure correction scheme for the Euler equations. Staggered discretization is used in space. It is based on the internal energy formulation of the Euler system, which insures its positivity and avoids tedious discretization of the total energy over staggered grids. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance at the limit. High order methods of MUSCL type are used in the discrete convective operators, based solely on material velocity. They lead to positivity of density and internal energy under CFL conditions. This ensures that the total energy cannot grow and we can furthermore derive a discrete entropy inequality. Under stability assumptions of the discrete L8 and BV norms of the scheme's solutions one can prove that a sequence of converging discrete solutions necessarily converges towards the weak solution of the Euler system. Besides it satisfies a weak entropy inequality at the limit. Concerning the front propagation, we transform the flame front evolution equation (the so
A numerical scheme for the generalized Burgers–Huxley equation
Directory of Open Access Journals (Sweden)
Brajesh K. Singh
2016-10-01
Full Text Available In this article, a numerical solution of generalized Burgers–Huxley (gBH equation is approximated by using a new scheme: modified cubic B-spline differential quadrature method (MCB-DQM. The scheme is based on differential quadrature method in which the weighting coefficients are obtained by using modified cubic B-splines as a set of basis functions. This scheme reduces the equation into a system of first-order ordinary differential equation (ODE which is solved by adopting SSP-RK43 scheme. Further, it is shown that the proposed scheme is stable. The efficiency of the proposed method is illustrated by four numerical experiments, which confirm that obtained results are in good agreement with earlier studies. This scheme is an easy, economical and efficient technique for finding numerical solutions for various kinds of (nonlinear physical models as compared to the earlier schemes.
Canonical, stable, general mapping using context schemes.
Novak, Adam M; Rosen, Yohei; Haussler, David; Paten, Benedict
2015-11-15
Sequence mapping is the cornerstone of modern genomics. However, most existing sequence mapping algorithms are insufficiently general. We introduce context schemes: a method that allows the unambiguous recognition of a reference base in a query sequence by testing the query for substrings from an algorithmically defined set. Context schemes only map when there is a unique best mapping, and define this criterion uniformly for all reference bases. Mappings under context schemes can also be made stable, so that extension of the query string (e.g. by increasing read length) will not alter the mapping of previously mapped positions. Context schemes are general in several senses. They natively support the detection of arbitrary complex, novel rearrangements relative to the reference. They can scale over orders of magnitude in query sequence length. Finally, they are trivially extensible to more complex reference structures, such as graphs, that incorporate additional variation. We demonstrate empirically the existence of high-performance context schemes, and present efficient context scheme mapping algorithms. The software test framework created for this study is available from https://registry.hub.docker.com/u/adamnovak/sequence-graphs/. anovak@soe.ucsc.edu Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Self-adjusting entropy-stable scheme for compressible Euler equations
International Nuclear Information System (INIS)
Cheng Xiao-Han; Nie Yu-Feng; Cai Li; Feng Jian-Hu; Luo Xiao-Yu
2015-01-01
In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, which is based on entropy variables, is employed to make the numerical diffusion term be automatically added around discontinuities. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy. (paper)
Simple Numerical Schemes for the Korteweg-deVries Equation
International Nuclear Information System (INIS)
McKinstrie, C. J.; Kozlov, M.V.
2000-01-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves
Energy Technology Data Exchange (ETDEWEB)
Silva, Filipe da, E-mail: tanatos@ipfn.ist.utl.pt [Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa (Portugal); Pinto, Martin Campos, E-mail: campos@ann.jussieu.fr [CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris (France); Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris (France); Després, Bruno, E-mail: despres@ann.jussieu.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris (France); CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris (France); Heuraux, Stéphane, E-mail: stephane.heuraux@univ-lorraine.fr [Institut Jean Lamour, UMR 7198, CNRS – University Lorraine, Vandoeuvre (France)
2015-08-15
This work analyzes the stability of the Yee scheme for non-stationary Maxwell's equations coupled with a linear current model with density fluctuations. We show that the usual procedure may yield unstable scheme for physical situations that correspond to strongly magnetized plasmas in X-mode (TE) polarization. We propose to use first order clustered discretization of the vectorial product that gives back a stable coupling. We validate the schemes on some test cases representative of direct numerical simulations of X-mode in a magnetic fusion plasma including turbulence.
A numerical relativity scheme for cosmological simulations
Daverio, David; Dirian, Yves; Mitsou, Ermis
2017-12-01
Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3 + 1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.
Numerical Differentiation and Integration through Aitken-Neville Schemes
Directory of Open Access Journals (Sweden)
Ramesh Kumar Muthumalai
2013-09-01
Full Text Available Some new formulas are given to approximate higher order derivatives and integrals through Aitken-Neville iterative schemes for arbitrary spaced grids. An algorithm is given in MATLAB for numerical differentiation. Also, numerical examples are provided to study error analysis of new formulas for numerical differentiation and integration.
Application of stable adaptive schemes to nuclear reactor systems, (1)
International Nuclear Information System (INIS)
Fukuda, Toshio
1978-01-01
Parameter identification and adaptive control schemes are presented for a point reactor with internal feedbacks which lead to the nonlinearity of the overall system. Both are shown stable with new representation of the system, which corresponds to the nonminimal system representation, in the vein of the Model Reference Adaptive System (MRAS) via the Lyapunov's method. For the sake of the parameter identification, model parameters can be adjusted adaptively as soon as measurements start, while plant parameters can also adaptively be compensated through control input to reduce the output error between the model and the plant for the case of the adaptive control. In the case of the adaptive control, control schemes are presented for two cases, the case of the unknown decay constant of the delayed neutron and the case of the known constant. The adaptive control scheme for the latter case is shown extremely simpler than that for the former. Furthermore, when plant parameters vary slowly with time, computer simulations show that the proposed adaptive control scheme works satisfactorily enough to stabilize an unstable reactor and that it does even in the noise with small variance. (auth.)
Class of unconditionally stable second-order implicit schemes for hyperbolic and parabolic equations
International Nuclear Information System (INIS)
Lui, H.C.
The linearized Burgers equation is considered as a model u/sub t/ tau/sub x/ = bu/sub xx/, where the subscripts t and x denote the derivatives of the function u with respect to time t and space x; a and b are constants (b greater than or equal to 0). Numerical schemes for solving the equation are described that are second-order accurate, unconditionally stable, and dissipative of higher order. (U.S.)
International Nuclear Information System (INIS)
Abgrall, Remi; Mezine, Mohamed
2003-01-01
The aim of this paper is to construct upwind residual distribution schemes for the time accurate solution of hyperbolic conservation laws. To do so, we evaluate a space-time fluctuation based on a space-time approximation of the solution and develop new residual distribution schemes which are extensions of classical steady upwind residual distribution schemes. This method has been applied to the solution of scalar advection equation and to the solution of the compressible Euler equations both in two space dimensions. The first version of the scheme is shown to be, at least in its first order version, unconditionally energy stable and possibly conditionally monotonicity preserving. Using an idea of Csik et al. [Space-time residual distribution schemes for hyperbolic conservation laws, 15th AIAA Computational Fluid Dynamics Conference, Anahein, CA, USA, AIAA 2001-2617, June 2001], we modify the formulation to end up with a scheme that is unconditionally energy stable and unconditionally monotonicity preserving. Several numerical examples are shown to demonstrate the stability and accuracy of the method
Numerical Comparison of Optimal Charging Schemes for Electric Vehicles
DEFF Research Database (Denmark)
You, Shi; Hu, Junjie; Pedersen, Anders Bro
2012-01-01
The optimal charging schemes for Electric vehicles (EV) generally differ from each other in the choice of charging periods and the possibility of performing vehicle-to-grid (V2G), and have different impacts on EV economics. Regarding these variations, this paper presents a numerical comparison...... of four different charging schemes, namely night charging, night charging with V2G, 24 hour charging and 24 hour charging with V2G, on the basis of real driving data and electricity price of Denmark in 2003. For all schemes, optimal charging plans with 5 minute resolution are derived through the solving...
Stable low-dissipation schemes for turbulent compressible flows
Subbareddy, Pramod Kumar V.
Shock capturing schemes, which are commonly used in compressible flow simulations, introduce excessive amounts of numerical viscosity which smears out small scale flow features. A few low-dissipation methods have been proposed in the recent literature. They are more selective in the sense that they explicitly identify the portion of the numerical flux that is diffusive and damp its effect in 'smooth' regions of the flow. This work employs flux vector splitting methods; the dissipative portions of the Steger-Warming schemes are explicitly identified and various shock detection switches are explored. For high Reynolds number flows, especially when the energetic scales are close to the Nyquist limits of the grids used, aliasing errors become noticeable. These high frequency oscillations that arise due to the nonlinear nature of the Navier-Stokes equations cause solutions to become unstable. When dissipative methods are used, these errors are suppressed; however when using low-dissipation schemes, they can be prominent and need to be addressed by some other means. In this thesis, we focus on methods that enhance stability by enforcing 'secondary conservation' - the fluxes are constrained in such a way that a conservation law for a secondary, positive quantity is also satisified. In particular, we focus on kinetic energy, and a fully discrete (in time and space) 'kinetic energy consistent' scheme is derived and tested. Hybrid RAMS-LES methods such as Detached Eddy Simulations are necessary in order to make simulations of high speed flows with attached boundary layers affordable. A popular DES model is based on the Spalart-Allmaras RANS equation; a minor modification to the length scale makes the model behave in a hybrid manner. The S-A model itself was constructed using mostly empirical arguments by the authors. This model is analyzed and its connection to other turbulence models, in particular, the ksgs equation, is explored. A dynamic version of the model is proposed
A gradient stable scheme for a phase field model for the moving contact line problem
Gao, Min
2012-02-01
In this paper, an efficient numerical scheme is designed for a phase field model for the moving contact line problem, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition [1,2,4]. The nonlinear version of the scheme is semi-implicit in time and is based on a convex splitting of the Cahn-Hilliard free energy (including the boundary energy) together with a projection method for the Navier-Stokes equations. We show, under certain conditions, the scheme has the total energy decaying property and is unconditionally stable. The linearized scheme is easy to implement and introduces only mild CFL time constraint. Numerical tests are carried out to verify the accuracy and stability of the scheme. The behavior of the solution near the contact line is examined. It is verified that, when the interface intersects with the boundary, the consistent splitting scheme [21,22] for the Navier Stokes equations has the better accuracy for pressure. © 2011 Elsevier Inc.
An energy-stable finite-difference scheme for the binary fluid-surfactant system
Gu, Shuting; Zhang, Hui; Zhang, Zhengru
2014-08-01
We present an unconditionally energy stable finite-difference scheme for the binary fluid-surfactant system. The proposed method is based on the convex splitting of the energy functional with two variables. Here are two distinct features: (i) the convex splitting energy method is applied to energy functional with two variables, and (ii) the stability issue is related to the decay of the corresponding energy. The full discrete scheme leads to a decoupled system including a linear sub-system and a nonlinear sub-system. Algebraic multigrid and Newton-multigrid methods are adopted to solve the linear and nonlinear systems, respectively. Numerical experiments are shown to verify the stability of such a scheme.
Numerical solution to nonlinear Tricomi equation using WENO schemes
Directory of Open Access Journals (Sweden)
Adrian Sescu
2010-09-01
Full Text Available Nonlinear Tricomi equation is a hybrid (hyperbolic-elliptic second order partial differential equation, modelling the sonic boom focusing. In this paper, the Tricomi equation is transformed into a hyperbolic system of first order equations, in conservation law form. On the upper boundary, a new mixed boundary condition for the acoustic pressure is used to avoid the inclusion of the Dirac function in the numerical solution. Weighted Essentially Non-Oscillatory (WENO schemes are used for the spatial discretization, and the time marching is carried out using the second order accurate Runge-Kutta total-variation diminishing (TVD scheme.
Stable schemes for dissipative particle dynamics with conserved energy
Energy Technology Data Exchange (ETDEWEB)
Stoltz, Gabriel, E-mail: stoltz@cermics.enpc.fr
2017-07-01
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis–Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiple timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.
Generalized Roe's numerical scheme for a two-fluid model
International Nuclear Information System (INIS)
Toumi, I.; Raymond, P.
1993-01-01
This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,
Chen, Huangxin
2017-09-01
In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.
International Nuclear Information System (INIS)
Zhong Xiaolin; Tatineni, Mahidhar
2003-01-01
The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier-Stokes equations for the wall bounded supersonic flow
An Energy stable Monolithic Eulerian Fluid-Structure Numerical Scheme *
Pironneau , Olivier
2017-01-01
The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown , monolithic methods for fluid structure interactions (FSI) are built. In this article such a formulation is analyzed when the fluid is compressible and the fluid is incompressible. The i...
A New Numerical Scheme for Cosmic-Ray Transport
Jiang, Yan-Fei; Oh, S. Peng
2018-02-01
Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.
Numerical schemes for solving the Euler equations of gas dynamics
International Nuclear Information System (INIS)
Dervieux, A.; Vijayasundaram, G.
1985-01-01
The first-order upwind schemes of Godunov-Van Leer, Steger-Warming, Godunov, Roe, Osher and Glimm; Godunov type scheme I; the second-order upwind schemes of Van Leer, Fromm-Van Leer, Hancock-Van Leer, and Moretti; and the second-order centered schemes of Richtmyer, Mac Cormack, Lerat-Peyrat, and Jameson are described. Their performances for the shock-tube problem proposed by Sod are compared. The schemes of Godunov-Van Leer, Glimm, Fromm-Van Leer, and Hancock-Van Leer produced the best results. All the First-order upwind schemes, the Glimm scheme, the Jameson scheme, and the Hancock-Van Leer scheme can be extended to two dimensions in the finite element setting. 30 references
A new numerical scheme for the simulation of active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, B.; Engelbrecht, Kurt; Payá, J.
2014-01-01
A 1D model of a parallel-plate active magnetic regenerator (AMR) has been developed based on a new numerical scheme. With respect to the implicit scheme, the new scheme achieves accurate results, minimizes computational time and prevents numerical errors. The model has been used to check the boun...
Numeric Analysis for Relationship-Aware Scalable Streaming Scheme
Directory of Open Access Journals (Sweden)
Heung Ki Lee
2014-01-01
Full Text Available Frequent packet loss of media data is a critical problem that degrades the quality of streaming services over mobile networks. Packet loss invalidates frames containing lost packets and other related frames at the same time. Indirect loss caused by losing packets decreases the quality of streaming. A scalable streaming service can decrease the amount of dropped multimedia resulting from a single packet loss. Content providers typically divide one large media stream into several layers through a scalable streaming service and then provide each scalable layer to the user depending on the mobile network. Also, a scalable streaming service makes it possible to decode partial multimedia data depending on the relationship between frames and layers. Therefore, a scalable streaming service provides a way to decrease the wasted multimedia data when one packet is lost. However, the hierarchical structure between frames and layers of scalable streams determines the service quality of the scalable streaming service. Even if whole packets of layers are transmitted successfully, they cannot be decoded as a result of the absence of reference frames and layers. Therefore, the complicated relationship between frames and layers in a scalable stream increases the volume of abandoned layers. For providing a high-quality scalable streaming service, we choose a proper relationship between scalable layers as well as the amount of transmitted multimedia data depending on the network situation. We prove that a simple scalable scheme outperforms a complicated scheme in an error-prone network. We suggest an adaptive set-top box (AdaptiveSTB to lower the dependency between scalable layers in a scalable stream. Also, we provide a numerical model to obtain the indirect loss of multimedia data and apply it to various multimedia streams. Our AdaptiveSTB enhances the quality of a scalable streaming service by removing indirect loss.
On a Stable and Consistent Finite Difference Scheme for a Time ...
African Journals Online (AJOL)
In this paper, a stable and consistent criterion to an explicit finite difference scheme for a time-dependent Schrodinger wave equation (TDSWE) was presented. This paper is a departure from the well-established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion for the scheme, the ...
Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng
2013-10-01
In this paper we present two unconditionally energy stable finite difference schemes for the modified phase field crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic phase field crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulated from the gradients of strictly convex, coercive functionals. Thus, both are uniquely solvable regardless of the time and space step sizes. The schemes are solved by efficient nonlinear multigrid methods. Numerical results are presented demonstrating the accuracy, energy stability, efficiency, and practical utility of the schemes. In particular, we show that our multigrid solvers enjoy optimal, or nearly optimal complexity in the solution of the nonlinear schemes.
Two adaptive radiative transfer schemes for numerical weather prediction models
Directory of Open Access Journals (Sweden)
V. Venema
2007-11-01
Full Text Available Radiative transfer calculations in atmospheric models are computationally expensive, even if based on simplifications such as the δ-two-stream approximation. In most weather prediction models these parameterisation schemes are therefore called infrequently, accepting additional model error due to the persistence assumption between calls. This paper presents two so-called adaptive parameterisation schemes for radiative transfer in a limited area model: A perturbation scheme that exploits temporal correlations and a local-search scheme that mainly takes advantage of spatial correlations. Utilising these correlations and with similar computational resources, the schemes are able to predict the surface net radiative fluxes more accurately than a scheme based on the persistence assumption. An important property of these adaptive schemes is that their accuracy does not decrease much in case of strong reductions in the number of calls to the δ-two-stream scheme. It is hypothesised that the core idea can also be employed in parameterisation schemes for other processes and in other dynamical models.
Stable Numerical Approach for Fractional Delay Differential Equations
Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.
2017-12-01
In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.
Stable Numerical Approach for Fractional Delay Differential Equations
International Nuclear Information System (INIS)
Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.
2017-01-01
In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods. (author)
Comparison of four stable numerical methods for Abel's integral equation
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
Analyzing numerics of bulk microphysics schemes in community models: warm rain processes
Directory of Open Access Journals (Sweden)
I. Sednev
2012-08-01
Full Text Available Implementation of bulk cloud microphysics (BLK parameterizations in atmospheric models of different scales has gained momentum in the last two decades. Utilization of these parameterizations in cloud-resolving models when timesteps used for the host model integration are a few seconds or less is justified from the point of view of cloud physics. However, mechanistic extrapolation of the applicability of BLK schemes to the regional or global scales and the utilization of timesteps of hundreds up to thousands of seconds affect both physics and numerics.
We focus on the mathematical aspects of BLK schemes, such as stability and positive-definiteness. We provide a strict mathematical definition for the problem of warm rain formation. We also derive a general analytical condition (SM-criterion that remains valid regardless of parameterizations for warm rain processes in an explicit Eulerian time integration framework used to advanced finite-difference equations, which govern warm rain formation processes in microphysics packages in the Community Atmosphere Model and the Weather Research and Forecasting model. The SM-criterion allows for the existence of a unique positive-definite stable mass-conserving numerical solution, imposes an additional constraint on the timestep permitted due to the microphysics (like the Courant-Friedrichs-Lewy condition for the advection equation, and prohibits use of any additional assumptions not included in the strict mathematical definition of the problem under consideration.
By analyzing the numerics of warm rain processes in source codes of BLK schemes implemented in community models we provide general guidelines regarding the appropriate choice of time steps in these models.
Al Jarro, Ahmed
2012-11-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Energy Technology Data Exchange (ETDEWEB)
Park, Ju Yeop; In, Wang Kee; Chun, Tae Hyun; Oh, Dong Seok [Korea Atomic Energy Research Institute, Taejeon (Korea)
2000-02-01
The development of orthogonal 2-dimensional numerical code is made. The present code contains 9 kinds of turbulence models that are widely used. They include a standard k-{epsilon} model and 8 kinds of low Reynolds number ones. They also include 6 kinds of numerical schemes including 5 kinds of low order schemes and 1 kind of high order scheme such as QUICK. To verify the present numerical code, pipe flow, channel flow and expansion pipe flow are solved by this code with various options of turbulence models and numerical schemes and the calculated outputs are compared to experimental data. Furthermore, the discretization error that originates from the use of standard k-{epsilon} turbulence model with wall function is much more diminished by introducing a new grid system than a conventional one in the present code. 23 refs., 58 figs., 6 tabs. (Author)
Linearly decoupled energy-stable numerical methods for multi-component two-phase compressible flow
Kou, Jisheng
2017-12-06
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are constructed based on the scalar auxiliary variable (SAV) approaches for Helmholtz free energy and the intermediate velocities that are designed to decouple the tight relationship between velocity and molar densities. The intermediate velocities are also involved in the discrete momentum equation to ensure a consistency relationship with the mass balance equations. Moreover, we propose a component-wise SAV approach for a multi-component fluid, which requires solving a sequence of linear, separate mass balance equations. We prove that the methods have the unconditional energy-dissipation feature. Numerical results are presented to verify the effectiveness of the proposed methods.
Numerical Simulations of Stably Stratified Fluid Flow Using Compact Finite-Difference Schemes
Bodnár, T.; Fraunié, Ph.; Kozel, K.
2010-09-01
The aim of this paper is to present the class of high order compact schemes in the context of numerical simulation of stratified flow. The numerical schemes presented here are based on the approach outlined in Lele [1]. The numerical model presented in this contribution is based on the solution of the Boussinesq approximation by a finite-difference scheme. The numerical scheme itself follows the principle of semi-discretization, with high order compact discretization in space, while the time integration is carried out by suitable Runge-Kutta time-stepping scheme. In the case presented here the steady flow was considered and thus the artificial compressibility method was used to resolve the pressure from the modified continuity equation. The test case used to demonstrate the capabilities of the selected model consists of the flow of stably stratified fluid over low, smooth hill.
Hybrid flux splitting schemes for numerical resolution of two-phase flows
Energy Technology Data Exchange (ETDEWEB)
Flaatten, Tore
2003-07-01
This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)
A new scheme to treat the numerical Tcherenkov instability for electromagnetic particle simulations
International Nuclear Information System (INIS)
Assous, F.; Degond, P.; Segre, J.; Degond, P.
1997-10-01
The aim of this paper is to present a new explicit time scheme for electromagnetic particle simulations. The main property of this new scheme, which depends on a parameter, is to reduce and in some cases to suppress numerical instabilities that can appear in this context, and are widely described in the literature. Other numerical properties are also investigated, and a numerical example is finally given to illustrate our purpose. This scheme is expected to be useful in the field of plasma modelling. (authors)
Numerical optimization schemes for the design of transportation packages
International Nuclear Information System (INIS)
Witkowski, W.R.; Harding, D.C.
1992-02-01
Numerical optimization has been successfully used to obtain optimal designs in a more efficient and structured manner in many industries. Optimization of sizing variables is already a widely used design tool and even though shape optimization is still an active research topic, significant successes have been achieved for many structural analysis problems. The transportation cask design problem seems to have the formulation and requirements to benefit from numerical optimization. Complex structural, thermal and radiation shielding analyses associated with cask design constraints can be integrated and automated through numerical optimization to help meet the growing needs for safe and reliable shipping containers. Improved overall package safety and efficiency with cost savings in the design and fabrication can also be realized. Sandia National Laboratories (SNL) has the opportunity to be a significant contributor in the development of new sophisticated transportation cask design tools. Current state-of-the-art technology at SNL in the areas of structural mechanics, thermal mechanics, numerical analysis, adaptive finite element analysis, automatic mesh generation, and transportation cask design can be combined to enhance current industry-standard cask design and analysis techniques through numerical optimization
Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD
Yee, H. C.; Sjoegreen, B.
2004-01-01
The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux
TLC scheme for numerical solution of the transport equation on equilateral triangular meshes
International Nuclear Information System (INIS)
Walters, W.F.
1983-01-01
A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy
Cures for the shock instability: Development of a shock-stable Roe scheme
Kim, S S; Rho, O H; Kyu-Hong, S
2003-01-01
This paper deals with the development of an improved Roe scheme that is free from the shock instability and still preserves the accuracy and efficiency of the original Roe's Flux Difference Splitting (FDS). Roe's FDS is known to possess good accuracy but to suffer from the shock instability, such as the carbuncle phenomenon. As the first step towards a shock-stable scheme, Roe's FDS is compared with the HLLE scheme to identify the source of the shock instability. Through a linear perturbation analysis on the odd-even decoupling problem, damping characteristic is examined and Mach number-based functions f and g are introduced to balance damping and feeding rates, which leads to a shock-stable Roe scheme. In order to satisfy the conservation of total enthalpy, which is crucial in predicting surface heat transfer rate in high-speed steady flows, an analysis of dissipation mechanism in the energy equation is carried out to find out the error source and to make the proposed scheme preserve total enthalpy. By modif...
Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results
Energy Technology Data Exchange (ETDEWEB)
Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young
2007-12-15
A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor.
Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results
International Nuclear Information System (INIS)
Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young
2007-12-01
A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor
Benes, Nieck Edwin; Verzijl, Richard; Verweij, H.
1999-01-01
A numerical scheme is presented for computer simulation of multicomponent gas transport possibly accompanied by reversible chemical reactions in a macroporous medium, based on the dusty gas model. Using analytical solutions for simple systems it is shown that the derivation of the scheme is
Numerical Schemes for Charged Particle Movement in PIC Simulations
International Nuclear Information System (INIS)
Kulhanek, P.
2001-01-01
A PIC model of plasma fibers is developed in the Department of Physics of the Czech Technical University for several years. The program code was written in FORTRAN 95, free-style (without compulsory columns). Fortran compiler and linker were used from Compaq Visual Fortran 6.1A embedded in the Microsoft Development studio GUI. Fully three-dimensional code with periodical boundary conditions was developed. Electromagnetic fields are localized on a grid and particles move freely through this grid. One of the partial problems of the PIC model is the numerical particle solver, which will be discussed in this paper. (author)
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
A stable higher order space time Galerkin marching-on-in-time scheme
Pray, Andrew J.
2013-07-01
We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order basis functions in time to improve the accuracy of the solver. The method is validated by showing convergence in temporal basis function order, time step size, and geometric discretization order. © 2013 IEEE.
Modeling stable orographic precipitation at small scales. The impact of the autoconversion scheme
Energy Technology Data Exchange (ETDEWEB)
Zaengl, Guenther; Seifert, Axel [Deutscher Wetterdienst, Offenbach (Germany); Wobrock, Wolfram [Clermont Univ., Univ. Blaise Pascal, Lab. de Meteorologie Physique, Clermont-Ferrand (France); CNRS, INSU, UMR, LaMP, Aubiere (France)
2010-10-15
This study presents idealized numerical simulations of moist airflow over a narrow isolated mountain in order to investigate the impact of the autoconversion scheme on simulated precipitation. The default setup generates an isolated water cloud over the mountain, implying that autoconversion of cloud water into rain is the only process capable of initiating precipitation. For comparison, a set of sensitivity experiments considers the classical seeder-feeder configuration, which means that ambient precipitation generated by large-scale lifting is intensified within the orographic cloud. Most simulations have been performed with the nonhydrostatic COSMO model developed at the German Weather Service (DWD), comparing three different autoconversion schemes of varying sophistication. For reference, a subset of experiments has also been performed with a spectral (bin) microphysics model. While precipitation enhancement via the seeder-feeder mechanism turns out to be relatively insensitive against the autoconversion scheme because accretion is the leading process in this case, simulated precipitation amounts can vary by 1-2 orders of magnitude for purely orographic precipitation. By comparison to the reference experiments conducted with the bin model, the Seifert-Beheng autoconversion scheme (which is the default in the COSMO model) and the Berry-Reinhardt scheme are found to represent the nonlinear behaviour of orographic precipitation reasonably well, whereas the linear approach of the Kessler scheme appears to be less adequate. (orig.)
DEFF Research Database (Denmark)
Hesthaven, Jan
1997-01-01
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...
Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification
Energy Technology Data Exchange (ETDEWEB)
Blottner, F.G.; Lopez, A.R.
1998-10-01
This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.
Discussion of the numerical stability of an improved upwinding scheme
International Nuclear Information System (INIS)
Hassan, Y.A.; Kim, J.H.
1986-01-01
The prediction of multidimensional heat transfer and fluid flow problems requires the solution of Navier-Stokes equations. Although the use of upwind approximation for the convection terms removes the potential of nonphysical spatial oscillations, such a procedure is burdened with excessive numerical diffusion. Recently published work by Smith and Hutton presented results for some 20 different candidate methods to estimate the convection terms. The overall conclusion was that none of the methods was totally successful. The more accurate methods exhibited nonphysical spatial oscillations. More recently, a procedure was proposed that alleviates the problem of false diffusion. The purpose of this paper is to present several challenging cases, with various flow orientation, to show that the proposed procedure always circumvents the negative coefficients in the discretization equation such that the influence coefficients cannot become negative. The Smith and Hutton test case has been examined to illustrate the merit of this technique. The results are competitive with a large majority of those examined by Smith and Hutton
Reinharz, Vladimir; Dahari, Harel; Barash, Danny
2018-03-15
Age-structured PDE models have been developed to study viral infection and treatment. However, they are notoriously difficult to solve. Here, we investigate the numerical solutions of an age-based multiscale model of hepatitis C virus (HCV) dynamics during antiviral therapy and compare them with an analytical approximation, namely its long-term approximation. First, starting from a simple yet flexible numerical solution that also considers an integral approximated over previous iterations, we show that the long-term approximation is an underestimate of the PDE model solution as expected since some infection events are being ignored. We then argue for the importance of having a numerical solution that takes into account previous iterations for the associated integral, making problematic the use of canned solvers. Second, we demonstrate that the governing differential equations are stiff and the stability of the numerical scheme should be considered. Third, we show that considerable gain in efficiency can be achieved by using adaptive stepsize methods over fixed stepsize methods for simulating realistic scenarios when solving multiscale models numerically. Finally, we compare between several numerical schemes for the solution of the equations and demonstrate the use of a numerical optimization scheme for the parameter estimation performed directly from the equations. Copyright © 2018 Elsevier Inc. All rights reserved.
A new numerical scheme for bounding acceleration in the LWR model
LECLERCQ, L; ELSEVIER
2005-01-01
This paper deals with the numerical resolution of bounded acceleration extensions of the LWR model. Two different manners for bounding accelerations in the LWR model will be presented: introducing a moving boundary condition in front of an accelerating flow or defining a field of constraints on the maximum allowed speed in the (x,t) plane. Both extensions lead to the same solutions if the declining branch of the fundamental diagram is linear. The existing numerical scheme for the latter exte...
RELAP5 two-phase fluid model and numerical scheme for economic LWR system simulation
International Nuclear Information System (INIS)
Ransom, V.H.; Wagner, R.J.; Trapp, J.A.
1981-01-01
The RELAP5 two-phase fluid model and the associated numerical scheme are summarized. The experience accrued in development of a fast running light water reactor system transient analysis code is reviewed and example of the code application are given
International Nuclear Information System (INIS)
Girardin, Mathieu
2014-01-01
Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author) [fr
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation
Liu, Yang
2010-03-01
We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge
2015-01-01
A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally...... combines explicit and implicit techniques in order to solve the one-dimensional conjugate heat transfer problem in an accurate and fast manner while ensuring energy conservation. The present model has been thoroughly validated against passive regenerator cases with an analytical solution. Compared...
A hybrid convection scheme for use in non-hydrostatic numerical weather prediction models
Directory of Open Access Journals (Sweden)
Volker Kuell
2008-12-01
Full Text Available The correct representation of convection in numerical weather prediction (NWP models is essential for quantitative precipitation forecasts. Due to its small horizontal scale convection usually has to be parameterized, e.g. by mass flux convection schemes. Classical schemes originally developed for use in coarse grid NWP models assume zero net convective mass flux, because the whole circulation of a convective cell is confined to the local grid column and all convective mass fluxes cancel out. However, in contemporary NWP models with grid sizes of a few kilometers this assumption becomes questionable, because here convection is partially resolved on the grid. To overcome this conceptual problem we propose a hybrid mass flux convection scheme (HYMACS in which only the convective updrafts and downdrafts are parameterized. The generation of the larger scale environmental subsidence, which may cover several grid columns, is transferred to the grid scale equations. This means that the convection scheme now has to generate a net convective mass flux exerting a direct dynamical forcing to the grid scale model via pressure gradient forces. The hybrid convection scheme implemented into the COSMO model of Deutscher Wetterdienst (DWD is tested in an idealized simulation of a sea breeze circulation initiating convection in a realistic manner. The results are compared with analogous simulations with the classical Tiedtke and Kain-Fritsch convection schemes.
Adaptive Numerical Dissipation Control in High Order Schemes for Multi-D Non-Ideal MHD
Yee, H. C.; Sjoegreen, B.
2005-01-01
The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.
Towards a stable numerical time scale for the early Paleogene
Hilgen, Frederik; Kuiper, Klaudia; Sierro, Francisco J.; Wotzlaw, Jorn; Schaltegger, Urs; Sahy, Diana; Condon, Daniel
2014-05-01
The construction of an astronomical time scale for the early Paleogene is hampered by ambiguities in the number, correlation and tuning of 405-kyr eccentricity related cycles in deep marine records from ODP cores and land-based sections. The two most competing age models result in astronomical ages for the K/Pg boundary that differ by ~750 kyr (~66.0 Ma of Vandenberghe et al. (2012) versus 65.25 Ma of Westerhold et al. (2012); these ages in turn are consistent with proposed ages for the Fish Canyon sanidine (FCs) that differ by ~300 kyr (28.201 Ma of Kuiper et al. (2008) versus 27.89 Ma of Westerhold et al. (2012)); an even older age of 28.294 Ma is proposed based on a statistical optimization model (Renne et al., 2011). The astronomically calibrated FCs age of 28.201 ± 0.046 Ma of Kuiper et al. (2008), which is consistent with the astronomical age of ~66.0 Ma for the K/Pg boundary, is currently adopted in the standard geological time scale (GTS2012). Here we combine new and published data in an attempt to solve the controversy and arrive at a stable nuemrical time scale for the early Paleogene. Supporting their younger age model, Westerhold et al. (2012) argue that the tuning of Miocene sections in the Mediterranean, which underlie the older FCs age of Kuiper et al. (2008) and, hence, the coupled older early Paleogene age model of Vandenberghe et al. (2012), might be too old by three precession cycles. We thoroughly rechecked this tuning; distinctive cycle patterns related to eccentricity and precession-obliquity interference make a younger tuning that would be consistent with the younger astronomical age of 27.89 Ma for the FCs of Westerhold et al. (2012) challenging. Next we compared youngest U/Pb zircon and astronomical ages for a number of ash beds in the tuned Miocene section of Monte dei Corvi. These ages are indistinguishable, indicating that the two independent dating methods yield the same age when the same event is dated. This is consistent with results
International Nuclear Information System (INIS)
Prinja, A.K.
1997-01-01
A nonlinear discretization scheme in space and energy, based on the recently developed exponential discontinuous method, is applied to continuous slowing down dominated electron transport (i.e., in the absence of scattering.) Numerical results for dose and charge deposition are obtained and compared against results from the ONELD and ONEBFP codes, and against exact results from an adjoint Monte Carlo code. It is found that although the exponential discontinuous scheme yields strictly positive and monotonic solutions, the dose profile is considerably straggled when compared to results from the linear codes. On the other hand, the linear schemes produce negative results which, furthermore, do not damp effectively in some cases. A general conclusion is that while yielding strictly positive solutions, the exponential discontinuous method does not show the crude cell accuracy for charged particle transport as was apparent for neutral particle transport problems
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
International Nuclear Information System (INIS)
Liu Di
2008-01-01
We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
Liu, Di
2008-10-01
We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples.
Development of a moisture scheme for the explicit numerical simulation of moist convection
CSIR Research Space (South Africa)
Bopape, Mary-Jane M
2010-09-01
Full Text Available .kashan.co.za] Development of a moisture scheme for the explicit numerical simulation of moist convection M BOPAPE, F ENGELBRECHT, D RANDALL AND W LANDMAN CSIR Natural Resources and the Environment, PO Box 395, Pretoria, 0001, South Africa Email: mbopape... sigma coordinate model that incorporates moisture effects, so that it can simulate convective clouds and precipitation. moisture terms equivalent to those of the miller and pearce (1974) model are incorporated in the equation set used: ; (1) ; (2...
Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods
Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard
2013-04-01
Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme
Stable water isotope simulation by current land-surface schemes:Results of IPILPS phase 1
Energy Technology Data Exchange (ETDEWEB)
Henderson-Sellers, A.; Fischer, M.; Aleinov, I.; McGuffie, K.; Riley, W.J.; Schmidt, G.A.; Sturm, K.; Yoshimura, K.; Irannejad, P.
2005-10-31
Phase 1 of isotopes in the Project for Intercomparison of Land-surface Parameterization Schemes (iPILPS) compares the simulation of two stable water isotopologues ({sup 1}H{sub 2} {sup 18}O and {sup 1}H{sup 2}H{sup 16}O) at the land-atmosphere interface. The simulations are off-line, with forcing from an isotopically enabled regional model for three locations selected to offer contrasting climates and ecotypes: an evergreen tropical forest, a sclerophyll eucalypt forest and a mixed deciduous wood. Here we report on the experimental framework, the quality control undertaken on the simulation results and the method of intercomparisons employed. The small number of available isotopically-enabled land-surface schemes (ILSSs) limits the drawing of strong conclusions but, despite this, there is shown to be benefit in undertaking this type of isotopic intercomparison. Although validation of isotopic simulations at the land surface must await more, and much more complete, observational campaigns, we find that the empirically-based Craig-Gordon parameterization (of isotopic fractionation during evaporation) gives adequately realistic isotopic simulations when incorporated in a wide range of land-surface codes. By introducing two new tools for understanding isotopic variability from the land surface, the Isotope Transfer Function and the iPILPS plot, we show that different hydrological parameterizations cause very different isotopic responses. We show that ILSS-simulated isotopic equilibrium is independent of the total water and energy budget (with respect to both equilibration time and state), but interestingly the partitioning of available energy and water is a function of the models' complexity.
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Energy Technology Data Exchange (ETDEWEB)
Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
A chaos detectable and time step-size adaptive numerical scheme for nonlinear dynamical systems
Chen, Yung-Wei; Liu, Chein-Shan; Chang, Jiang-Ren
2007-02-01
The first step in investigation the dynamics of a continuous time system described by ordinary differential equations is to integrate them to obtain trajectories. In this paper, we convert the group-preserving scheme (GPS) developed by Liu [International Journal of Non-Linear Mechanics 36 (2001) 1047-1068] to a time step-size adaptive scheme, x=x+hf(x,t), where x∈R is the system variables we are concerned with, and f(x,t)∈R is a time-varying vector field. The scheme has the form similar to the Euler scheme, x=x+Δtf(x,t), but our step-size h is adaptive automatically. Very interestingly, the ratio h/Δt, which we call the adaptive factor, can forecast the appearance of chaos if the considered dynamical system becomes chaotical. The numerical examples of the Duffing equation, the Lorenz equation and the Rossler equation, which may exhibit chaotic behaviors under certain parameters values, are used to demonstrate these phenomena. Two other non-chaotic examples are included to compare the performance of the GPS and the adaptive one.
An efficient numerical progressive diagonalization scheme for the quantum Rabi model revisited
International Nuclear Information System (INIS)
Pan, Feng; Bao, Lina; Dai, Lianrong; Draayer, Jerry P
2017-01-01
An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model. (paper)
Global communication schemes for the numerical solution of high-dimensional PDEs
DEFF Research Database (Denmark)
Hupp, Philipp; Heene, Mario; Jacob, Riko
2016-01-01
The numerical treatment of high-dimensional partial differential equations is among the most compute-hungry problems and in urgent need for current and future high-performance computing (HPC) systems. It is thus also facing the grand challenges of exascale computing such as the requirement...... to reduce global communication. To cope with high dimensionalities we employ a hierarchical discretization scheme, the sparse grid combination technique. Based on an extrapolation scheme, the combination technique additionally mitigates the need for global communication: multiple and much smaller problems...... with the experiments. The model can be used to predict the runtime of the reduce/broadcast step for dimensionalities that are yet out of scope on current supercomputers....
International Nuclear Information System (INIS)
Kiefer, B; Bartel, T; Menzel, A
2012-01-01
Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases. (paper)
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
Directory of Open Access Journals (Sweden)
Hakon A. Hoel
2007-07-01
Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case
Fernández-Nieto, Enrique D.; Gallardo, José M.; Vigneaux, Paul
2018-01-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such schemes in 2D as the follow up of the companion paper treating the 1D case. Numerical tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham-Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix-Mont-Blanc to show the usability of these schemes on real topographies from digital elevation models (DEM).
Numerical Optimization of an Organic Rankine Cycle Scheme for Co-generation
Potenza, Marco; Naccarato, Fabrizio; Stigliano, Gianbattista; Risi, Arturo de
2016-01-01
The aim of the present work was the optimization of a small size Organic Rankine Cycle (ORC) system powered by a linear Parabolic Trough Collector (PTC) solar field by means of numerical model code developed on purpose. In the proposed scheme the solar energy is collected by a newly designed low cost PTC of 20m2 with a single tracking axis and it is concentrated on an opaque pipe collector in which flows as thermal fluid the Therminol® 66 oil. An oil-free scroll expander coupled with a 2 kW e...
Response of multiferroic composites inferred from a fast-Fourier-transform-based numerical scheme
International Nuclear Information System (INIS)
Brenner, Renald; Bravo-Castillero, Julián
2010-01-01
The effective response and the local fields within periodic magneto-electric multiferroic composites are investigated by means of a numerical scheme based on fast Fourier transforms. This computational framework relies on the iterative resolution of coupled series expansions for the magnetic, electric and strain fields. By using an augmented Lagrangian formulation, a simple and robust procedure which makes use of the uncoupled Green operators for the elastic, electrostatics and magnetostatics problems is proposed. Its accuracy is assessed in the cases of laminated and fibrous two-phase composites for which analytical solutions exist
Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.
2018-01-01
Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.
Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications
Elkhalil, Khalil
2017-07-31
This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.
Numerical solution of the 1D kinetics equations using a cubic reduced nodal scheme
International Nuclear Information System (INIS)
Gomez T, A.M.; Valle G, E. del; Delfin L, A.; Alonso V, G.
2003-01-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as Θ scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows
Energy Technology Data Exchange (ETDEWEB)
Johnson, B M; Guan, X; Gammie, F
2008-04-11
In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the timestep is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves {del} {center_dot} B = 0 to machine precision. The main restriction is that B must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.
Numerical Investigation of the Influence of Injection Scheme on the Ethylene Supersonic Combustion
Directory of Open Access Journals (Sweden)
Hao Ouyang
2014-02-01
Full Text Available Ethylene supersonic combustion flow field in different injection schemes was studied numerically in the flight Mach 4. The results show that injection pressure has significant influence on the location of the separation zone and the heat release region, but the starting point of the separation region was mostly influenced by the heat release rather than by the injection pressure; the combustion efficiency of the injection schemes including two injection points is higher than that of three injection points, while the total pressure recovery coefficient of the former injection schemes is lower than the latter; excessive ethylene injected in upstream will lead to the change of free-stream flow conditions, which behaves as the inlet unstart in practical application; more ethylene could be injected in downstream to avoid the problem; on the condition of avoiding thermal choke in isolator, it is more advantageous that injection points were arranged more closely to the starting point of separation zone in upside and to the front of the cavity in downside.
A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics
Energy Technology Data Exchange (ETDEWEB)
Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo; Teatini, Pietro
2016-06-01
The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.
Numerical scheme of WAHA code for simulation of fast transients in piping systems
International Nuclear Information System (INIS)
Iztok Tiselj
2005-01-01
Full text of publication follows: A research project of the 5. EU program entitled 'Two-phase flow water hammer transients and induced loads on materials and structures of nuclear power plants' (WAHA loads) has been initiated in Fall 2000 and ended in Spring 2004. Numerical scheme used in WAHA code is responsibility of 'Jozef Stefan Institute and is briefly described in the present work. Mathematical model is based on a 6-equation two-fluid model for inhomogeneous non-equilibrium two-phase flow, which can be written in vectorial form as: A δΨ-vector/δt + B δΨ-vector/δx = S-vector. Hyperbolicity of the equations is a prerequisite and is ensured with virtual mass term and interfacial pressure term, however, equations are not unconditionally hyperbolic. Flow-regime map used in WAHA code consists of dispersed, and horizontally stratified flow correlations. The closure laws describe interface heat and mass transfer (condensation model, flashing...), the inter-phase friction, and wall friction. For the modeling of water hammer additional terms due to the pipe elasticity are considered. For the calculation of the thermodynamic state a new set of water properties subroutines was created. Numerical scheme of the WAHA code is based on Godunov characteristic upwind methods. Advanced numerical methods based on high-resolution shock-capturing schemes, which were originally developed for high-speed gas dynamics are used. These schemes produce solutions with a substantially reduced numerical diffusion and allow the accurate modeling of flow discontinuities. Code is using non-conservative variables Ψ-vector = (p, α, ν f , ν g , u f , u g ), however, according to current experience, the non-conservation is not a major problem for the fast transients like water hammers. The following operator splitting is used in the code: 1) Convection and non-relaxation source terms: A δΨ-vector/δt + B δΨ-vector/δx S-vector non relaxation 2) Relaxation (inter-phase exchange) source
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
The novel stable control scheme of the light source power in the closed-loop fiber optic gyroscope
Energy Technology Data Exchange (ETDEWEB)
Ji Zhongxiao [Graduate University of the Chinese Academy of Sciences, Beijing (China); Ma Caiwen, E-mail: jzx@opt.ac.cn [Xi' an Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences, NO.17 Xinxi Road, New Industrial Park, Xi' an Hi-Tech Industrial Development Zone, Xi' an, Shaanxi (China)
2011-02-01
The light source power stability of the Fiber-Optic Gyroscope (FOG) affects directly the scale factor and bias stability of FOG. The typical control scheme of the light source power employs an additional photodetector to detect the output power of the light source. When the fiber loss of FOG varied due to the temperature change, the light power in the additional photodetector did not indicate this change, which decreased the control effect. The spike pulse overlapping on the gyro signal denotes potentially the change of the light power and fiber loss. In the novel scheme, the spike pulse is extracted from the gyro signal, and is transformed into the square wave by the differential circuit. According to the change of the square wave amplitude, FOG adjusts the bias current of the light source to keep the stable light power in the signal photodetector. It is a simple and low-cost scheme without an additional photodetector.
International Nuclear Information System (INIS)
Abgrall, Remi; Mezine, Mohamed
2004-01-01
After having recalled the basic concepts of residual distribution (RD) schemes, we provide a systematic construction of distribution schemes able to handle general unstructured meshes, extending the work of Sidilkover. Then, by using the concept of simple waves, we show how to generalize this technique to symmetrizable linear systems. A stability analysis is provided. We formally extend this construction to the Euler equations. Several test cases are presented to validate our approach
Zhu, Guangpu
2018-01-26
In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation with the generalized Navier boundary condition. Variable densities and viscosities are incorporated in this model. A rigorous proof of energy stability is provided for the fully discrete scheme based on a semi-implicit temporal discretization and a finite difference method on the staggered grids for the spatial discretization. A splitting method based on the pressure stabilization is implemented to solve the Navier-Stokes equation, while the stabilization approach is also used for the Cahn-Hilliard equation. Numerical results in both 2-D and 3-D demonstrate the accuracy, efficiency and decaying property of discrete energy of the proposed scheme.
On numerical schemes for solving the Euler equations of gas dynamics
Dervieux, A.; Vijayasundaram, G.
The first-order upwind schemes of Godunov-Van Leer, Steger-Warming, Godunov, Roe, Osher and Glimm; Godunov type scheme I; the second-order upwind schemes of Van Leer, Fromm-Van Leer, Hancock-Van Leer, and Moretti; and the second-order centered schemes of Richtmyer, Mac Cormack, Lerat-Peyrat, and Jameson are described. Their performances for the shock-tube problem proposed by Sod are compared. The schemes of Godunov-Van Leer, Glimm, Fromm-Van Leer, and Hancock-Van Leer produced the best results. All the First-order upwind schemes, the Glimm scheme, the Jameson scheme, and the Hancock-Van Leer scheme can be extended to two dimensions in the finite element setting.
International Nuclear Information System (INIS)
Angstmann, C.N.; Donnelly, I.C.; Henry, B.I.; Jacobs, B.A.; Langlands, T.A.M.; Nichols, J.A.
2016-01-01
We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.
Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad
2017-07-01
This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.
Mukkavilli, S. K.; Kay, M. J.; Taylor, R.; Prasad, A. A.; Troccoli, A.
2014-12-01
The Australian Solar Energy Forecasting System (ASEFS) project requires forecasting timeframes which range from nowcasting to long-term forecasts (minutes to two years). As concentrating solar power (CSP) plant operators are one of the key stakeholders in the national energy market, research and development enhancements for direct normal irradiance (DNI) forecasts is a major subtask. This project involves comparing different radiative scheme codes to improve day ahead DNI forecasts on the national supercomputing infrastructure running mesoscale simulations on NOAA's Weather Research & Forecast (WRF) model. ASEFS also requires aerosol data fusion for improving accurate representation of spatio-temporally variable atmospheric aerosols to reduce DNI bias error in clear sky conditions over southern Queensland & New South Wales where solar power is vulnerable to uncertainities from frequent aerosol radiative events such as bush fires and desert dust. Initial results from thirteen years of Bureau of Meteorology's (BOM) deseasonalised DNI and MODIS NASA-Terra aerosol optical depth (AOD) anomalies demonstrated strong negative correlations in north and southeast Australia along with strong variability in AOD (~0.03-0.05). Radiative transfer schemes, DNI and AOD anomaly correlations will be discussed for the population and transmission grid centric regions where current and planned CSP plants dispatch electricity to capture peak prices in the market. Aerosol and solar irradiance datasets include satellite and ground based assimilations from the national BOM, regional aerosol researchers and agencies. The presentation will provide an overview of this ASEFS project task on WRF and results to date. The overall goal of this ASEFS subtask is to develop a hybrid numerical weather prediction (NWP) and statistical/machine learning multi-model ensemble strategy that meets future operational requirements of CSP plant operators.
International Nuclear Information System (INIS)
Brocks, W.; Krafka, H.; Mueller, W.; Wobst, K.
1988-01-01
In connection with the problem of the transferability of parameters obtained experimentally with the help of fracture-mechanical test specimens and used for the initiation and the stable propagation of cracks in cases of pulsating stress and of the elasto-plastic behaviour of construction components, a pressure vessel with an inside diameter of 1500 mm, a cylindrical length of 3000 mm and a wall thickness of 40 mm was hydraulically loaded with the help of internal pressure in the first stage, to attain an average crack growth of 1 mm at Δ a ≅, the loading taking place at about 21deg C. This stress-free annealed vessel exhibited an axial semielliptical vibration-induced surface crack about 181 mm long and 20 mm deep, as a test defect, in a welded circular blank made of the steel 20MnMoNi 55. The fractographic analysis of the first stable crack revealed that its growth rate of Δa was highest in the area of transition from the weak to the strong bend of the crack front (55deg m /σ v (average principal stress: σ m , Mises' reference stress: σ v v). A comparison of the experimental with the numerical results from the first stable crack shows that the local stable crack growth Δa cannot be calculated solely with reference to J, because Δa appears to depend essentially on the quotient σ m /σ v . (orig./MM) [de
Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier
2014-05-01
Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the numerical solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit scheme, and the friction contribution to the dynamics is treated with a suited numerical scheme [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by
Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars
2018-02-01
The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration
Directory of Open Access Journals (Sweden)
T. Rößler
2018-02-01
Full Text Available The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge–Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge–Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The
Han, Lanshan; Camlibel, M. Kanat; Pang, Jong-Shi; Heemels, W. P. Maurice H.
2012-01-01
This paper presents a numerical scheme for solving the continuous-time convex linear-quadratic (LQ) optimal control problem with mixed polyhedral state and control constraints. Unifying a discretization of this optimal control problem as often employed in model predictive control and that obtained
A stable numerical inversion of Abel's integral equation using almost Bernstein operational matrix
International Nuclear Information System (INIS)
Singh, Om P.; Singh, Vineet K.; Pandey, Rajesh K.
2010-01-01
Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel's type integral equation. The aim of this communication is to modify the stable algorithm proposed in [Singh VK, Pandey RK, Singh OP. New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials. Applied Mathematical Sciences 2009;3(5):241-255] which is based on normalized Bernstein polynomial approximation of the projected intensity profile. So, first we construct an orthonormal family {b i5 } i=0 5 of polynomials of degree 5 from the 5th degree Bernstein polynomials B i5 and use them as a basis to approximate the projected intensity profile. Then, a 6x6 matrix P, named as almost Bernstein operational matrix of integration is constructed and used to reduce the integral equation to a system of algebraic equation which can be solved easily. The method is quite accurate and stable even though the approximations are performed by polynomials of degree 5, as illustrated by applying the method to intensity data with and without random noise to invert and compare it with those obtained by the other methods or with the known analytical inverse. Thus it is good method for applying to experimental intensities distorted by noise.
Ellmer, Matthias; Mayer-Gürr, Torsten
2016-04-01
Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability. When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer. Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy. We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.
Sjoegreen, Bjoern; Yee, H. C.
2003-01-01
The generalization of a class of low-dissipative high order filter finite difference schemes for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been developed. The new scheme consists of a divergence free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta * B) numerical error in the sense that no standard divergence cleaning is required. Performance evaluation of these variants, and the key role that the proper treatment of their corresponding numerical boundary conditions can play will be illustrated. Many levels of grid refinement and detailed comparison with several commonly used compressible MHD shock-capturing schemes will be sought. For certain MHD 2-D test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.
Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa
2015-11-01
We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the course of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well.
Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models
Directory of Open Access Journals (Sweden)
Leo G. Rebholz
2009-01-01
Full Text Available We present enhanced physics-based finite element schemes for two families of turbulence models, the NS- models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007, that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.
A hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments.
Shamim, M. A.; Bray, M.; Ishak, A. M.; Remesan, R.; Han, D.
2009-09-01
The importance of solar radiation on earth's surface is depicted in its wide range of applications in the fields of meteorology, agricultural sciences, engineering, hydrology, crop water requirements, climatic changes and energy assessment. It is quite random in nature as it has to go through different processes of assimilation and dispersion while on its way to earth. Compared to other meteorological parameters, solar radiation is quite infrequently measured, for example, the worldwide ratio of stations collecting solar radiation to those collecting temperature is 1:500 (Badescu, 2008). Researchers, therefore, have to rely on indirect techniques of estimation that include nonlinear models, artificial intelligence (e.g. neural networks), remote sensing and numerical weather predictions (NWP). This study proposes a hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments. It uses the PSU/NCAR's Mesoscale Modelling system (MM5) (Grell et al., 1995) to parameterise the cloud effect on extraterrestrial radiation by dividing the atmosphere into four layers of very high (6-12 km), high (3-6 km), medium (1.5-3) and low (0-1.5) altitudes from earth. It is believed that various cloud forms exist within each of these layers. An hourly time series of upper air pressure and relative humidity data sets corresponding to all of these layers is determined for the Brue catchment, southwest UK, using MM5. Cloud Index (CI) was then determined using (Yang and Koike, 2002): 1 p?bi [ (Rh - Rh )] ci =------- max 0.0,---------cri dp pbi - ptipti (1- Rhcri) where, pbi and pti represent the air pressure at the top and bottom of each layer and Rhcri is the critical value of relative humidity at which a certain cloud type is formed. Output from a global clear sky solar radiation model (MRM v-5) (Kambezidis and Psiloglu, 2008) is used along with meteorological datasets of temperature and precipitation and astronomical information. The analysis is aided by the
Directory of Open Access Journals (Sweden)
Bingke Yan
2015-11-01
Full Text Available With a higher penetration of distributed generation in the power system, the application of microgrids is expected to increase dramatically in the future. This paper proposes a novel method to design optimal droop coefficients of dispatchable distributed energy resources for a microgrid in the Energy Internet considering the volatility of renewable energy generation, such as wind and photovoltaics. The uncertainties of renewable energy generation are modeled by a limited number of scenarios with high probabilities. In order to achieve stable and economical operation of a microgrid that is also suitable for plug-and-play distributed renewable energy and distributed energy storage devices, a multi-objective optimization model of droop coefficients compromising between operational cost and the integral of time-weighted absolute error criterion is developed. The optimization is solved by using a differential evolution algorithm. Case studies demonstrate that the economy and transient behavior of microgrids in the Energy Internet can both be improved significantly using the proposed method.
Husic, A.; Fox, J.; Ford, W. I., III; Agouridis, C.; Currens, J. C.; Taylor, C. J.
2017-12-01
Sediment tracing tools provide an insight into provenance, fate, and transport of sediment and, when coupled to stable isotopes, can elucidate in-stream biogeochemical processes. Particulate nitrogen fate in fluviokarst systems is a relatively unexplored area of research partially due to the complex hydrodynamics at play in karst systems. Karst topography includes turbulent conduits that transport groundwater and contaminants at speeds more typical of open channel flows than laminar Darcian flows. While it is accepted that karst hydro-geomorphology represents a hybrid surface-subsurface system for fluid, further investigation is needed to determine whether, and to what extent, karst systems behave like surface agricultural streams or porous media aquifers with respect to their role in nitrogen cycling. Our objective is to gain an understanding of in-conduit nitrogen processes and their effect on net nitrogen-exports from karst springs to larger waterbodies. The authors apply water, sediment, carbon, and nitrogen tracing techniques to analyze water for nitrate, sediment carbon and nitrogen, and stable sediment nitrogen isotope (δ15N). Thereafter, a new numerical model is formulated that: simulates dissolved inorganic nitrogen and sediment nitrogen transformations in the phreatic karst conduit; couples carbon turnover and nitrogen transformations in the model structure; and simulates the nitrogen stable isotope mass balance for the dissolved and sediment phases. Nitrogen tracing data results show a significant increase in δ15N of sediment nitrogen at the spring outlet relative to karst inputs indicating the potential for isotope fractionation during dissolved N uptake by bed sediments in the conduit and during denitrification within bed sediments. The new numerical modeling structure is then used to reproduce the data results and provide an estimate of the relative dominance of N uptake and denitrification within the surficial sediments of the karst conduit system
Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites
Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.
2018-04-01
Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.
Johnson, M. T.
2010-10-01
The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest). Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone), such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases), but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility) are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.
Directory of Open Access Journals (Sweden)
M. T. Johnson
2010-10-01
Full Text Available The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest. Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone, such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases, but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
Entropy conservative finite element schemes
Tadmor, E.
1986-01-01
The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.
Numerical Simulations of Reacting Flows Using Asynchrony-Tolerant Schemes for Exascale Computing
Cleary, Emmet; Konduri, Aditya; Chen, Jacqueline
2017-11-01
Communication and data synchronization between processing elements (PEs) are likely to pose a major challenge in scalability of solvers at the exascale. Recently developed asynchrony-tolerant (AT) finite difference schemes address this issue by relaxing communication and synchronization between PEs at a mathematical level while preserving accuracy, resulting in improved scalability. The performance of these schemes has been validated for simple linear and nonlinear homogeneous PDEs. However, many problems of practical interest are governed by highly nonlinear PDEs with source terms, whose solution may be sensitive to perturbations caused by communication asynchrony. The current work applies the AT schemes to combustion problems with chemical source terms, yielding a stiff system of PDEs with nonlinear source terms highly sensitive to temperature. Examples shown will use single-step and multi-step CH4 mechanisms for 1D premixed and nonpremixed flames. Error analysis will be discussed both in physical and spectral space. Results show that additional errors introduced by the AT schemes are negligible and the schemes preserve their accuracy. We acknowledge funding from the DOE Computational Science Graduate Fellowship administered by the Krell Institute.
A numerical scheme for the two phase Mullins-Sekerka problem
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Peter W. Bates
1995-08-01
Full Text Available problem arising in the theory of phase transition. The problem is one in which a collection of simple closed curves (particles evolves in such a way that the enclosed area remains constant while the total arclength decreases. Material is transported between particles and within particles by diffusion, driven by curvature which expresses the effect of surface tension. The algorithm is based on a reformulation of the problem, using boundary integrals, which is then discretized and cast as a semi-implicit scheme. This scheme is implemented with a variety of configurations of initial curves showing that convexity or even topological type may not be preserved.
El-Amin, Mohamed
2012-06-02
The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.
Development of a moisture scheme for the explicit numerical simulation of moist convection
CSIR Research Space (South Africa)
Bopape, Mary-Jane M
2010-09-01
Full Text Available . The aim of this study is to add a moisture scheme to the NSM. As a first step a simple model that is equivalent to the first pressure-coordinate nonhydrostatic model used to simulate cumulonimbus clouds in 1974 is developed. The equation set that includes...
Symbolic-numeric stability investigations of Jameson's scheme for this-layer Navier-Stokes equations
Ganzha, V.G.; Vorozhtsov, E.V.; Boers, J.; van Hulzen, J.A.; van Hulzen, J.A.
1994-01-01
The Navier-Stokes equations governing the three-dimensional flows of viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes
Energy Technology Data Exchange (ETDEWEB)
Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu
2017-02-01
The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.
Numerical and experimental investigation on static electric charge model at stable cone-jet region
Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.
2018-03-01
In a typical electro-spinning process, the steady stretching process of the jet beyond the Taylor cone has a significant effect on the dimensions of resulting nanofibers. Also, it sets up the conditions for the onset of the bending instability. The focus of this work is the modeling and simulation of the initial stable jet phase seen during the electro-spinning process. The perturbation method was applied to solve hydrodynamic equations, and the electrostatic equation was solved by a boundary integral method. These equations were coupled with the stress boundary conditions derived appropriate at the fluid-fluid interface. Perturbation equations were discretized by the second-order finite difference method, and the Newton method was implemented to solve the discretized nonlinear system. Also, the boundary element method was utilized to solve the electrostatic equation. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface in dielectric air. In this study, electric charges were modeled as static. Comparison of numerical and experimental results shows that at low flow rates and high electric field, good agreement was achieved because of the superior importance of the charge transport by conduction rather than convection and charge concentration. In addition, the effect of unevenness of the electric field around the nozzle tip was experimentally studied through plate-plate geometry as well as point-plate geometry.
Implementation of a gust front head collapse scheme in the WRF numerical model
Lompar, Miloš; Ćurić, Mladjen; Romanic, Djordje
2018-05-01
Gust fronts are thunderstorm-related phenomena usually associated with severe winds which are of great importance in theoretical meteorology, weather forecasting, cloud dynamics and precipitation, and wind engineering. An important feature of gust fronts demonstrated through both theoretical and observational studies is the periodic collapse and rebuild of the gust front head. This cyclic behavior of gust fronts results in periodic forcing of vertical velocity ahead of the parent thunderstorm, which consequently influences the storm dynamics and microphysics. This paper introduces the first gust front pulsation parameterization scheme in the WRF-ARW model (Weather Research and Forecasting-Advanced Research WRF). The influence of this new scheme on model performances is tested through investigation of the characteristics of an idealized supercell cumulonimbus cloud, as well as studying a real case of thunderstorms above the United Arab Emirates. In the ideal case, WRF with the gust front scheme produced more precipitation and showed different time evolution of mixing ratios of cloud water and rain, whereas the mixing ratios of ice and graupel are almost unchanged when compared to the default WRF run without the parameterization of gust front pulsation. The included parameterization did not disturb the general characteristics of thunderstorm cloud, such as the location of updraft and downdrafts, and the overall shape of the cloud. New cloud cells in front of the parent thunderstorm are also evident in both ideal and real cases due to the included forcing of vertical velocity caused by the periodic collapse of the gust front head. Despite some differences between the two WRF simulations and satellite observations, the inclusion of the gust front parameterization scheme produced more cumuliform clouds and seem to match better with real observations. Both WRF simulations gave poor results when it comes to matching the maximum composite radar reflectivity from radar
Difference schemes for numerical solutions of lagging models of heat conduction
Cabrera Sánchez, Jesús; Castro López, María Ángeles; Rodríguez Mateo, Francisco; Martín Alustiza, José Antonio
2013-01-01
Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the...
Energy Technology Data Exchange (ETDEWEB)
Assous, F.; Degond, P.; Segre, J. [CEA Limeil, 94 - Villeneuve-Saint-Georges (France); Degond, P. [MIP, UFR MIG, UPS, 31 - Toulouse (France)
1997-10-01
The aim of this paper is to present a new explicit time scheme for electromagnetic particle simulations. The main property of this new scheme, which depends on a parameter, is to reduce and in some cases to suppress numerical instabilities that can appear in this context, and are widely described in the literature. Other numerical properties are also investigated, and a numerical example is finally given to illustrate our purpose. This scheme is expected to be useful in the field of plasma modelling. (authors) 16 refs.
International Nuclear Information System (INIS)
Li, R.
2012-01-01
The aim of this research dissertation is at studying natural and mixed convections of fluid flows, and to develop and validate numerical schemes for interface tracking in order to treat incompressible and immiscible fluid flows, later. In a first step, an original numerical method, based on Finite Volume discretizations, is developed for modeling low Mach number flows with large temperature gaps. Three physical applications on air flowing through vertical heated parallel plates were investigated. We showed that the optimum spacing corresponding to the peak heat flux transferred from an array of isothermal parallel plates cooled by mixed convection is smaller than those for natural or forced convections when the pressure drop at the outlet keeps constant. We also proved that mixed convection flows resulting from an imposed flow rate may exhibit unexpected physical solutions; alternative model based on prescribed total pressure at inlet and fixed pressure at outlet sections gives more realistic results. For channels heated by heat flux on one wall only, surface radiation tends to suppress the onset of re-circulations at the outlet and to unify the walls temperature. In a second step, the mathematical model coupling the incompressible Navier-Stokes equations and the Level-Set method for interface tracking is derived. Improvements in fluid volume conservation by using high order discretization (ENO-WENO) schemes for the transport equation and variants of the signed distance equation are discussed. (author)
Directory of Open Access Journals (Sweden)
Saulo Frietas
2012-01-01
Full Text Available An advection scheme, which maintains the initial monotonic characteristics of a tracer field being transported and at the same time produces low numerical diffusion, is implemented in the Coupled Chemistry-Aerosol-Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CCATT-BRAMS. Several comparisons of transport modeling using the new and original (non-monotonic CCATT-BRAMS formulations are performed. Idealized 2-D non-divergent or divergent and stationary or time-dependent wind fields are used to transport sharply localized tracer distributions, as well as to verify if an existent correlation of the mass mixing ratios of two interrelated tracers is kept during the transport simulation. Further comparisons are performed using realistic 3-D wind fields. We then perform full simulations of real cases using data assimilation and complete atmospheric physics. In these simulations, we address the impacts of both advection schemes on the transport of biomass burning emissions and the formation of secondary species from non-linear chemical reactions of precursors. The results show that the new scheme produces much more realistic transport patterns, without generating spurious oscillations and under- and overshoots or spreading mass away from the local peaks. Increasing the numerical diffusion in the original scheme in order to remove the spurious oscillations and maintain the monotonicity of the transported field causes excessive smoothing in the tracer distribution, reducing the local gradients and maximum values and unrealistically spreading mass away from the local peaks. As a result, huge differences (hundreds of % for relatively inert tracers (like carbon monoxide are found in the smoke plume cores. In terms of the secondary chemical species formed by non-linear reactions (like ozone, we found differences of up to 50% in our simulations.
A high-order solver for aerodynamic flow simulations and comparison of different numerical schemes
Mikhaylov, Sergey; Morozov, Alexander; Podaruev, Vladimir; Troshin, Alexey
2017-11-01
An implementation of high order of accuracy Discontinuous Galerkin method is presented. Reconstruction is done for the conservative variables. Gradients are calculated using the BR2 method. Coordinate transformations are done by serendipity elements. In computations with schemes of order higher than 2, curvature of the mesh lines is taken into account. A comparison with finite volume methods is performed, including WENO method with linear weights and single quadrature point on a cell side. The results of the following classical tests are presented: subsonic flow around a circular cylinder in an ideal gas, convection of two-dimensional isentropic vortex, and decay of the Taylor-Green vortex.
Numerical Investigation of a Novel Wiring Scheme Enabling Simple and Accurate Impedance Cytometry
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Federica Caselli
2017-09-01
Full Text Available Microfluidic impedance cytometry is a label-free approach for high-throughput analysis of particles and cells. It is based on the characterization of the dielectric properties of single particles as they flow through a microchannel with integrated electrodes. However, the measured signal depends not only on the intrinsic particle properties, but also on the particle trajectory through the measuring region, thus challenging the resolution and accuracy of the technique. In this work we show via simulation that this issue can be overcome without resorting to particle focusing, by means of a straightforward modification of the wiring scheme for the most typical and widely used microfluidic impedance chip.
Dawid, H.; Keoula, M.Y.; Kort, Peter
2017-01-01
This paper presents a numerical method for the characterization of Markov-perfect equilibria of symmetric differential games exhibiting coexisting stable steady states. The method relying on the calculation of ‘local value functions’ through collocation in overlapping parts of the state space, is
Keslerová, Radka; Trdlička, David
2015-09-01
This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.
European Workshop on High Order Nonlinear Numerical Schemes for Evolutionary PDEs
Beaugendre, Héloïse; Congedo, Pietro; Dobrzynski, Cécile; Perrier, Vincent; Ricchiuto, Mario
2014-01-01
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Directory of Open Access Journals (Sweden)
B. Kafash
2014-04-01
Full Text Available In this paper, we present a computational method for solving optimal control problems and the controlled Duffing oscillator. This method is based on state parametrization. In fact, the state variable is approximated by Boubaker polynomials with unknown coefficients. The equation of motion, performance index and boundary conditions are converted into some algebraic equations. Thus, an optimal control problem converts to a optimization problem, which can then be solved easily. By this method, the numerical value of the performance index is obtained. Also, the control and state variables can be approximated as functions of time. Convergence of the algorithms is proved. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.
Burke, Jan
2010-08-01
Phase-shifting Fizeau interferometry on spherical surfaces is impaired by phase-shift errors increasing with the numerical aperture, unless a custom optical set-up or wavelength shifting is used. This poses a problem especially for larger numerical apertures, and requires good error tolerance of the phase-shift method used; but it also constitutes a useful testing facility for phase-shift formulae, because a vast range of phase-shift intervals can be tested in a single measurement. In this paper I show how the "characteristic polynomials" method can be used to generate a phase-shifting method for the actual numerical aperture, and analyse residual cyclical phase errors by comparing a phase map from an interferogram with a few fringes to a phase mpa from a nulled fringe. Unrelated to the phase-shift miscalibration, thirdharmonic error fringes are found. These can be dealt with by changing the nominal phase shift from 90°/step to 60°/step and re-tailoring the evaluation formula for third-harmonic rejection. The residual error has the same frequency as the phase-shift signal itself, and can be removed by averaging measurements. Some interesting features of the characteristic polynomials for the averaged formulae emerge, which also shed some light on the mechanism that generates cyclical phase errors.
Development of Non-staggered, SMAC numerical scheme for a two-fluid model
International Nuclear Information System (INIS)
Yoon, H. Y.; Jeong, Jae Jun
2007-06-01
The SMAC(Simplified Marker And Cell) method, along with the SIMPLE, has long been used efficiently for the computational fluid dynamics. Usually, the majority of the applications are single phase compressible or incompressible fluids, and the numerical methods are to be modified to implement the following items for the analysis of two-phase flows. - Non-staggered grid for the analysis of a complex geometry - Application of the two-phase models - Coupling of the energy conservation equations - Two-phase flows with phase change. In this report, the SMAC Method is reviewed and extended to compressible two-phase flows with phase change. A pilot code CUPID-M is developed using the proposed numerical method. A set of verification calculations are carried out for th CUPID-M. At first, isothermal air-water flow is simulated to verify the numerical method against two-phase flow flow problems. Next, the two-phase flows with phase change are calculated using CUPID-M and the results are compared to that of CUPID-I, which is based on the coupled ICE method. The calculation time is shorter with CUPID-M than with CUPID-I, while the calculations are unstable with CUPID-M for the rapid phase change problems. Thus, CUPID-M and CUPID-I can be used as an user input considering the application problems
Energy Technology Data Exchange (ETDEWEB)
Lode, Axel U.J.
2013-06-03
This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one- and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.
Johnson, M. T.
2010-02-01
The transfer velocity determines the rate of exchange of a gas across the air-water interface for a given deviation from Henry's law equilibrium between the two phases. In the thin film model of gas exchange, which is commonly used for calculating gas exchange rates from measured concentrations of trace gases in the atmosphere and ocean/freshwaters, the overall transfer is controlled by diffusion-mediated films on either side of the air-water interface. Calculating the total transfer velocity (i.e. including the influence from both molecular layers) requires the Henry's law constant and the Schmidt number of the gas in question, the latter being the ratio of the viscosity of the medium and the molecular diffusivity of the gas in the medium. All of these properties are both temperature and (on the water side) salinity dependent and extensive calculation is required to estimate these properties where not otherwise available. The aim of this work is to standardize the application of the thin film approach to flux calculation from measured and modelled data, to improve comparability, and to provide a numerical framework into which future parameter improvements can be integrated. A detailed numerical scheme is presented for the calculation of the gas and liquid phase transfer velocities (ka and kw respectively) and the total transfer velocity, K. The scheme requires only basic physical chemistry data for any gas of interest and calculates K over the full range of temperatures, salinities and wind-speeds observed in and over the ocean. Improved relationships for the wind-speed dependence of ka and for the salinity-dependence of the gas solubility (Henry's law) are derived. Comparison with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general but significant improvements under certain conditions. The scheme is provided as a downloadable program in the supplementary material, along with input files containing molecular
Li, Fu; Zhang, Jun-Xiang; Zhu, Shi-Yao
2015-06-01
Recently, the direct counterfactual communication protocol, proposed by Salih et al (2013 Phys. Rev. Lett. 110 170502) using a single photon source under ideal conditions (no dissipation, no phase fluctuation and an infinite number of beam splitters), has attracted much interest from a broad range of scientists. In order to put the direct communication protocol into a realistic framework, we numerically simulate the effect of the dissipation and the phase fluctuation with a finite number of beam splitters. Our calculation shows that the dissipation and phase fluctuation will dramatically decrease the reliability and the efficiency of communication, and even corrupt the communication. To counteract the negative effect of dissipation, we propose the balanced dissipation method, which substantially improves the reliability of the protocol at the expense of decreasing communication efficiency. Meanwhile, our theoretical derivation shows that the reliability and efficiency of communication are independent of the input state: a single photon state or a coherent state.
International Nuclear Information System (INIS)
Li, Fu; Zhu, Shi-Yao; Zhang, Jun-Xiang
2015-01-01
Recently, the direct counterfactual communication protocol, proposed by Salih et al (2013 Phys. Rev. Lett. 110 170502) using a single photon source under ideal conditions (no dissipation, no phase fluctuation and an infinite number of beam splitters), has attracted much interest from a broad range of scientists. In order to put the direct communication protocol into a realistic framework, we numerically simulate the effect of the dissipation and the phase fluctuation with a finite number of beam splitters. Our calculation shows that the dissipation and phase fluctuation will dramatically decrease the reliability and the efficiency of communication, and even corrupt the communication. To counteract the negative effect of dissipation, we propose the balanced dissipation method, which substantially improves the reliability of the protocol at the expense of decreasing communication efficiency. Meanwhile, our theoretical derivation shows that the reliability and efficiency of communication are independent of the input state: a single photon state or a coherent state. (paper)
Toivanen, Elias A; Losilla, Sergio A; Sundholm, Dage
2015-12-21
Algorithms and working expressions for a grid-based fast multipole method (GB-FMM) have been developed and implemented. The computational domain is divided into cubic subdomains, organized in a hierarchical tree. The contribution to the electrostatic interaction energies from pairs of neighboring subdomains is computed using numerical integration, whereas the contributions from further apart subdomains are obtained using multipole expansions. The multipole moments of the subdomains are obtained by numerical integration. Linear scaling is achieved by translating and summing the multipoles according to the tree structure, such that each subdomain interacts with a number of subdomains that are almost independent of the size of the system. To compute electrostatic interaction energies of neighboring subdomains, we employ an algorithm which performs efficiently on general purpose graphics processing units (GPGPU). Calculations using one CPU for the FMM part and 20 GPGPUs consisting of tens of thousands of execution threads for the numerical integration algorithm show the scalability and parallel performance of the scheme. For calculations on systems consisting of Gaussian functions (α = 1) distributed as fullerenes from C20 to C720, the total computation time and relative accuracy (ppb) are independent of the system size.
Probabilistic Simulation of Subsurface Fluid Flow: A Study Using a Numerical Scheme
Energy Technology Data Exchange (ETDEWEB)
Buscheck, Timothy Eric [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Earth Sciences Division; Univ. of California, Berkeley, CA (United States)
1980-03-01
There has been an increasing interest in probabilistic modeling of hydrogeologic systems. The classical approach to groundwater modeling has been deterministic in nature, where individual layers and formations are assumed to be uniformly homogeneous. Even in the case of complex heterogeneous systems, the heterogeneities describe the differences in parameter values between various layers, but not within any individual layer. In a deterministic model a single-number is assigned to each hydrogeologic parameter, given a particular scale of interest. However, physically there is no such entity as a truly uniform and homogeneous unit. Single-number representations or deterministic predictions are subject to uncertainties. The approach used in this work models such uncertainties with probabilistic parameters. The resulting statistical distributions of output variables are analyzed. A numerical algorithm, based on axiomatic principles of probability theory, performs arithmetic operations between probability distributions. Two subroutines are developed from the algorithm and incorporated into the computer program TERZAGI, which solves groundwater flow problems in saturated, multi-dimensional systems. The probabilistic computer program is given the name, PROGRES. The algorithm has been applied to study the following problems: one-dimensional flow through homogeneous media, steady-state and transient flow conditions, one-dimensional flow through heterogeneous media, steady-state and transient flow conditions, and two-dimensional steady-state flow through heterogeneous media. The results are compared with those available in the literature.
International Nuclear Information System (INIS)
Guertin, Chantal
1995-01-01
This thesis is part of the validation process of using coupled 3D neutronics and thermal-hydraulics codes for studying accidental situations with boiling. First part is dedicated to a numerical stability analysis of neutronics and thermal-hydraulics coupled schemes. Both explicit and semi-implicit coupling schemes were applied to solve the set of equations describing the linearized neutronics and thermal-hydraulics of point reactor. Point reactor modelling was preferred to obtain analytical expressions of eigenvalues of the discretized Systems. Stability criteria, based on eigenvalues, was calculated as well as neutronic and thermalhydraulic responses of the System following insertion of a reactivity step. Results show no severe restriction of time domain, stability wise. Actual transient calculations using coupled neutronics and thermal-hydraulics codes, like COCCINELLE and THYC developed at Electricite de France, do not show stability problems. Second part introduces surface spline as a new neutronic feedback model. The cross influences of feedback parameters is now taken into account. Moderator temperature and density were modeled. This method, simple and accurate, allows an homogeneous description of cross-sections overall operating reactor situations including accidents with boiling. (author) [fr
Hybrid Semi-numerical Simulation Scheme to Predict Transducer Outputs of Acoustic Microscopes.
Nierla, Michael; Rupitsch, Stefan
2015-12-18
We present a semi-numerical simulation method called SIRFEM, which enables the efficient prediction of high frequency transducer outputs. In particular, this is important for acoustic microscopy where the specimen under investigation is immersed in a coupling fluid. Conventional Finite Element (FE) simulations for such applications would consume too much computational power due to the required spatial and temporal discretization, especially for the coupling fluid between ultrasonic transducer and specimen. However, FE simulations are in most cases essential to consider the mode conversion at and inside the solid specimen as well as the wave propagation in its interior. SIRFEM reduces the computational effort of pure FE simulations by treating only the solid specimen and a small part of the fluid layer with FE. The propagation in the coupling fluid from transducer to specimen and back is processed by the so-called spatial impulse response (SIR). Through this hybrid approach, the number of elements as well as the number of time steps for the FE simulation can be reduced significantly, as it is presented for an axis-symmetric setup. Three B-mode images of a plane 2-D setup - computed at a transducer center frequency of 20 MHz - show that SIRFEM is, furthermore, able to predict reflections at inner structures as well as multiple reflections between those structures and the specimen's surface. For the purpose of a pure 2-D setup, the spatial impulse response of a curved-line transducer is derived and compared to the response function of a cylindrically focused aperture of negligible extend in the third spatial dimension.
International Nuclear Information System (INIS)
Li Li; Zhang Xinlu; Chen Lixue
2008-01-01
In this paper, we predict and numerically demonstrate the intrinsic intensity bistability, spectra bistability and chromatic switching of visible-infrared emission in Tm 3+ single-doped systems that are pumped by the photon avalanche scheme at 648 nm. Based on the coupled rate equation theory, the evolutions of the populations at various Tm 3+ energy levels, emission spectra and fluorescence intensity versus pump excitation are numerically investigated in detail. The results show that intrinsic optical bistability (IOB) associated with emission spectra and luminescence intensity takes place in the vicinity of the avalanche threshold (∼10 kW cm -2 ). When the pump excitation rises above the switching threshold (∼17.5 kW cm -2 ), the chromatic switching between the infrared (1716 nm) and the visible blue (452/469 nm) spectra can be performed. Moreover, the influences of system parameters on IOB and the origin of chromatic switching are discussed. These unique characteristics of Tm 3+ -doped systems would lead to the new possibility of the development of pump-controlled all-solid-state luminescence switches and optical bistability switches.
Fumagalli, Ivan; Parolini, Nicola; Verani, Marco
2018-02-01
We analyze a free-surface problem described by time-dependent Navier-Stokes equations. Surface tension, capillary effects and wall friction are taken into account in the evolution of the system, influencing the motion of the contact line - where the free surface hits the wall - and of the dynamics of the contact angle. The differential equations governing the phenomenon are first derived from the variational principle of minimum reduced dissipation, and then discretized by means of the ALE approach. The numerical properties of the resulting scheme are investigated, drawing a parallel with the physical properties holding at the continuous level. Some instability issues are addressed in detail, in the case of an explicit treatment of the geometry, and novel additional terms are introduced in the discrete formulation in order to damp the instabilities. Numerical tests assess the suitability of the approach, the influence of the parameters, and the effectiveness of the new stabilizing terms.
Stable unitary integrators for the numerical implementation of continuous unitary transformations
Savitz, Samuel; Refael, Gil
2017-09-01
The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the "uniform tangent decay flow" and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.
International Nuclear Information System (INIS)
Guenther, C.
1988-08-01
This report describes numerical tests with various difference schemes to solve the convection-diffusion equation. Starting point of this investigation has been a scheme proposed by the author, the so-called 'LECUSSO-scheme', which is of order O(Δx 2 ) and avoids unphysical spatial oscillations meaning that this scheme does not suffer from any mesh-Reynolds-number-restriction. To test this scheme a previously described example introduced by Beier et al. with known analytical solution was adoptd and numerically solved using a variety of difference schemes. This is done for a wide range of Reynolds-numbers (20 ≤ Re' ≤ 5000) and equidistant meshes of different size, the comparison being done with respect to the space-dependent error and to the maximum spatial error of the numerical solution. The results of the numerical tests may be summarized as follows: Flows with boundary layers, as the most interesting case are very favourably calculated using upwind methods of second or higher order in conservation form with respect to the absolute value of the maximum spatial error. The amount of this error is near 1/3 of the error obtained with standard schemes unless these schemes not yet produced obsolete results since a mesh-Reynolds-number condition had been violated. As to the increased amount of work (additional 5th point, two different additional types of modified difference approximations with fewer points near the boundary), LSUDS-C (in conservation form) is not better than LECUSSO-C and QUICK-PLUS. The reduced errors of the upwind methods of higher order enable us to proceed to the numerical calculation of flows with higher Reynolds-numbers than before. (orig./GL [de
Numerical study of aircraft wake vortex evolution near ground in stable atmospheric boundary layer
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Mengda LIN
2017-12-01
Full Text Available The evolutions of aircraft wake vortices near ground in stable atmospheric boundary layer are studied by Large Eddy Simulation (LES. The sensitivity of vortex evolution to the Monin-Obukhov (M-O scale is studied for the first time. The results indicate that increasing stability leads to longer lifetimes of upwind vortices, while downwind vortices will decay faster due to a stronger crosswind shear under stable conditions. Based on these results, an empirical model of the vortex lifetime as a function of 10-m-high crosswind and the M-O scale is summarized. This model can provide an estimate of the upper boundary of the vortex lifetime according to the real-time crosswind and atmospheric stability. In addition, the lateral translation of vortices is also inspected. The results show that vortices can travel a furthest distance of 722 m in the currently-studied parameter range. This result is meaningful to safety analysis of airports that have parallel runways. Keywords: Aerodynamics, Aircraft, Aircraft wake vortex, Large eddy simulation, Stable atmosphere boundary layer
Cao, Renfeng; Pope, Stephen B.
2003-02-01
In this paper, a weak second-order accurate mid-point scheme for the stochastic differential equations (SDEs) arising in the composition PDF method for turbulent reactive flows is proposed and tested. The results are compared with two other schemes which are commonly used in the composition PDF method. In contrast to most higher-order schemes for SDEs, the present scheme uses a mid-point, which makes it especially suitable for the implementation of the position-advance fractional step in the composition PDF method. The scheme can also be applied to the PDF method used in conjunction with large eddy simulation (LES), since the SDEs considered in this paper include explicit time dependence of the drift and diffusion coefficients. Test calculations are reported, including a 2D unsteady case, to demonstrate the weak second-order accuracy of the scheme and to compare its performance to that of two first-order schemes. A new methodology for developing higher-order scheme for SDEs (by comparing the moments of the increments of the numerical approximation with those of the exact increments) is used to develop this scheme.
Directory of Open Access Journals (Sweden)
Shun Takahashi
2014-01-01
Full Text Available A computational code adopting immersed boundary methods for compressible gas-particle multiphase turbulent flows is developed and validated through two-dimensional numerical experiments. The turbulent flow region is modeled by a second-order pseudo skew-symmetric form with minimum dissipation, while the monotone upstream-centered scheme for conservation laws (MUSCL scheme is employed in the shock region. The present scheme is applied to the flow around a two-dimensional cylinder under various freestream Mach numbers. Compared with the original MUSCL scheme, the minimum dissipation enabled by the pseudo skew-symmetric form significantly improves the resolution of the vortex generated in the wake while retaining the shock capturing ability. In addition, the resulting aerodynamic force is significantly improved. Also, the present scheme is successfully applied to moving two-cylinder problems.
Sayed, Sadeed Bin
2015-05-05
A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.
Directory of Open Access Journals (Sweden)
Yandy G. Mayor
2015-01-01
Full Text Available This paper evaluates the sensitivity to cumulus and microphysics schemes, as represented in numerical simulations of the Weather Research and Forecasting model, in characterizing a deep convection event over the Cuban island on 1 May 2012. To this end, 30 experiments combining five cumulus and six microphysics schemes, in addition to two experiments in which the cumulus parameterization was turned off, are tested in order to choose the combination that represents the event precipitation more accurately. ERA Interim is used as lateral boundary condition data for the downscaling procedure. Results show that convective schemes are more important than microphysics schemes for determining the precipitation areas within a high-resolution domain simulation. Also, while one cumulus scheme captures the overall spatial convective structure of the event more accurately than others, it fails to capture the precipitation intensity. This apparent discrepancy leads to sensitivity related to the verification method used to rank the scheme combinations. This sensitivity is also observed in a comparison between parameterized and explicit cumulus formation when the Kain-Fritsch scheme was used. A loss of added value is also found when the Grell-Freitas cumulus scheme was activated at 1 km grid spacing.
Two Conservative Difference Schemes for Rosenau-Kawahara Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2014-01-01
Full Text Available Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.
International Nuclear Information System (INIS)
Georges, Gabriel
2016-01-01
High Energy Density Physics (HEDP) flows are multi-material flows characterized by strong shock waves and large changes in the domain shape due to rare faction waves. Numerical schemes based on the Lagrangian formalism are good candidates to model this kind of flows since the computational grid follows the fluid motion. This provides accurate results around the shocks as well as a natural tracking of multi-material interfaces and free-surfaces. In particular, cell-centered Finite Volume Lagrangian schemes such as GLACE (Godunov-type Lagrangian scheme Conservative for total Energy) and EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian Hydrodynamics) provide good results on both the modeling of gas dynamics and elastic-plastic equations. The work produced during this PhD thesis is in continuity with the work of Maire and Nkonga [JCP, 2009] for the hydrodynamic part and the work of Kluth and Despres [JCP, 2010] for the hyper elasticity part. More precisely, the aim of this thesis is to develop robust and accurate methods for the 3D extension of the EUCCLHYD scheme with a second-order extension based on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) and GRP (Generalized Riemann Problem) procedures. A particular care is taken on the preservation of symmetries and the monotonicity of the solutions. The scheme robustness and accuracy are assessed on numerous Lagrangian test cases for which the 3D extensions are very challenging. (author) [fr
Umgiesser, Georg; Razinkovas-Baziukas, Arturas; Barisevičiūtė, Ruta; Baziukė, Dalia; Ertürk, Ali; Gasiūnaitė, Jovita; Gulbinskas, Saulius; Lubienė, Irma; Maračkinaite, Jurgita; Petkuvienė, Jolita; Pilkaitytė, Renata; Ruginis, Tomas; Zemlys, Petras; Žilius, Mindaugas
2013-04-01
The spatial pattern of the hydrodynamic circulation of the Curonian lagoon, the largest European coastal lagoon, is still little understood. In absence of automatic current registration data all the existing models relied mostly on such data as water levels leaving high level of uncertainty. Here we present CISOCUR, a new project financed by the European Social Fund under the Global Grant measure. The project applies a new methodology that uses the carbon stable isotope (SI) ratio of C12 and C13 that characterize different water sources entering the lagoon and may be altered by internal kinetic processes. Through the tracing of these isotope ratios different water masses can be identified. This gives the possibility to validate several hypotheses of water circulation and validate hydrodynamic models. In particular it will be possible to 1) trace water masses entering the lagoon through the Nemunas and the Klaipeda strait; 2) test the hypothesis of sediment transport mechanisms inside the lagoon; 3) evaluate the importance of physical forcing on the lagoon circulation. The use of a hydrodynamic finite element model, coupled with the SI method, will allow for a realistic description of the transport processes inside the Curonian lagoon. So the main research goal is to apply the stable isotope tracers and a finite element model to determine the circulation patterns in the Curonian lagoon. Overall, the project will develop according to 4 main phases: 1) A pilot study to measure the isotope composition of different carbon compounds (dissolved and suspended) in different water bodies that feed water into the central lagoon. Through this pilot study the optimal study sites for the seasonal campaign will be identified as well. 2) Seasonal field campaigns in the monitoring stations identified in phase 1 to measure the carbon isotope ratio. 3) Development of a model that describes the kinetics of carbon isotopes and its transformation. 4) Application of a hydrodynamic model
Numerically stable fluid–structure interactions between compressible flow and solid structures
Grétarsson, Jón Tómas
2011-04-01
We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tn+1 using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluid-structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of [16]. Because our method handles the fluid-structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid-structure interactions are not considered) at the fluid-structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions. © 2011 Elsevier Inc.
DEFF Research Database (Denmark)
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland
2014-01-01
the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly...... an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D...... in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems...
Cody, Alison J; Bray, James E; Jolley, Keith A; McCarthy, Noel D; Maiden, Martin C J
2017-07-01
Human campylobacteriosis, caused by Campylobacter jejuni and C. coli , remains a leading cause of bacterial gastroenteritis in many countries, but the epidemiology of campylobacteriosis outbreaks remains poorly defined, largely due to limitations in the resolution and comparability of isolate characterization methods. Whole-genome sequencing (WGS) data enable the improvement of sequence-based typing approaches, such as multilocus sequence typing (MLST), by substantially increasing the number of loci examined. A core genome MLST (cgMLST) scheme defines a comprehensive set of those loci present in most members of a bacterial group, balancing very high resolution with comparability across the diversity of the group. Here we propose a set of 1,343 loci as a human campylobacteriosis cgMLST scheme (v1.0), the allelic profiles of which can be assigned to core genome sequence types. The 1,343 loci chosen were a subset of the 1,643 loci identified in the reannotation of the genome sequence of C. jejuni isolate NCTC 11168, chosen as being present in >95% of draft genomes of 2,472 representative United Kingdom campylobacteriosis isolates, comprising 2,207 (89.3%) C. jejuni isolates and 265 (10.7%) C. coli isolates. Validation of the cgMLST scheme was undertaken with 1,478 further high-quality draft genomes, containing 150 or fewer contiguous sequences, from disease isolate collections: 99.5% of these isolates contained ≥95% of the 1,343 cgMLST loci. In addition to the rapid and effective high-resolution analysis of large numbers of diverse isolates, the cgMLST scheme enabled the efficient identification of very closely related isolates from a well-defined single-source campylobacteriosis outbreak. Copyright © 2017 Cody et al.
Nogherotto, Rita; Tompkins, Adrian Mark; Giuliani, Graziano; Coppola, Erika; Giorgi, Filippo
2016-07-01
We implement and evaluate a new parameterization scheme for stratiform cloud microphysics and precipitation within regional climate model RegCM4. This new parameterization is based on a multiple-phase one-moment cloud microphysics scheme built upon the implicit numerical framework recently developed and implemented in the ECMWF operational forecasting model. The parameterization solves five prognostic equations for water vapour, cloud liquid water, rain, cloud ice, and snow mixing ratios. Compared to the pre-existing scheme, it allows a proper treatment of mixed-phase clouds and a more physically realistic representation of cloud microphysics and precipitation. Various fields from a 10-year long integration of RegCM4 run in tropical band mode with the new scheme are compared with their counterparts using the previous cloud scheme and are evaluated against satellite observations. In addition, an assessment using the Cloud Feedback Model Intercomparison Project (CFMIP) Observational Simulator Package (COSP) for a 1-year sub-period provides additional information for evaluating the cloud optical properties against satellite data. The new microphysics parameterization yields an improved simulation of cloud fields, and in particular it removes the overestimation of upper level cloud characteristics of the previous scheme, increasing the agreement with observations and leading to an amelioration of a long-standing problem in the RegCM system. The vertical cloud profile produced by the new scheme leads to a considerably improvement of the representation of the longwave and shortwave components of the cloud radiative forcing.
Energy Technology Data Exchange (ETDEWEB)
López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es
2017-03-15
Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.
Directory of Open Access Journals (Sweden)
A. Benmouna
2013-01-01
Full Text Available Research efforts to improve our understanding of electronic polymers are developing fast because of their promising advantages over silicon in photovoltaic solar cells. A major challenge in the development of polymer photovoltaic devices is the viable fabrication strategies of stable bulk heterojunction architecture that will retain functionality during the expected lifetime of the device. Block copolymer self-assembly strategies have attracted particular attention as a scalable means toward thermodynamically stable microstructures that combine the ideal geometrical characteristics of a bulk heterojunction with the fortuitous combination of properties of the constituent blocks. Two primary routes that have been proposed in the literature involve the coassembly of block copolymers in which one domain is a hole conductor with the electron-conducting filler (such as fullerene derivatives or the self-assembly of block copolymers in which the respective blocks function as hole and electron conductor. Either way has proven difficult because of the combination of synthetic challenges as well as the missing understanding of the complex governing parameters that control structure formation in semiconducting block copolymer blends. This paper summarizes important findings relating to structure formation of block copolymer and block copolymer/nanoparticle blend assembly that should provide a foundation for the future design of block copolymer-based photovoltaic systems.
Sarkadi, N.; Geresdi, I.; Thompson, G.
2016-11-01
In this study, results of bulk and bin microphysical schemes are compared in the case of idealized simulations of pre-frontal orographic clouds with enhanced embedded convection. The description graupel formation by intensive riming of snowflakes was improved compared to prior versions of each scheme. Two methods of graupel melting coincident with collisions with water drops were considered: (1) all simulated melting and collected water drops increase the amount of melted water on the surface of graupel particles with no shedding permitted; (2) also no shedding permitted due to melting, but the collision with the water drops can induce shedding from the surface of the graupel particles. The results of the numerical experiments show: (i) The bin schemes generate graupel particles more efficiently by riming than the bulk scheme does; the intense riming of snowflakes was the most dominant process for the graupel formation. (ii) The collision-induced shedding significantly affects the evolution of the size distribution of graupel particles and water drops below the melting level. (iii) The three microphysical schemes gave similar values for the domain integrated surface precipitation, but the patterns reveal meaningful differences. (iv) Sensitivity tests using the bulk scheme show that the depth of the melting layer is sensitive to the description of the terminal velocity of the melting snow. (v) Comparisons against Convair-580 flight measurements suggest that the bin schemes simulate well the evolution of the pristine ice particles and liquid drops, while some inaccuracy can occur in the description of snowflakes riming. (vi) The bin scheme with collision-induced shedding reproduced well the quantitative characteristics of the observed bright band.
Energy Technology Data Exchange (ETDEWEB)
Pebay, Philippe [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Terriberry, Timothy B. [Xiph.Org Foundation, Arlington, VA (United States); Kolla, Hemanth [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Bennett, Janine [Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
2016-03-29
Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Formulas such as these, are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.
Cissé, Aïta Sarr; Dossou, Nicole; Ndiaye, Mamadou; Guèye, Amadou Lamine; Diop, El Hadji Issakha; Diaham, Babou; Guiro, Amadou Tidiane; Cissé, Djibril; Sarr, Cheikh Saad Bouh; Wade, Salimata
2002-09-01
The supplementation program of the community nutrition project (PNC) launched by the Senegalese Government in order to protect the most vulnerable groups (children and women) was evaluated. Using a stable isotope (deuterium), we assessed the effect of the PNC on breastmilk output, mother's body composition, and baby's growth at three months of lactation. Breastmilk triglycerides, lactose, protein, and zinc were also determined. Mothers who were supplemented more than 60 days during pregnancy showed a significant increase in fat-free mass as compared to those who were supplemented for less than 30 days (p = .03). Breastmilk output was not influenced by the supplementation, but breastmilk lactose, total protein, and zinc contents increased significantly (p supplemented mothers. Growth of the babies of the supplemented mothers was better than that of those whose mothers were not supplemented. It was concluded that the food supplementation had beneficial effects on both mothers' and babies' nutritional status depending on the onset of the supplementation.
Zhu, Jun; Shu, Chi-Wang
2017-11-01
A new class of high order weighted essentially non-oscillatory (WENO) schemes (Zhu and Qiu, 2016, [50]) is applied to solve Euler equations with steady state solutions. It is known that the classical WENO schemes (Jiang and Shu, 1996, [23]) might suffer from slight post-shock oscillations. Even though such post-shock oscillations are small enough in magnitude and do not visually affect the essentially non-oscillatory property, they are truly responsible for the residue to hang at a truncation error level instead of converging to machine zero. With the application of this new class of WENO schemes, such slight post-shock oscillations are essentially removed and the residue can settle down to machine zero in steady state simulations. This new class of WENO schemes uses a convex combination of a quartic polynomial with two linear polynomials on unequal size spatial stencils in one dimension and is extended to two dimensions in a dimension-by-dimension fashion. By doing so, such WENO schemes use the same information as the classical WENO schemes in Jiang and Shu (1996) [23] and yield the same formal order of accuracy in smooth regions, yet they could converge to steady state solutions with very tiny residue close to machine zero for our extensive list of test problems including shocks, contact discontinuities, rarefaction waves or their interactions, and with these complex waves passing through the boundaries of the computational domain.
Additive operator-difference schemes splitting schemes
Vabishchevich, Petr N
2013-01-01
Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy
International Nuclear Information System (INIS)
Sarr Cisse, Aita; Dossou, Nicole; Ndiaye, Mamadou
2002-01-01
The supplementation program of the community nutrition project (PNC) launched by the Senegalese Government in order to protect the most vulnerable groups (children and women) was evaluated. Using a stable isotope (deuterium), we assessed the effect of the PNC on breastmilk output, mother's body composition, and baby's growth at three months of lactation. Breastmilk triglycerides, lactose, protein, and zinc were also determined. Mothers who were supplemented more than 60 days during pregnancy showed a significant increase in fot- free mass as compared to those who were supplemented for less than 30 days (p= .03). Breastmilk output was not influenced by the supplementation, but breastmilk lactose, total protein, and zinc contents increased significantly (p < .01) in the supplemented mothers. Growth of the babies of the supplemented mothers was better than that of those whose mothers were not supplemented. It was concluded that the food supplementation had beneficial effects on both mothers' and babies' nutritional status depending on the onset of the supplementation.
International Nuclear Information System (INIS)
Xing, Changhu; Folsom, Charles; Jensen, Colby; Ban, Heng; Marshall, Douglas W
2014-01-01
As an important factor affecting the accuracy of thermal conductivity measurement, systematic (bias) error in the guarded comparative axial heat flow (cut-bar) method was mostly neglected by previous researches. This bias is primarily due to the thermal conductivity mismatch between sample and meter bars (reference), which is common for a sample of unknown thermal conductivity. A correction scheme, based on finite element simulation of the measurement system, was proposed to reduce the magnitude of the overall measurement uncertainty. This scheme was experimentally validated by applying corrections on four types of sample measurements in which the specimen thermal conductivity is much smaller, slightly smaller, equal and much larger than that of the meter bar. As an alternative to the optimum guarding technique proposed before, the correction scheme can be used to minimize the uncertainty contribution from the measurement system with non-optimal guarding conditions. It is especially necessary for large thermal conductivity mismatches between sample and meter bars. (paper)
International Nuclear Information System (INIS)
Wei, Xiao
2016-01-01
An experimental program has been designed in order to study pollutants dispersion at a complex site with a focus on stable conditions, which are still challenging for numerical modelling. This experimental program is being conducted at the SIRTA site in a southern suburb of Paris and consists in measuring, in near field, the turbulence and the pollutants dispersion. The aim of this program is to characterize the fine structure of turbulence and associated dispersion through high temporal and spatial resolution measurements. Then, these measurements allow to validate and improve the performance of CFD simulation for turbulence and dispersion in a heterogeneous field. The instrumental set up includes 12 ultrasonic anemometers measuring continuously wind velocity and temperature at 10 Hz, and 6 photo-ionization detectors (PIDs) measuring gas concentration at 50 Hz during tracer tests. Intensive observations periods (IOPs) with gas releases have been performed since March 2012.First of all, a detailed study of flow on the site is made, because it must be characterised and properly simulated before attempting to simulate the pollutants dispersion. This study is based on two years of continuous measurements and on measurements performed during IOPs. Turbulence strong anisotropy in the surface layer is characterized by calculating variances, integral length scales and power spectra of the three wind velocity components. Propagation of turbulent structures between sensors has been characterized with velocity correlations. Energy spectra show several slopes in different frequency regions. Also, data analyses show impact of terrain heterogeneity on the measurements. The forest to the north of experimental field modifies wind velocity and direction for a large northerly sector. It induces a strong directional wind shear and a wind deceleration below the forest height. Numerical simulations are carried out using the CFD code Code-Saturne in RANS mode with a standard κ
International Nuclear Information System (INIS)
Wei, Xiao
2016-01-01
An experimental program has been designed in order to study pollutants dispersion at a complex site with a focus on stable conditions, which are still challenging for numerical modelling. This experimental program is being conducted at the SIRTA site in a southern suburb of Paris and consists in measuring, in near field, the turbulence and the pollutants dispersion. The aim of this program is to characterize the fine structure of turbulence and associated dispersion through high temporal and spatial resolution measurements. Then, these measurements allow to validate and improve the performance of CFD simulation for turbulence and dispersion in a heterogeneous field. The instrumental set up includes 12 ultrasonic anemometers measuring continuously wind velocity and temperature at 10 Hz, and 6 photo-ionization detectors (PIDs) measuring gas concentration at 50 Hz during tracer tests. Intensive observations periods (IOPs) with gas releases have been performed since March 2012. First of all, a detailed study of flow on the site is made, because it must be characterised and properly simulated before attempting to simulate the pollutants dispersion. This study is based on two years of continuous measurements and on measurements performed during IOPs. Turbulence strong anisotropy in the surface layer is characterized by calculating variances, integral length scales and power spectra of the three wind velocity components. Propagation of turbulent structures between sensors has been characterized with velocity correlations. Energy spectra show several slopes in different frequency regions. Also, data analyses show impact of terrain heterogeneity on the measurements. The forest to the north of the experimental field modifies wind velocity and direction for a large northerly sector. It induces a strong directional wind shear and a wind deceleration below the forest height. Numerical simulations are carried out using the CFD code, Code-Saturne, in RANS mode with a standard k
International Nuclear Information System (INIS)
Zhou, Lei; Luo, Kai Hong; Qin, Wenjin; Jia, Ming; Shuai, Shi Jin
2015-01-01
Highlights: • MUSCL differencing scheme in LES method is used to investigate liquid fuel spray and combustion process. • Using MUSCL can accurately capture the gas phase velocity distribution and liquid spray features. • Detailed chemistry mechanism with a parallel algorithm was used to calculate combustion process. • Increasing oxygen concentration can decrease ignition delay time and flame LOL. - Abstract: The accuracy of large eddy simulation (LES) for turbulent combustion depends on suitably implemented numerical schemes and chemical mechanisms. In the original KIVA3V code, finite difference schemes such as QSOU (Quasi-second-order upwind) and PDC (Partial Donor Cell Differencing) cannot achieve good results or even computational stability when using coarse grids due to large numerical diffusion. In this paper, the MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) differencing scheme is implemented into KIVA3V-LES code to calculate the convective term. In the meantime, Lu’s n-heptane reduced 58-species mechanisms (Lu, 2011) is used to calculate chemistry with a parallel algorithm. Finally, improved models for spray injection are also employed. With these improvements, the KIVA3V-LES code is renamed as KIVALES-CP (Chemistry with Parallel algorithm) in this study. The resulting code was used to study the gas–liquid two phase jet and combustion under various diesel engine-like conditions in a constant volume vessel. The results show that using the MUSCL scheme can accurately capture the spray shape and fuel vapor penetration using even a coarse grid, in comparison with the Sandia experimental data. Similarly good results are obtained for three single-component fuels, i-Octane (C8H18), n-Dodecanese (C12H26), and n-Hexadecane (C16H34) with very different physical properties. Meanwhile the improved methodology is able to accurately predict ignition delay and flame lift-off length (LOL) under different oxygen concentrations from 10% to 21
International Nuclear Information System (INIS)
Alonso-Vargas, G.
1991-01-01
A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)
Ramani, Geetha B.; Siegler, Robert S.
2008-01-01
Theoretical analyses of the development of numerical representations suggest that playing linear number board games should enhance young children's numerical knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased low-income preschoolers' (mean age = 5.4 years) proficiency on 4 diverse numerical tasks: numerical…
J.K. Hoogland (Jiri); C.D.D. Neumann
2000-01-01
textabstractIn this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing
Directory of Open Access Journals (Sweden)
Mohamed Ramadan
2016-06-01
Full Text Available In this paper, a rational Chebyshev collocation method is presented to solve high-order linear Fredholm integro-differential equations with variable coefficients under the mixed conditions in terms of rational Chebyshev functions by two proposed schemes. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the semi–infinite interval, which corresponding to systems of linear algebraic equations with rational Chebyshev coefficients. Thus, by solving the matrix equation, rational Chebyshev coefficients are obtained and hence the approximate solution is expressed in terms of rational Chebyshev functions. Numerical examples are given to illustrate the validity and applicability of the method. The proposed method is numerically compared with others existing methods as well as the exact solutions where it maintains better accuracy.
Shen, Jianguo; Wu, Guiling; Zou, Weiwen; Chen, Ruihao; Chen, Jianping
2013-12-01
We theoretically and experimentally demonstrate a linear and stable photonic RF phase shifter based on a dual-parallel Mach-Zehnder modulator (DPMZM) using a two-drive scheme. To avoid the effect of the residual optical carrier and overcome the lowest frequency limit from the optical filter, a local microwave signal and a signal up-converted from the under-phase-shifted RF signal are applied to the two RF inputs of the DPMZM, respectively. A phase-shifted RF signal is generated by beating the two first-order upper sidebands located in the passband of the optical filter. A continuous and linear phase shift of more than 360° and power variation of less than ±0.15 dB at 1 GHz are achieved by simply tuning the bias voltage of the modulator. A phase tuning bandwidth of more than 17 MHz and phase drift of less than 0.5° within 2000 s are also observed.
A high-order CESE scheme with a new divergence-free method for MHD numerical simulation
Yang, Yun; Feng, Xue-Shang; Jiang, Chao-Wei
2017-11-01
In this paper, we give a high-order space-time conservation element and solution element (CESE) method with a most compact stencil for magneto-hydrodynamics (MHD) equations. This is the first study to extend the second-order CESE scheme to a high order for MHD equations. In the CESE method, the conservative variables and their spatial derivatives are regarded as the independent marching quantities, making the CESE method significantly different from the finite difference method (FDM) and finite volume method (FVM). To utilize the characteristics of the CESE method to the maximum extent possible, our proposed method based on the least-squares method fundamentally keeps the magnetic field divergence-free. The results of some test examples indicate that this new method is very efficient.
Llagostera, Jorge; Figueiredo, José R.
2000-01-01
Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. T...
Directory of Open Access Journals (Sweden)
Buscaglia Gustavo C.
2001-01-01
Full Text Available A new numerical approach is proposed to alleviate the computational cost of solving non-linear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost. The overall efficiency of the numerical methodology makes it feasible to apply rigorous homogenization techniques in the analysis of compressible fluid contact considering roughness effects. Previous work makes use of an heuristic averaging technique. Numerical comparison proves that homogenization-based methods are superior when the roughness is strongly anisotropic and not aligned with the flow direction.
Mihailovic, Dragutin T.; Lazic, Jelena; Leśny, Jacek; Olejnik, Janusz; Lalic, Branislava; Kapor, Darko; Cirisan, Ana
2010-05-01
Numerical simulations and tests with the recently redesigned land-air parameterization scheme (LAPS) are presented. In all experiments, supported either by one-point micrometeorological, 1D or 3D simulations, the attention has been directed to: (1) comparison of simulation outputs, expressing the energy transfer over and through heterogeneous and non-heterogeneous surfaces, versus observations and (2) analysis of uncertainties occurring in the solution of the energy balance equation at the land-air interface. To check the proposed method for aggregation of albedo, "propagating hole" sensitivity tests with LAPS over a sandstone rock grid cell have been performed with the forcing meteorological data for July 17, 1999 in Baxter site, Philadelphia (USA). Micrometeorological and biophysical measurements from the surface experiments conducted over crops and apple orchard in Serbia, Poland, Austria and France were used to test the operation of LAPS in calculating surface fluxes and canopy environment temperatures within and above plant covers of different densities. In addition, sensitivity tests with single canopy covers over the Central Europe region and comparison against the observations taken from SYNOP data using 3D simulations were made. Validation of LAPS performances over a solid surface has been done by comparison of 2 m air temperature observations against 5-day simulations over the Sahara Desert rocky ground using 3D model. To examine how realistically the LAPS simulates surface processes over a heterogeneous surface, we compared the air temperature measured at 2 m and that predicted by the 1D model with the LAPS as the surface scheme. Finally, the scheme behaviour over urban surface was tested by runs over different parts of a hypothetical urban area. The corresponding 1D simulations were carried out with an imposed meteorological dataset collected during HAPEX-MOBILHY experiment at Caumont (France). The quantities predicted by the LAPS compare well with the
An improved numerical scheme with the fully-implicit two-fluid model for a fast-running system code
International Nuclear Information System (INIS)
Jeong, J.J.; No, H.C.
1987-01-01
A new computational method is implemented in the FIDA-2 (Fully-Implicit Safety Analysis-2) code to simulate the thermal-hydraulic response to hypothetical accidents in nuclear power plants. The basis field equations of FISA-2 consist of the mixture continuity equation, void propagation equation, two phasic momentum equations, and two phasic energy equations. The fully-implicit scheme is used to elimate a time step limitation and the computation time per time step is minimized as much as possible by reducing the matrix-size to be solved. The phasic energy equations written in the nonconservation form are solved after they are set up to be decoupled from other field equations. The void propagation equation is solved to obtain the void fraction. Spatial acceleration terms in the phasic momentum equations are manipulated with the phasic continiuity equations so that pseudo-phasic mass flux may be expressed in terms of pressure only. Putting the pseudo-phasic mass flux into the mixture continuity equation, we obtain linear equations with pressure variables only as unknowns. By solving the linear equations, pressures at all the nodes are obtained and in turn other variables are obtained by back-substitution. The above procedure is performed until the convergence criterion is satisfied. Reasonable accuracy and no stability limitation with fast-running are confirmed by comparing results from FISA-2 with experimental data and results from other codes. (orig.)
Kawata, Daisuke; Gibson, Brad K.; Barnes, David J.; Grand, Robert J. J.; Rahimi, Awat
2014-02-01
To study the star formation and feedback mechanism, we simulate the evolution of an isolated dwarf irregular galaxy (dIrr) in a fixed dark matter halo, similar in size to Wolf-Lundmark-Melotte, using a new stellar feedback scheme. We use the new version of our original N-body/smoothed particle chemodynamics code, GCD+, which adopts improved hydrodynamics, metal diffusion between the gas particles and new modelling of star formation and stellar wind and supernovae feedback. Comparing the simulations with and without stellar feedback effects, we demonstrate that the collisions of bubbles produced by strong feedback can induce star formation in a more widely spread area. We also demonstrate that the metallicity in star-forming regions is kept low due to the mixing of the metal-rich bubbles and the metal-poor interstellar medium. Our simulations also suggest that the bubble-induced star formation leads to many counter-rotating stars. The bubble-induced star formation could be a dominant mechanism to maintain star formation in dIrrs, which is different from larger spiral galaxies where the non-axisymmetric structures, such as spiral arms, are a main driver of star formation.
Ciliberti, Stefania Angela; Peneva, Elisaveta; Storto, Andrea; Rostislav, Kandilarov; Lecci, Rita; Yang, Chunxue; Coppini, Giovanni; Masina, Simona; Pinardi, Nadia
2016-04-01
This study describes a new model implementation for the Black Sea, which uses data assimilation, towards operational forecasting, based on NEMO (Nucleus for European Modelling of the Ocean, Madec et al., 2012). The Black Sea domain is resolved with 1/27°×1/36° horizontal resolution (~3 km) and 31 z-levels with partial steps based on the GEBCO bathymetry data (Grayek et al., 2010). The model is forced by momentum, water and heat fluxes interactively computed by bulk formulae using high resolution atmospheric forcing provided by the European Centre for Medium-Range Forecast (ECMWF). The initial condition is calculated from long-term climatological temperature and salinity 3D fields. Precipitation field over the basin has been computed from the climatological GPCP rainfall monthly data (Adler et al., 2003; Huffman et al., 2009), while the evaporation is derived from the latent heat flux. The climatological monthly mean runoff of the major rivers in the Black Sea is computed using the hydrological dataset provided by SESAME project (Ludvig et al., 2009). The exchange with Mediterranean Sea through the Bosporus Straits is represented by a surface boundary condition taking into account the barotropic transport calculated to balance the fresh water fluxes on monthly bases (Stanev and Beckers, 1999, Peneva et al., 2001). A multi-annual run 2011-2015 has been completed in order to describe the main characteristics of the Black Sea circulation dynamics and thermohaline structure and the numerical results have been validated using in-situ (ARGO) and satellite (SST, SLA) data. The Black Sea model represents also the core of the new Black Sea Forecasting System, implemented at CMCC operationally since January 2016, which produces at daily frequency 10-day forecasts, 3-days analyses and 1-day simulation. Once a week, the system is run 15-day in the past in analysis mode to compute the new optimal initial condition for the forecast cycle. The assimilation is performed by a
Ashyralyyeva, Maral; Ashyraliyev, Maksat
2016-08-01
In the present paper, a second order of accuracy difference scheme for the approximate solution of a source identification problem for hyperbolic-parabolic equations is constructed. Theorem on stability estimates for the solution of this difference scheme and their first and second order difference derivatives is presented. In applications, this abstract result permits us to obtain the stability estimates for the solutions of difference schemes for approximate solutions of two source identification problems for hyperbolic-parabolic equations.
Directory of Open Access Journals (Sweden)
V. N. Romaniuk
2016-01-01
Full Text Available Further improvement of natural gas usage in power industry is associated with transition to the combined-cycle gas technology, primarily at combined heat and power plants (CHP. Renovation of technology of conversion of fuel energy into heat and electricity flows is effective while it is performed simultaneously with the elaboration of thermal circuits of CHP by insertion heat accumulators and absorption lithium bromide heat pumps (ALBHP in the structure of CHP; the mentioned insertion amends thermodynamic as well as economic and environmental indicators of CHP renovation and also develops CHP maneuverability. The ability of CHP to provide heat in required quantity, their capacity to change electricity generation output without excessive fuel consumption is extremely relevant for the energy system that incorporates thermal power plants as dominating component. At the same time the displacement of traditional electrical power regulators take place. Implementation of projects of this kind requires the elaboration of CHP flow diagram calculation methods and determining relevant indicators. The results of the numerical study of the energy characteristics of CHP with the aid of the topological models of the existing heat flow diagrams of CHP that incorporate ALBHP for recovery of low-temperature waste of heat flows of systems of cooling water circulating are presented in the article. An example of calculation, the results of the CHP thermodynamic efficiency evaluation, the change of the energy characteristics for different modes of operation of CHP caused by implementation of ALBHP are shown. The conditions for the effective application of lithium bromide absorption heat pumps are specified, as well as the rate of increase of thermodynamic efficiency; the changes of maneuverability of CHP with high initial parameters are identified, the natural gas savings in The Republic of Belarus are determined.
Ida, Masato; Taniguchi, Nobuyuki
2003-09-01
This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.
Calatroni, Luca
2013-08-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli
2016-10-01
The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.
Stamnes, Knut; Tsay, S.-CHEE; Jayaweera, Kolf; Wiscombe, Warren
1988-01-01
The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.
International Nuclear Information System (INIS)
Angelini, O.
2010-01-01
The two-phase flow in porous media is a complex phenomenon and which relate to many industrial problems. EDF works on the feasibility and the safety of a storage in deep geologic layer of nuclear waste. In this domain the simulation of the two-phase flow in porous media is particularly important in at least three domains: first of all during the phase of ventilation of the galleries of the storage which could de-saturate the rock and so modify its properties, but also during the phase of re-saturation of the materials and finally during the arrival of the water on the metal parts contained in the storage which will then involve phenomena of corrosion and a hydrogen release. In this context, EDF wishes to obtain robust numerical methods without restrictive condition on the mesh. This work is dedicated at first to the development of the finite volume scheme SUSHI (Scheme Using Stabilization and Hybrid Interfaces) in the code of mechanics of EDF, Code Aster in order to simulate the two-phase flow in porous media. This scheme was developed in 2D and in 3D. At the same time a new formulation which allows to simulate in a uniform way the flows in saturated and unsaturated porous media for miscible and immiscible problems is proposed. Various studies simulating difficulties related to the problems of the storage of nuclear waste in deep geological layers were study. We can quote the study of a bi-material which advances the capillary re-balancing of a material by an other one possessing properties and initial very heterogeneous conditions in saturation. We will also quote the study of the injection of hydrogen in an porous media initially saturated in pure water which is proposed by the benchmark 'two-phase Flow' proposed by the GNR MOMAS. This study had for objective to bring to light the good treatment of the appearance of a phase in a saturated porous media and thus the relevance of our new formulation to study with a way unified a problem of saturated flow and a
International Nuclear Information System (INIS)
Chen, Jiajie; Ling, Ziye; Fang, Xiaoming; Zhang, Zhengguo
2015-01-01
Highlights: • Form-stable dodecane/fumed silica composite for cold storage is prepared. • A suggesting hypothesis that explains infiltration mechanism is proposed. • The performance of the composite phase change material is investigated. • Numerical simulation of system is carried out and results fit well. - Abstract: A kind of form-stable composite phase change materials used for cold thermal energy storage is prepared by absorbing dodecane into the hydrophobic fumed silica. With relatively suitable pore diameter and hydrophobic groups, hydrophobic fumed silica is beneficial to the penetration and infiltration of dodecane and the leakage problem solving. Scanned by electron micrographs and Fourier transformation infrared, the composite phase change material is characterized to be just physical penetration. Besides, the differential scanning calorimeter and thermo gravimetric analysis reveals the high enthalpy, good thermal stability and cycling performance of this composite phase change material. What’s more, Hot-Disk thermal constants analyzer demonstrates that the composite phase change material has low thermal conductivity which is desired in cold storage application. In the experiment, a cold energy storage system is set up and the results from the experiment show that the system has excellent performance of cold storage by incorporating composite phase change material. Apart from that, the experimental data is found to have a great agreement with the numerical simulation which is carried out by using the commercial computational fluid dynamics software FLUENT.
Senent, Juan
2011-01-01
The first part of the paper presents some closed-form solutions to the optimal two-impulse transfer between fixed position and velocity vectors on Keplerian orbits when some constraints are imposed on the magnitude of the initial and final impulses. Additionally, a numerically-stable gradient-free algorithm with guaranteed convergence is presented for the minimum delta-v two-impulse transfer. In the second part of the paper, cooperative bargaining theory is used to solve some two-impulse transfer problems when the initial and final impulses are carried by different vehicles or when the goal is to minimize the delta-v and the time-of-flight at the same time.
An extended Finite Variable Difference Method with application to QUICK scheme. Optimized QUICK
International Nuclear Information System (INIS)
Sakai, Katsuhiro
1996-01-01
A Finite Variable Difference Method (FVDM) proposed previously by the author for locally exact numerical schemes is extended so as to be applicable to polynomial expansion schemes. This extended FVDM is applied to the QUICK scheme. The optimum differencing points are analytically derived in terms of mesh Reynolds numbers so that the variance of the numerical solution is minimized under the condition that roots of the resulting characteristic equation are nonnegative to insure the numerical stability. This optimized scheme coincides with the original QUICK scheme at Rm=8/3, which is the critical value of its stability, and complements a stable scheme for Rm greater than 8/3. This optimization improves the numerical solution for the steady and unsteady convection-diffusion equations without numerical oscillations. In the same manner as the previous result for the locally exact numerical schemes, it has been made clear based on the extended FVDM that optimum differencing points from the view point of numerical stability and accuracy exist for the polynomial expansion schemes. (author)
National Aeronautics and Space Administration — The code in the stableGP package implements Gaussian process calculations using efficient and numerically stable algorithms. Description of the algorithms is in the...
Relaxation schemes for Chebyshev spectral multigrid methods
Kang, Yimin; Fulton, Scott R.
1993-01-01
Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.
International Nuclear Information System (INIS)
Silva, R.S.; Galeao, A.C.; Carmo, E.G.D. do
1989-07-01
In this paper a new finite element model is constructed combining an r- refinement scheme with the CCAU method. The new formulation gives better approximation for boundary and internal layers compared to the standard CCAU, without increasing computer codes. (author) [pt
Ulku, Huseyin Arda
2012-09-01
An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.
Khan, M O; Steinman, D A; Valen-Sendstad, K
2017-07-01
Computational fluid dynamics (CFD) shows promise for informing treatment planning and rupture risk assessment for intracranial aneurysms. Much attention has been paid to the impact on predicted hemodynamics of various modelling assumptions and uncertainties, including the need for modelling the non-Newtonian, shear-thinning rheology of blood, with equivocal results. Our study clarifies this issue by contextualizing the impact of rheology model against the recently demonstrated impact of CFD solution strategy on the prediction of aneurysm flow instabilities. Three aneurysm cases were considered, spanning a range of stable to unstable flows. Simulations were performed using a high-resolution/accuracy solution strategy with Newtonian and modified-Cross rheology models and compared against results from a so-called normal-resolution strategy. Time-averaged and instantaneous wall shear stress (WSS) distributions, as well as frequency content of flow instabilities and dome-averaged WSS metrics, were minimally affected by the rheology model, whereas numerical solution strategy had a demonstrably more marked impact when the rheology model was fixed. We show that point-wise normalization of non-Newtonian by Newtonian WSS values tended to artificially amplify small differences in WSS of questionable physiological relevance in already-low WSS regions, which might help to explain the disparity of opinions in the aneurysm CFD literature regarding the impact of non-Newtonian rheology. Toward the goal of more patient-specific aneurysm CFD, we conclude that attention seems better spent on solution strategy and other likely "first-order" effects (eg, lumen segmentation and choice of flow rates), as opposed to "second-order" effects such as rheology. Copyright © 2016 John Wiley & Sons, Ltd.
Energy Technology Data Exchange (ETDEWEB)
Zou, Ling [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhao, Haihua [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Hongbin [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists.
A New Inverse Runge–Kutta Scheme for Stiff Ordinary Differential ...
African Journals Online (AJOL)
... of the form y'=f(x,y), a≤x≤b. Its derivation adopts Taylor and binomial series expansion , while it analysis of its stability uses the well known A-stability test model equation. Both theoretical and experimental results show that the scheme is A-stable. Numerical results compared favourably with existing Euler's method.
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Directory of Open Access Journals (Sweden)
Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
Energy Technology Data Exchange (ETDEWEB)
Gomez T, A.M.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico); Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)] e-mail: armagotorres@aol.com
2003-07-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as {theta} scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR ...
African Journals Online (AJOL)
The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give better results than Euler backward method and trapezoidal method near a singular point. KEY WORDS: backward differentiation scheme, collocation, initial value problems.
A predictor-corrector scheme for solving the Volterra integral equation
Al Jarro, Ahmed
2011-08-01
The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.
Unconditionally stable diffusion-acceleration of the transport equation
International Nuclear Information System (INIS)
Larson, E.W.
1982-01-01
The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results
Amezcua, Javier
This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn't represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion
DEFF Research Database (Denmark)
van Leeuwen, Theo
2013-01-01
This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation.......This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation....
Towards the ultimate variance-conserving convection scheme
International Nuclear Information System (INIS)
Os, J.J.A.M. van; Uittenbogaard, R.E.
2004-01-01
In the past various arguments have been used for applying kinetic energy-conserving advection schemes in numerical simulations of incompressible fluid flows. One argument is obeying the programmed dissipation by viscous stresses or by sub-grid stresses in Direct Numerical Simulation and Large Eddy Simulation, see e.g. [Phys. Fluids A 3 (7) (1991) 1766]. Another argument is that, according to e.g. [J. Comput. Phys. 6 (1970) 392; 1 (1966) 119], energy-conserving convection schemes are more stable i.e. by prohibiting a spurious blow-up of volume-integrated energy in a closed volume without external energy sources. In the above-mentioned references it is stated that nonlinear instability is due to spatial truncation rather than to time truncation and therefore these papers are mainly concerned with the spatial integration. In this paper we demonstrate that discretized temporal integration of a spatially variance-conserving convection scheme can induce non-energy conserving solutions. In this paper the conservation of the variance of a scalar property is taken as a simple model for the conservation of kinetic energy. In addition, the derivation and testing of a variance-conserving scheme allows for a clear definition of kinetic energy-conserving advection schemes for solving the Navier-Stokes equations. Consequently, we first derive and test a strictly variance-conserving space-time discretization for the convection term in the convection-diffusion equation. Our starting point is the variance-conserving spatial discretization of the convection operator presented by Piacsek and Williams [J. Comput. Phys. 6 (1970) 392]. In terms of its conservation properties, our variance-conserving scheme is compared to other spatially variance-conserving schemes as well as with the non-variance-conserving schemes applied in our shallow-water solver, see e.g. [Direct and Large-eddy Simulation Workshop IV, ERCOFTAC Series, Kluwer Academic Publishers, 2001, pp. 409-287
Two different methods for numerical solution of the modified Burgers' equation.
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.
Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme
Energy Technology Data Exchange (ETDEWEB)
Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)
A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos
Directory of Open Access Journals (Sweden)
Shiyun Shen
2017-01-01
Full Text Available One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.
On a method of numerical calculation of nonlinear radial pulsations of stars
International Nuclear Information System (INIS)
Kosovichev, A.G.
1984-01-01
Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars
Second-order accurate kinetic schemes for the ultra-relativistic Euler equations
International Nuclear Information System (INIS)
Kunik, Matthias; Qamar, Shamsul; Warnecke, Gerald
2003-01-01
A second-order accurate kinetic scheme for the numerical solution of the relativistic Euler equations is presented. These equations describe the flow of a perfect fluid in terms of the particle density n, the spatial part of the four-velocity u and the pressure p. The kinetic scheme, is based on the well-known fact that the relativistic Euler equations are the moments of the relativistic Boltzmann equation of the kinetic theory of gases when the distribution function is a relativistic Maxwellian. The kinetic scheme consists of two phases, the convection phase (free-flight) and collision phase. The velocity distribution function at the end of the free-flight is the solution of the collisionless transport equation. The collision phase instantaneously relaxes the distribution to the local Maxwellian distribution. The fluid dynamic variables of density, velocity, and internal energy are obtained as moments of the velocity distribution function at the end of the free-flight phase. The scheme presented here is an explicit method and unconditionally stable. The conservation laws of mass, momentum and energy as well as the entropy inequality are everywhere exactly satisfied by the solution of the kinetic scheme. The scheme also satisfies positivity and L 1 -stability. The scheme can be easily made into a total variation diminishing method for the distribution function through a suitable choice of the interpolation strategy. In the numerical case studies the results obtained from the first- and second-order kinetic schemes are compared with the first- and second-order upwind and central schemes. We also calculate the experimental order of convergence and numerical L 1 -stability of the scheme for smooth initial data
Bachir-Bey, Nassim; Matray, Jean-Michel
2014-05-01
This work is part of research conducted by the Institute of Radiological and Nuclear Safety (IRSN) on the geological disposal of High-Level and Intermediate-Level Long-Lived (HL-ILLL) radioactive waste in deep clayrocks. In France, the choice of the potential host rock for the geological storage is focused on the Callovian-Oxfordian (COx) of Meuse/Haute-Marne from its low permeability, capacity for self- sealing, high sorption and ability to radionuclide (RN) transport by diffusion. IRSN, which plays an expert role for ASN has its own underground research laboratory in a clayrock which has strong analogies to the COx. This is the Toarcian/Domerian clayrock located at Tournemire in southern Aveyron in France. The purpose of this study was to assess the transfer of RN in the Tournemire clayrock through the study of halides contents and of their stable isotopes (Cl-, Br-, Cl-/Br-, d37Cl, d81Br). The approach used was multiple and consisted for halides to: 1) Assess their stock in different fractions of the rock by applying several techniques including i) alkaline fusion for their total stock, ii) leaching to access their stock in porewater and to mineral phases sensitive to dissolution iii) cubic diffusion for their stock in porewater, 2) Get their diffusive transport parameters of a selection of samples from the upper Toarcian by cubic diffusion experiments modelled using the Hytec transport code developed by Mines ParisTech and 3) Model their transport after palaeohydrogeological known changes of the Tournemire massif. The experimental approach, conducted at the LAME lab, did not lead to an operational protocol for the alkaline fusion due to an incomplete rock dissolution. Leaching was used to characterize the concentrations of halides in the fractions of pore water and of minerals sensitive to dissolution. The results show levels of halides much higher than those of pore water with very low Cl/Br ratios likely resulting from the dissolution of mineral species. The
Numerical solution of 3D Stokes problems
International Nuclear Information System (INIS)
Zhou, R.Q.N.
1993-01-01
Preconditions conjugate gradient algorithms for solving 3D Stokes problems by stable piecewise discontinuous pressure finite elements are presented. The emphasis is on the preconditioning schemes and their numerical implementation for use with Hermitian-based discontinuous pressure elements. For the piecewise constant discontinuous pressure elements, a variant implementation of the preconditioner proposed by Cahouet and Chabard for the continuous pressure elements is employed. For the piecewise linear discontinuous pressure elements, a new preconditioner is presented. Numerical examples are presented for the cubic lid driven cavity problem with two representative elements (i.e., the Q2-P0 and the Q2-P1 brick elements). Numerical results show that the preconditioning schemes are very effective in reducing the number of pressure iterations at very reasonable costs. It is also shown that they are insensitive to the mesh Reynolds number, except for nearly steady flows (R em → 0), and are almost independent of mesh sizes. It is demonstrated that the schemes performed reasonably well on nonuniform meshes. 15 refs., 6 figs., 1 tab
A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations
Directory of Open Access Journals (Sweden)
Zhuo Su
2013-01-01
Full Text Available Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.
International Nuclear Information System (INIS)
Evans, D.K.
1986-01-01
Seventy-five percent of the world's stable isotope supply comes from one producer, Oak Ridge Nuclear Laboratory (ORNL) in the US. Canadian concern is that foreign needs will be met only after domestic needs, thus creating a shortage of stable isotopes in Canada. This article describes the present situation in Canada (availability and cost) of stable isotopes, the isotope enrichment techniques, and related research programs at Chalk River Nuclear Laboratories (CRNL)
Scheme Program Documentation Tools
DEFF Research Database (Denmark)
Nørmark, Kurt
2004-01-01
This paper describes and discusses two different Scheme documentation tools. The first is SchemeDoc, which is intended for documentation of the interfaces of Scheme libraries (APIs). The second is the Scheme Elucidator, which is for internal documentation of Scheme programs. Although the tools...... as named functions in Scheme. Finally, the Scheme Elucidator is able to integrate SchemeDoc resources as part of an internal documentation resource....
Energy Technology Data Exchange (ETDEWEB)
Franz, A., LLNL
1998-02-17
The numerical simulation of chemically reacting flows is a topic, that has attracted a great deal of current research At the heart of numerical reactive flow simulations are large sets of coupled, nonlinear Partial Differential Equations (PDES). Due to the stiffness that is usually present, explicit time differencing schemes are not used despite their inherent simplicity and efficiency on parallel and vector machines, since these schemes require prohibitively small numerical stepsizes. Implicit time differencing schemes, although possessing good stability characteristics, introduce a great deal of computational overhead necessary to solve the simultaneous algebraic system at each timestep. This thesis examines an algorithm based on a preconditioned time differencing scheme. The algorithm is explicit and permits a large stable time step. An investigation of the algorithm`s accuracy, stability and performance on a parallel architecture is presented
Shishkin, G. I.
2015-11-01
An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2018-02-01
We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.
Performance of Several High Order Numerical Methods for Supersonic Combustion
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
Boson expansion theory in the seniority scheme
International Nuclear Information System (INIS)
Tamura, T.; Li, C.; Pedrocchi, V.G.
1985-01-01
A boson expansion formalism in the seniority scheme is presented and its relation with number-conserving quasiparticle calculations is elucidated. Accuracy and convergence are demonstrated numerically. A comparative discussion with other related approaches is given
Park, Young Choon; Senn, Florian; Krykunov, Mykhaylo; Ziegler, Tom
2016-11-08
In this paper, the relaxed self-consistent field infinite order constricted variational density functional theory (RSCF-CV(∞)-DFT) for triplet calculations is presented. Here, we focus on two main features of our implementation. First, as an extension of our previous work by Krykunov and Ziegler ( J. Chem. Theory Comput. 2013 , 9 , 2761 ), the optimization of the transition matrix representing the orbital transition is implemented and applied for vertical triplet excitations. Second, restricting the transition matrix, we introduce RSCF-CV(∞)-DFT-based numerically stable ΔSCF-DFT-like methods, the most general of them being SVD-RSCF-CV(∞)-DFT. The reliability of the different methods, RSCF-CV(∞)-DFT and its restricted versions, is examined using the benchmark test set of Silva-Junior et al. ( J. Chem. Phys. 2008 , 129 , 104103 ). The obtained excitation energies validate our approach and implementation for RSCF-CV(∞)-DFT and also show that SVD-RSCF-CV(∞)-DFT mimics very well ΔSCF-DFT, as the root-mean-square deviations between these methods are less than 0.1 eV for all functionals examined.
A rational function based scheme for solving advection equation
Energy Technology Data Exchange (ETDEWEB)
Xiao, Feng [Gunma Univ., Kiryu (Japan). Faculty of Engineering; Yabe, Takashi
1995-07-01
A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author).
Numerical performance of the parabolized ADM formulation of general relativity
International Nuclear Information System (INIS)
Paschalidis, Vasileios; Hansen, Jakob; Khokhlov, Alexei
2008-01-01
In a recent paper [Vasileios Paschalidis, Phys. Rev. D 78, 024002 (2008).], the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner (ADM) formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM formulation turns it into a well-posed system which resembles the structure of mixed hyperbolic-second-order parabolic partial differential equations. The surface of constraints of PADM becomes a local attractor for all solutions and all possible well-posed gauge conditions. This paper describes a numerical implementation of PADM and studies its accuracy and stability in a series of standard numerical tests. Numerical properties of PADM are compared with those of standard ADM and its hyperbolic Kidder, Scheel, Teukolsky (KST) extension. The PADM scheme is numerically stable, convergent, and second-order accurate. The new formulation has better control of the constraint-violating modes than ADM and KST.
Electrical Injection Schemes for Nanolasers
DEFF Research Database (Denmark)
Lupi, Alexandra; Chung, Il-Sug; Yvind, Kresten
2014-01-01
Three electrical injection schemes based on recently demonstrated electrically pumped photonic crystal nanolasers have been numerically investigated: 1) a vertical p-i-n junction through a post structure; 2) a lateral p-i-n junction with a homostructure; and 3) a lateral p-i-n junction....... For this analysis, the properties of different schemes, i.e., electrical resistance, threshold voltage, threshold current, and internal efficiency as energy requirements for optical interconnects are compared and the physics behind the differences is discussed....
Generalized finite-difference time-domain schemes for solving nonlinear Schrodinger equations
Moxley, Frederick Ira, III
The nonlinear Schrodinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, higher-order accurate and stable schemes are often required to solve a large-scale linear system. Conversely, spectral methods via Fourier transforms for space discretization coupled with Runge-Kutta methods for time stepping become too complex when applied to multidimensional problems. One of the most prevalent challenges in developing these numerical schemes is that they satisfy the conservation laws. The objective of this dissertation was to develop a higher-order accurate and simple finite difference scheme for solving the NLSE. First, the wave function was split into real and imaginary components and then substituted into the NLSE to obtain coupled equations. These components were then approximated using higher-order Taylor series expansions in time, where the derivatives in time were replaced by the derivatives in space via the coupled equations. Finally, the derivatives in space were approximated using higher-order accurate finite difference approximations. As such, an explicit and higher order accurate finite difference scheme for solving the NLSE was obtained. This scheme is called the explicit generalized finite-difference time-domain (explicit G-FDTD). For purposes of completeness, an implicit G-FDTD scheme for solving the NLSE was also developed. In this
Duru, Kenneth
2014-12-01
© 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.
Electrical injection schemes for nanolasers
DEFF Research Database (Denmark)
Lupi, Alexandra; Chung, Il-Sug; Yvind, Kresten
2013-01-01
injection schemes have been compared: vertical pi- n junction through a current post structure as in1 and lateral p-i-n junction with either uniform material as in2 or with a buried heterostructure (BH) as in3. To allow a direct comparison of the three schemes the same active material composition consisting......The performance of injection schemes among recently demonstrated electrically pumped photonic crystal nanolasers has been investigated numerically. The computation has been carried out at room temperature using a commercial semiconductor simulation software. For the simulations two electrical...... threshold current has been achieved with the lateral electrical injection through the BH; while the lowest resistance has been obtained from the current post structure even though this model shows a higher current threshold because of the lack of carrier confinement. Final scope of the simulations...
Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method
Korkmaz, Bahar; Dereli, Yilmaz
2016-04-01
In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.
Finite volume schemes for Vlasov
Directory of Open Access Journals (Sweden)
Crouseilles Nicolas
2013-01-01
Full Text Available We present finite volume schemes for the numerical approximation of the one-dimensional Vlasov-Poisson equation (FOV CEMRACS 2011 project. Stability analysis is performed for the linear advection and links with semi-Lagrangian schemes are made. Finally, numerical results enable to compare the different methods using classical plasma test cases. Des schémas de type volumes finis sont étudiés ici pour l’approximation de l’équation de Vlasov-Poisson (projet FOV, CEMRACS 2011. Une analyse de stabilité est effectuée dans le cas de l’advection linéaire et plusieurs liens sont faits entre les méthodes volumes finis et semi-Lagrangiennes. Enfin, les méthodes sont comparées sur des cas tests académiques de la physique des plasmas.
A Numerical Solution for Hirota-Satsuma Coupled KdV Equation
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M. S. Ismail
2014-01-01
Full Text Available A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B-splines as test functions and a linear B-spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.
On Optimal Designs of Some Censoring Schemes
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Dr. Adnan Mohammad Awad
2016-03-01
Full Text Available The main objective of this paper is to explore suitability of some entropy-information measures for introducing a new optimality censoring criterion and to apply it to some censoring schemes from some underlying life-time models. In addition, the paper investigates four related issues namely; the effect of the parameter of parent distribution on optimal scheme, equivalence of schemes based on Shannon and Awad sup-entropy measures, the conjecture that the optimal scheme is one stage scheme, and a conjecture by Cramer and Bagh (2011 about Shannon minimum and maximum schemes when parent distribution is reflected power. Guidelines for designing an optimal censoring plane are reported together with theoretical and numerical results and illustrations.
International Nuclear Information System (INIS)
Samios, N.P.
1994-01-01
I have been asked to review the subject of stable particles, essentially the particles that eventually comprised the meson and baryon octets, with a few more additions - with an emphasis on the contributions made by experiments utilizing the bubble chamber technique. In this activity, much work had been done by the photographic emulsion technique and cloud chambers - exposed to cosmic rays as well as accelerator based beams. In fact, many if not most of the stable particles were found by these latter two techniques, however, the foree of the bubble chamber (coupled with the newer and more powerful accelerators) was to verify, and reinforce with large statistics, the existence of these states, to find some of the more difficult ones, mainly neutrals and further to elucidate their properties, i.e., spin, parity, lifetimes, decay parameters, etc. (orig.)
International Nuclear Information System (INIS)
Samios, N.P.
1993-01-01
I have been asked to review the subject of stable particles, essentially the particles that eventually comprised the meson and baryon octets. with a few more additions -- with an emphasis on the contributions made by experiments utilizing the bubble chamber technique. In this activity, much work had been done by the photographic emulsion technique and cloud chambers-exposed to cosmic rays as well as accelerator based beams. In fact, many if not most of the stable particles were found by these latter two techniques, however, the forte of the bubble chamber (coupled with the newer and more powerful accelerators) was to verify, and reinforce with large statistics, the existence of these states, to find some of the more difficult ones, mainly neutrals and further to elucidate their properties, i.e., spin, parity, lifetimes, decay parameters, etc
Multiuser switched diversity scheduling schemes
Shaqfeh, Mohammad
2012-09-01
Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback systems in Rayleigh fading conditions. © 2012 IEEE.
Numerical simulation of Burgers' equation using cubic B-splines
Lakshmi, C.; Awasthi, Ashish
2017-03-01
In this paper, a numerical θ scheme is proposed for solving nonlinear Burgers' equation. By employing Hopf-Cole transformation, the nonlinear Burgers' equation is linearized to the linear Heat equation. The resulting Heat equation is further solved by cubic B-splines. The time discretization of linear Heat equation is carried out using Crank-Nicolson scheme (θ = {1 \\over 2}) as well as backward Euler scheme (θ = 1). Accuracy in temporal direction is improved by using Richardson extrapolation. This method hence possesses fourth order accuracy both in space and time. The system of matrix which arises by using cubic splines is always diagonal. Therefore, working with splines has the advantage of reduced computational cost and easy implementation. Stability of the schemes have been discussed in detail and shown to be unconditionally stable. Three examples have been examined and the L2 and L∞ error norms have been calculated to establish the performance of the method. The numerical results obtained on applying this method have shown to give more accurate results than existing works of Kutluay et al. [1], Ozis et al. [2], Dag et al. [3], Salkuyeh et al. [4] and Korkmaz et al. [5].
Generalization of binary tensor product schemes depends upon four parameters
International Nuclear Information System (INIS)
Bashir, R.; Bari, M.; Mustafa, G.
2018-01-01
This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes. (author)
Generalization of Binary Tensor Product Schemes Depends upon Four Parameters
Directory of Open Access Journals (Sweden)
Robina Bashir
2018-01-01
Full Text Available This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes.
Computational evaluation of convection schemes in fluid dynamics problems
Directory of Open Access Journals (Sweden)
Paulo Laerte Natti
2012-11-01
Full Text Available This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are analyzed and implemented in the context of normalized variables of Leonard. In order to access the performance of the schemes, Riemann problems for 1D Burgers, Euler and shallow water equations are considered. From the numerical results, the schemes are ranked according to their performance in solving these non-linear equations. The best scheme is then applied in the numerical simulation of tridimensional incompressible moving free surface flows.
Directory of Open Access Journals (Sweden)
M. Tudor
2013-07-01
Full Text Available Meteorological numerical weather prediction (NWP models solve a system of partial differential equations in time and space. Semi-lagrangian advection schemes allow for long time steps. These longer time steps can result in instabilities occurring in the model physics. A system of differential equations in which some solution components decay more rapidly than others is stiff. In this case it is stability rather than accuracy that restricts the time step. The vertical diffusion parametrization can cause fast non-meteorological oscillations around the slowly evolving true solution (fibrillations. These are treated with an anti-fibrillation scheme, but small oscillations remain in operational weather forecasts using ARPÉGE and ALADIN models. In this paper, a simple test is designed to reveal if the formulation of particular a physical parametrization is a stiff problem or potentially numerically unstable in combination with any other part of the model. When the test is applied to a stable scheme, the solution remains stable. However, applying the test to a potentially unstable scheme yields a solution with fibrillations of substantial amplitude. The parametrizations of the NWP model ARPÉGE were tested one by one to see which one may be the source of unstable model behaviour. The test identified the set of equations in the stratiform precipitation scheme (a diagnostic Kessler-type scheme as a stiff problem, particularly the combination of terms arising due to the evaporation of snow.
New Numerical Treatment for Solving the KDV Equation
Directory of Open Access Journals (Sweden)
khalid ali
2017-01-01
Full Text Available In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using collocation method with the modified exponential cubic B-spline. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.
Numerical simulation of the drop spreading on a horizontal plane
Zyuzina, N. A.; Ostapenko, V. V.
2017-10-01
A shallow water model of film flow is used to describe the process of a drop spreading on a horizontal plane, taking into account the liquid viscosity, heat-mass transfer and surface tension forces. To simulate this flow numerically in polar coordinates an unconditionally stable implicit difference scheme has been developed, which (in the case of evaporation) can calculate the drop spreading over a dry surface without special allocation of the drop boundary. A region of dimensionless parameters is singled out under which the evaporating droplet, as a result of surface tension forces, transforms into a circular ring before complete evaporation.
2015-01-01
Stable beams: two simple words that carry so much meaning at CERN. When LHC page one switched from "squeeze" to "stable beams" at 10.40 a.m. on Wednesday, 3 June, it triggered scenes of jubilation in control rooms around the CERN sites, as the LHC experiments started to record physics data for the first time in 27 months. This is what CERN is here for, and it’s great to be back in business after such a long period of preparation for the next stage in the LHC adventure. I’ve said it before, but I’ll say it again. This was a great achievement, and testimony to the hard and dedicated work of so many people in the global CERN community. I could start to list the teams that have contributed, but that would be a mistake. Instead, I’d simply like to say that an achievement as impressive as running the LHC – a machine of superlatives in every respect – takes the combined effort and enthusiasm of everyone ...
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
Computer difference scheme for a singularly perturbed convection-diffusion equation
Shishkin, G. I.
2014-08-01
The Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation with a perturbation parameter ɛ (that takes arbitrary values from the half-open interval (0, 1]) is considered. For this problem, an approach to the construction of a numerical method based on a standard difference scheme on uniform meshes is developed in the case when the data of the grid problem include perturbations and additional perturbations are introduced in the course of the computations on a computer. In the absence of perturbations, the standard difference scheme converges at an (δ st ) rate, where δ st = (ɛ + N -1)-1 N -1 and N + 1 is the number of grid nodes; the scheme is not ɛ-uniformly well conditioned or stable to perturbations of the data. Even if the convergence of the standard scheme is theoretically proved, the actual accuracy of the computed solution in the presence of perturbations degrades with decreasing ɛ down to its complete loss for small ɛ (namely, for ɛ = (δ-2max i, j |δ a {/i j }| + δ-1 max i, j |δ b {/i j }|), where δ = δ st and δ a {/i j }, δ b {/i j } are the perturbations in the coefficients multiplying the second and first derivatives). For the boundary value problem, we construct a computer difference scheme, i.e., a computing system that consists of a standard scheme on a uniform mesh in the presence of controlled perturbations in the grid problem data and a hypothetical computer with controlled computer perturbations. The conditions on admissible perturbations in the grid problem data and on admissible computer perturbations are obtained under which the computer difference scheme converges in the maximum norm for ɛ ∈ (0, 1] at the same rate as the standard scheme in the absence of perturbations.
Description and Application of the CE-SE Scheme
Directory of Open Access Journals (Sweden)
Martin KOSÍK
2010-12-01
Full Text Available The CE-SE scheme is new numerical methodology for conservation laws. It was developed by Dr.Chang of NASA Glenn Research Center and his collaborators. The 1D and 2D variant of CE-SE scheme for scalar convection and for Euler equations for incompressible flows is described. The CESE scheme is compared with classical schemes in 1D. The solution to inviscid incompressible flow in GAMM channel in 2D is presented.
Relaxation schemes for the shallow water equations
Delis, A. I.; Katsaounis, Th.
2003-03-01
We present a class of first and second order in space and time relaxation schemes for the shallow water (SW) equations. A new approach of incorporating the geometrical source term in the relaxation model is also presented. The schemes are based on classical relaxation models combined with Runge-Kutta time stepping mechanisms. Numerical results are presented for several benchmark test problems with or without the source term present.
Homogenization scheme for acoustic metamaterials
Yang, Min
2014-02-26
We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial\\'s structural unit cell with a piece of homogenized material. From the Green\\'s theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme\\'s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2000-05-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented.
Towards stable acceleration in LINACS
Dubrovskiy, A D
2014-01-01
Ultra-stable and -reproducible high-energy particle beams with short bunches are needed in novel linear accelerators and, in particular, in the Compact Linear Collider CLIC. A passive beam phase stabilization system based on a bunch compression with a negative transfer matrix element R56 and acceleration at a positive off-crest phase is proposed. The motivation and expected advantages of the proposed scheme are outlined.
Error Analysis of the K-Rb-21Ne Comagnetometer Space-Stable Inertial Navigation System
Directory of Open Access Journals (Sweden)
Qingzhong Cai
2018-02-01
Full Text Available According to the application characteristics of the K-Rb-21Ne comagnetometer, a space-stable navigation mechanization is designed and the requirements of the comagnetometer prototype are presented. By analysing the error propagation rule of the space-stable Inertial Navigation System (INS, the three biases, the scale factor of the z-axis, and the misalignment of the x- and y-axis non-orthogonal with the z-axis, are confirmed to be the main error source. A numerical simulation of the mathematical model for each single error verified the theoretical analysis result of the system’s error propagation rule. Thus, numerical simulation based on the semi-physical data result proves the feasibility of the navigation scheme proposed in this paper.
Error Analysis of the K-Rb-21Ne Comagnetometer Space-Stable Inertial Navigation System.
Cai, Qingzhong; Yang, Gongliu; Quan, Wei; Song, Ningfang; Tu, Yongqiang; Liu, Yiliang
2018-02-24
According to the application characteristics of the K-Rb- 21 Ne comagnetometer, a space-stable navigation mechanization is designed and the requirements of the comagnetometer prototype are presented. By analysing the error propagation rule of the space-stable Inertial Navigation System (INS), the three biases, the scale factor of the z -axis, and the misalignment of the x - and y -axis non-orthogonal with the z -axis, are confirmed to be the main error source. A numerical simulation of the mathematical model for each single error verified the theoretical analysis result of the system's error propagation rule. Thus, numerical simulation based on the semi-physical data result proves the feasibility of the navigation scheme proposed in this paper.
Fan, Xiaolin
2017-01-19
This paper presents a componentwise convex splitting scheme for numerical simulation of multicomponent two-phase fluid mixtures in a closed system at constant temperature, which is modeled by a diffuse interface model equipped with the Van der Waals and the Peng-Robinson equations of state (EoS). The Van der Waals EoS has a rigorous foundation in physics, while the Peng-Robinson EoS is more accurate for hydrocarbon mixtures. First, the phase field theory of thermodynamics and variational calculus are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic equations with extremely strong nonlinear source terms. The steady state equations are transformed into a transient system as a numerical strategy on which the scheme is based. The proposed numerical algorithm avoids the indefiniteness of the Hessian matrix arising from the second-order derivative of homogeneous contribution of total Helmholtz free energy; it is also very efficient. This scheme is unconditionally componentwise energy stable and naturally results in unconditional stability for the Van der Waals model. For the Peng-Robinson EoS, it is unconditionally stable through introducing a physics-preserving correction term, which is analogous to the attractive term in the Van der Waals EoS. An efficient numerical algorithm is provided to compute the coefficient in the correction term. Finally, some numerical examples are illustrated to verify the theoretical results and efficiency of the established algorithms. The numerical results match well with laboratory data.
Numerical methods for incompressible viscous flows with engineering applications
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.
2018-03-01
We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.
Hybrid undulator numerical optimization
Energy Technology Data Exchange (ETDEWEB)
Hairetdinov, A.H. [Kurchatov Institute, Moscow (Russian Federation); Zukov, A.A. [Solid State Physics Institute, Chernogolovka (Russian Federation)
1995-12-31
3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Wintermeyer, Niklas [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Winters, Andrew R., E-mail: awinters@math.uni-koeln.de [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Gassner, Gregor J. [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Kopriva, David A. [Department of Mathematics, The Florida State University, Tallahassee, FL 32306 (United States)
2017-07-01
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.
de Bont, Chris
2018-01-01
This booklet was written to share research results with farmers and practitioners in Tanzania. It gives a summary of the empirical material collected during three months of field work in the Mawala irrigation scheme (Kilimanjaro Region), and includes maps, tables and photos. It describes the history of the irrigation scheme, as well current irrigation and farming practices. It especially focuses on the different kinds of infrastructural improvement in the scheme (by farmers and the government...
Directory of Open Access Journals (Sweden)
D. S. Moreira
2013-08-01
Full Text Available This article presents the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. This new numerical system is denominated JULES-CCATT-BRAMS. We demonstrate the performance of this new model system in relation to several meteorological variables and the CO2 mixing ratio over a large part of South America, focusing on the Amazon basin. The evaluation was conducted for two time periods, the wet (March and dry (September seasons of 2010. The model errors were calculated in relation to meteorological observations at conventional stations in airports and automatic stations. In addition, CO2 mixing ratios in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with observations obtained with airborne instruments. The results of this study show that the JULES-CCATT-BRAMS modeling system provided a significant gain in performance for the considered atmospheric fields relative to those simulated by the LEAF (version 3 surface model originally employed by CCATT-BRAMS. In addition, the new system significantly increases the ability to simulate processes involving air–surface interactions, due to the ability of JULES to simulate photosynthesis, respiration and dynamic vegetation, among other processes. We also discuss a wide range of numerical studies involving coupled atmospheric, land surface and chemistry processes that could be done with the system introduced here. Thus, this work presents to the scientific community a free modeling tool, with good performance in comparison with observational data and reanalysis model data, at least for the region and time period discussed here. Therefore, in principle, this model is able to produce atmospheric hindcast/forecast simulations at different spatial resolutions for any time period and any region of the globe.
Gnedin, Nickolay Y.; Semenov, Vadim A.; Kravtsov, Andrey V.
2018-04-01
An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be "weak" in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves. We use an experimental fluid dynamics code that allows cubic "patches" of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a constraint on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty.
A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications
Directory of Open Access Journals (Sweden)
Zhu Shuai
2016-01-01
Full Text Available Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case which the system is badly stiff. High Precision Direct integration based on variational principle is given (HPD-VP for homogeneous systems and HHPD-VP method for the nonhomogeneous systems are given. This method not only takes the advantage of variational principle formula, which is much precise and is stiff A-stable, but also can avoid the truncation error of the computer. For the large systems, especially, the systems with different frequency or the stiff systems, our methods are stable, accurate and efficient. Numerical experiments show the convergence order of the scheme derived from the variational principle, and is much precise and is effective in engineering.
Energy Technology Data Exchange (ETDEWEB)
D' Ambros, Alder C.; Vitorassi, Pedro H.; Franco, Admilson T.; Morales, Rigoberto E.M. [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Matins, Andre Leibsohn [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES). Tecnologia de Engenharia de Perfuracao
2008-07-01
The success of oil well drilling process depends on the correct prediction of the velocities and stresses fields inside the gap between the drill string and the rock formation. Using CFD is possible to predict the behavior of the drilling fluid flow along the annular space, from the bottom to the top of the well. Commonly the drilling fluid is modeled as a Herschel-Bulkley fluid. An alternative is to employ a non-linear viscoelastic model, like the one developed by Phan-Thien-Tanner (PTT). In the present work the PTT constitutive equation is used to model the drilling fluid flow along the annular space. Thus, this work investigates the influence of the Deborah number on the laminar flow pattern through the numerical solution of the equations formed by the coupled velocity-pressure-stress fields. The results are analyzed and validated against the analytical solution for the fully developed annular pipe flow. The relation between the Deborah number (De) and the entry length is investigated, along with the influence of high values of Deborah number on the friction factor, stress and velocity fields. (author)
International Nuclear Information System (INIS)
Johnston, Hans; Liu Jianguo
2004-01-01
We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C 0 elements to implement
DEFF Research Database (Denmark)
Juhl, Hans Jørn; Stacey, Julia
2001-01-01
to carry out a campaign targeted at this segment. The awareness percentage is already 92 % and 67% of the respondents believe they know the meaning of the scheme. But it stands to reason to study whether the respondents actually know what the labelling scheme stands for or if they just think they do...
Directory of Open Access Journals (Sweden)
R. Sitharthan
2016-09-01
Full Text Available This paper aims at modelling an electronically coupled distributed energy resource with an adaptive protection scheme. The electronically coupled distributed energy resource is a microgrid framework formed by coupling the renewable energy source electronically. Further, the proposed adaptive protection scheme provides a suitable protection to the microgrid for various fault conditions irrespective of the operating mode of the microgrid: namely, grid connected mode and islanded mode. The outstanding aspect of the developed adaptive protection scheme is that it monitors the microgrid and instantly updates relay fault current according to the variations that occur in the system. The proposed adaptive protection scheme also employs auto reclosures, through which the proposed adaptive protection scheme recovers faster from the fault and thereby increases the consistency of the microgrid. The effectiveness of the proposed adaptive protection is studied through the time domain simulations carried out in the PSCAD⧹EMTDC software environment.
Directory of Open Access Journals (Sweden)
G. F. Sun
2015-01-01
Full Text Available A novel explicit finite-difference (FD method is presented to simulate the positive and bounded development process of a microbial colony subjected to a substrate of nutrients, which is governed by a nonlinear parabolic partial differential equations (PDE system. Our explicit FD scheme is uniquely designed in such a way that it transfers the nonlinear terms in the original PDE into discrete sets of linear ones in the algebraic equation system that can be solved very efficiently, while ensuring the stability and the boundedness of the solution. This is achieved through (1 a proper design of intertwined FD approximations for the diffusion function term in both time and spatial variations and (2 the control of the time-step through establishing theoretical stability criteria. A detailed theoretical stability analysis is conducted to reveal that our FD method is indeed stable. Our examples verified the fact that the numerical solution can be ensured nonnegative and bounded to simulate the actual physics. Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme. The present scheme is applicable for solving similar systems of PDEs in the investigation of the dynamics of biological films.
Shibata, Masaru
2016-01-01
This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.
Stable Boundary Layer Education (STABLE) Final Campaign Summary
Energy Technology Data Exchange (ETDEWEB)
Turner, David D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2016-03-01
The properties of, and the processes that occur in, the nocturnal stable boundary layer are not well understood, making it difficult to represent adequately in numerical models. The nocturnal boundary layer often is characterized by a temperature inversion and, in the Southern Great Plains region, a low-level jet. To advance our understanding of the nocturnal stable boundary layer, high temporal and vertical resolution data on the temperature and wind properties are needed, along with both large-eddy simulation and cloud-resolving modeling.
Symplectic and multisymplectic schemes with the simple finite element method
International Nuclear Information System (INIS)
Zhen Liu; Bai Yongqiang; Li Qisheng; Wu Ke
2003-01-01
We study the numerical scheme of elliptic equations by the finite element method. With the special finite element domain, we can find that the scheme can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case. Then we consider the discrete variational principle with the finite element method in the corresponding Lagrangian formalism for classical mechanics and field theory and get the symplectic or multisymplectic scheme of the Euler-Lagrangian equation
Threshold Signature Schemes Application
Directory of Open Access Journals (Sweden)
Anastasiya Victorovna Beresneva
2015-10-01
Full Text Available This work is devoted to an investigation of threshold signature schemes. The systematization of the threshold signature schemes was done, cryptographic constructions based on interpolation Lagrange polynomial, elliptic curves and bilinear pairings were examined. Different methods of generation and verification of threshold signatures were explored, the availability of practical usage of threshold schemes in mobile agents, Internet banking and e-currency was shown. The topics of further investigation were given and it could reduce a level of counterfeit electronic documents signed by a group of users.
Nested Hilbert schemes on surfaces: Virtual fundamental class
DEFF Research Database (Denmark)
Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung
We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of Durr-Kabanov-Okonek and the stable pair invariants of Kool......-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial...
Additive Difference Schemes for Filtration Problems in Multilayer Systems
Ayrjan, E A; Pavlush, M; Fedorov, A V
2000-01-01
In the present paper difference schemes for solution of the plane filtration problem in multilayer systems are analyzed within the framework of difference schemes general theory. Attention is paid to splitting the schemes on physical processes of filtration along water-carring layers and vertical motion between layers. Some absolutely stable additive difference schemes are obtained the realization of which needs no software modification. Parallel algorithm connected with the solving of the filtration problem in every water-carring layer on a single processor is constructed. Program realization on the multi-processor system SPP2000 at JINR is discussed.
Advanced numerical methods for three dimensional two-phase flow calculations
Energy Technology Data Exchange (ETDEWEB)
Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
On numerical Bessel transformation
International Nuclear Information System (INIS)
Sommer, B.; Zabolitzky, J.G.
1979-01-01
The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)
Numerical experiments modelling turbulent flows
Trefilík, Jiří; Kozel, Karel; Příhoda, Jaromír
2014-03-01
The work aims at investigation of the possibilities of modelling transonic flows mainly in external aerodynamics. New results are presented and compared with reference data and previously achieved results. For the turbulent flow simulations two modifications of the basic k - ω model are employed: SST and TNT. The numerical solution was achieved by using the MacCormack scheme on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability.
Numerical experiments modelling turbulent flows
Directory of Open Access Journals (Sweden)
Trefilík Jiří
2014-03-01
Full Text Available The work aims at investigation of the possibilities of modelling transonic flows mainly in external aerodynamics. New results are presented and compared with reference data and previously achieved results. For the turbulent flow simulations two modifications of the basic k – ω model are employed: SST and TNT. The numerical solution was achieved by using the MacCormack scheme on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability.
Energy Technology Data Exchange (ETDEWEB)
Willcock, J J; Lumsdaine, A; Quinlan, D J
2008-08-19
Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.
International Nuclear Information System (INIS)
2002-04-01
This scheme defines the objectives relative to the renewable energies and the rational use of the energy in the framework of the national energy policy. It evaluates the needs and the potentialities of the regions and preconizes the actions between the government and the territorial organizations. The document is presented in four parts: the situation, the stakes and forecasts; the possible actions for new measures; the scheme management and the regional contributions analysis. (A.L.B.)
Toward Practical Secure Stable Matching
Directory of Open Access Journals (Sweden)
Riazi M. Sadegh
2017-01-01
Full Text Available The Stable Matching (SM algorithm has been deployed in many real-world scenarios including the National Residency Matching Program (NRMP and financial applications such as matching of suppliers and consumers in capital markets. Since these applications typically involve highly sensitive information such as the underlying preference lists, their current implementations rely on trusted third parties. This paper introduces the first provably secure and scalable implementation of SM based on Yao’s garbled circuit protocol and Oblivious RAM (ORAM. Our scheme can securely compute a stable match for 8k pairs four orders of magnitude faster than the previously best known method. We achieve this by introducing a compact and efficient sub-linear size circuit. We even further decrease the computation cost by three orders of magnitude by proposing a novel technique to avoid unnecessary iterations in the SM algorithm. We evaluate our implementation for several problem sizes and plan to publish it as open-source.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2003-01-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.
A robust anonymous biometric-based authenticated key agreement scheme for multi-server environments
Guo, Hua; Wang, Pei; Zhang, Xiyong; Huang, Yuanfei; Ma, Fangchao
2017-01-01
In order to improve the security in remote authentication systems, numerous biometric-based authentication schemes using smart cards have been proposed. Recently, Moon et al. presented an authentication scheme to remedy the flaws of Lu et al.'s scheme, and claimed that their improved protocol supports the required security properties. Unfortunately, we found that Moon et al.'s scheme still has weaknesses. In this paper, we show that Moon et al.'s scheme is vulnerable to insider attack, server...
Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations
Rihan, Fathalla A.; Al-Salti, Nasser S.
2017-09-01
In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.
Carbon trading: Current schemes and future developments
International Nuclear Information System (INIS)
Perdan, Slobodan; Azapagic, Adisa
2011-01-01
This paper looks at the greenhouse gas (GHG) emissions trading schemes and examines the prospects of carbon trading. The first part of the paper gives an overview of several mandatory GHG trading schemes around the world. The second part focuses on the future trends in carbon trading. It argues that the emergence of new schemes, a gradual enlargement of the current ones, and willingness to link existing and planned schemes seem to point towards geographical, temporal and sectoral expansion of emissions trading. However, such expansion would need to overcome some considerable technical and non-technical obstacles. Linking of the current and emerging trading schemes requires not only considerable technical fixes and harmonisation of different trading systems, but also necessitates clear regulatory and policy signals, continuing political support and a more stable economic environment. Currently, the latter factors are missing. The global economic turmoil and its repercussions for the carbon market, a lack of the international deal on climate change defining the Post-Kyoto commitments, and unfavourable policy shifts in some countries, cast serious doubts on the expansion of emissions trading and indicate that carbon trading enters an uncertain period. - Highlights: → The paper provides an extensive overview of mandatory emissions trading schemes around the world. → Geographical, temporal and sectoral expansion of emissions trading are identified as future trends. → The expansion requires considerable technical fixes and harmonisation of different trading systems. → Clear policy signals, political support and a stable economic environment are needed for the expansion. → A lack of the post-Kyoto commitments and unfavourable policy shifts indicate an uncertain future for carbon trading.
National Oceanic and Atmospheric Administration, Department of Commerce — Tissue samples (skin, bone, blood, muscle) are analyzed for stable carbon, stable nitrogen, and stable sulfur analysis. Many samples are used in their entirety for...
Difference Schemes and Applications
2015-02-06
finite difference stability, grid generation, finite element methods , numerical solution of stochastic differential equations , numerical ...Physics, Vol. 243 (2013) pp. 305-322. [6] S. Britt, S. Tsynkov, and E. Turkel. A High Order Numerical Method for the Helmholtz Equation with Non...the nonlinear kinetic equation is given. A new DSMC method is tested by comparison with
Sotiropoulos, Vassilios; Kaznessis, Yiannis N
2008-01-07
Models involving stochastic differential equations (SDEs) play a prominent role in a wide range of applications where systems are not at the thermodynamic limit, for example, biological population dynamics. Therefore there is a need for numerical schemes that are capable of accurately and efficiently integrating systems of SDEs. In this work we introduce a variable size step algorithm and apply it to systems of stiff SDEs with multiple multiplicative noise. The algorithm is validated using a subclass of SDEs called chemical Langevin equations that appear in the description of dilute chemical kinetics models, with important applications mainly in biology. Three representative examples are used to test and report on the behavior of the proposed scheme. We demonstrate the advantages and disadvantages over fixed time step integration schemes of the proposed method, showing that the adaptive time step method is considerably more stable than fixed step methods with no excessive additional computational overhead.
Siegler, Robert S.; Braithwaite, David W.
2016-01-01
In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…
Bright, William
In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…
Numerical methods for stochastic differential equations.
Wilkie, Joshua
2004-01-01
Stochastic differential equations (SDE's) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here. High-order numerical methods are developed for the integration of stochastic differential equations with strong solutions. We demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for SDE's which have known exact solutions.
Construct the stable vendor managed inventory partnership through a profit-sharing approach
Li, S.; Yu, Z.; Dong, M.
2015-01-01
In real life, the vendor managed inventory (VMI) model is not always a stable supply chain partnership. This paper proposes a cooperative game based profit-sharing method to stabilize the VMI partnership. Specifically, in a B2C setting, we consider a VMI program including a manufacturer and multiple online retailers. The manufacturer provides the finished product at the equal wholesale price to multiple online retailers. The online retailers face the same customer demand information. We offer the model to compute the increased profits generated by information sharing for total possible VMI coalitions. Using the solution concept of Shapley value, the profit-sharing scheme is produced to fairly divide the total increased profits among the VMI members. We find that under a fair allocation scheme, the higher inventory cost of one VMI member increases the surplus of the other members. Furthermore, the manufacturer is glad to increase the size of VMI coalition, whereas, the retailers are delighted to limit the size of the alliance. Finally, the manufacturer can select the appropriate retailer to boost its surplus, which has no effect on the surplus of the other retailers. The numerical examples indicate that the grand coalition is stable under the proposed allocation scheme.
Rao, G Shanker
2006-01-01
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...
Karki, K. C.; Mongia, H. C.; Patankar, Suhas V.; Runchal, A. K.
1987-01-01
The objective of this effort is to develop improved numerical schemes for predicting combustor flow fields. Various candidate numerical schemes were evaluated, and promising schemes were selected for detailed assessment. The criteria for evaluation included accuracy, computational efficiency, stability, and ease of extension to multidimensions. The candidate schemes were assessed against a variety of simple one- and two-dimensional problems. These results led to the selection of the following schemes for further evaluation: flux spline schemes (linear and cubic) and controlled numerical diffusion with internal feedback (CONDIF). The incorporation of the flux spline scheme and direct solution strategy in a computer program for three-dimensional flows is in progress.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Two stable steady states in the Hodgkin-Huxley axons
Aihara, K.; Matsumoto, G.
1983-01-01
Two stable steady states were found in the numerical solution of the Hodgkin-Huxley equations for the intact squid axon bathed in potassium-rich sea water with an externally applied inward current. Under the conditions the two stable steady-states exist, the Hodgkin-Huxley equations have a complex bifurcation structure including, in addition to the two stable steady-states, a stable limit cycle, two unstable equilibrium points, and one asymptotically stable equilibrium point. It was also conc...
Scheme for achieving coherent perfect absorption by anisotropic metamaterials
Zhang, Xiujuan
2017-02-22
We propose a unified scheme to achieve coherent perfect absorption of electromagnetic waves by anisotropic metamaterials. The scheme describes the condition on perfect absorption and offers an inverse design route based on effective medium theory in conjunction with retrieval method to determine practical metamaterial absorbers. The scheme is scalable to frequencies and applicable to various incident angles. Numerical simulations show that perfect absorption is achieved in the designed absorbers over a wide range of incident angles, verifying the scheme. By integrating these absorbers, we further propose an absorber to absorb energy from two coherent point sources.
Improving Wind-Ramp Forecasts in the Stable Boundary Layer
Jahn, David E.; Takle, Eugene S.; Gallus, William A.
2017-06-01
The viability of wind-energy generation is dependent on highly accurate numerical wind forecasts, which are impeded by inaccuracies in model representation of boundary-layer processes. This study revisits the basic theory of the Mellor, Yamada, Nakanishi, and Niino (MYNN) planetary boundary-layer parametrization scheme, focusing on the onset of wind-ramp events related to nocturnal low-level jets. Modifications to the MYNN scheme include: (1) calculation of new closure parameters that determine the relative effects of turbulent energy production, dissipation, and redistribution; (2) enhanced mixing in the stable boundary layer when the mean wind speed exceeds a specified threshold; (3) explicit accounting of turbulent potential energy in the energy budget. A mesoscale model is used to generate short-term (24 h) wind forecasts for a set of 15 cases from both the U.S.A. and Germany. Results show that the new set of closure parameters provides a marked forecast improvement only when used in conjunction with the new mixing length formulation and only for cases that are originally under- or over-forecast (10 of the 15 cases). For these cases, the mean absolute error (MAE) of wind forecasts at turbine-hub height is reduced on average by 17%. A reduction in MAE values on average by 26% is realized for these same cases when accounting for the turbulent potential energy together with the new mixing length. This last method results in an average reduction by at least 13% in MAE values across all 15 cases.
An Energy Preserving Monolithic Eulerian Fluid-Structure Numerical Scheme *
Pironneau, Olivier
2016-01-01
The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown , monolithic methods for fluid structure interactions (FSI) are built. In this article such a formulation is analyzed when the fluid is compressible and the fluid is incompressible. The i...
Novel Discretization Schemes for the Numerical Simulation of Membrane Dynamics
2012-09-13
inflated from below, and the displacement field was extracted by optically tracking a random speck- ling pattern on the membrane surface. Strains were...Sun Jun-yi, Song Wei-ju, Xu Yun -ping, and Long Jun. “L-P Perturbation Solution of Nonlinear Free Vibration of Prestressed Orthotropic Membrane in...912, 2003. [62] Idesman, A. V. “A new high-order accurate continuous Galerkin method for lin - ear elastodynamics problems”. Computational Mechanics, 40
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J.-Y.; Ratti, A.; Sun, C., E-mail: csun@lbl.gov
2014-12-21
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
Scott, L Ridgway
2011-01-01
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that ex...
Comments on numerical simulations
International Nuclear Information System (INIS)
Sato, T.
1984-01-01
The author comments on a couple of things about numerical simulation. One is just about the philosophical discussion that is, spontaneous or driven. The other thing is the numerical or technical one. Frankly, the author didn't want to touch on the technical matter because this should be a common sense one for those who are working at numerical simulation. But since many people take numerical simulation results at their face value, he would like to remind you of the reality hidden behind them. First, he would point out that the meaning of ''driven'' in driven reconnection is different from that defined by Schindler or Akasofu. The author's definition is closer to Axford's definition. In the spontaneous case, for some unpredicted reason an excess energy of the system is suddenly released at a certain point. However, one does not answer how such an unstable state far beyond a stable limit is realized in the magnetotail. In the driven case, there is a definite energy buildup phase starting from a stable state; namely, energy in the black box increases from a stable level subject to an external source. When the state has reached a certain position, the energy is released suddenly. The difference between driven and spontaneous is whether the cause (plasma flow) to trigger reconnection is specified or reconnection is triggered unpredictably. Another difference is that in driven reconnection the reconnection rate is dependent on the speed of the external plasma flow, but in spontaneous reconnection the rate is dependent on the internal condition such as the resistivity
A numerical spectral approach to solve the dislocation density transport equation
International Nuclear Information System (INIS)
Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C
2015-01-01
A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)
Zhu, Guangpu
2018-04-17
In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.
Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...
African Journals Online (AJOL)
A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...
MFIX documentation numerical technique
Energy Technology Data Exchange (ETDEWEB)
Syamlal, M.
1998-01-01
MFIX (Multiphase Flow with Interphase eXchanges) is a general-purpose hydrodynamic model for describing chemical reactions and heat transfer in dense or dilute fluid-solids flows, which typically occur in energy conversion and chemical processing reactors. The calculations give time-dependent information on pressure, temperature, composition, and velocity distributions in the reactors. The theoretical basis of the calculations is described in the MFIX Theory Guide. Installation of the code, setting up of a run, and post-processing of results are described in MFIX User`s manual. Work was started in April 1996 to increase the execution speed and accuracy of the code, which has resulted in MFIX 2.0. To improve the speed of the code the old algorithm was replaced by a more implicit algorithm. In different test cases conducted the new version runs 3 to 30 times faster than the old version. To increase the accuracy of the computations, second order accurate discretization schemes were included in MFIX 2.0. Bubbling fluidized bed simulations conducted with a second order scheme show that the predicted bubble shape is rounded, unlike the (unphysical) pointed shape predicted by the first order upwind scheme. This report describes the numerical technique used in MFIX 2.0.
Stable convergence and stable limit theorems
Häusler, Erich
2015-01-01
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...
Energy Technology Data Exchange (ETDEWEB)
Zou, Ling; Zhao, Haihua; Zhang, Hongbin
2016-04-01
The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integration methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Electronic Commerce - Payment Schemes. V Rajaraman. Series Article Volume 6 Issue 2 February 2001 pp 6-13. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/02/0006-0013 ...
Link Monotonic Allocation Schemes
Slikker, M.
1999-01-01
A network is a graph where the nodes represent players and the links represent bilateral interaction between the players. A reward game assigns a value to every network on a fixed set of players. An allocation scheme specifies how to distribute the worth of every network among the players. This
Alternative health insurance schemes
DEFF Research Database (Denmark)
Keiding, Hans; Hansen, Bodil O.
2002-01-01
In this paper, we present a simple model of health insurance with asymmetric information, where we compare two alternative ways of organizing the insurance market. Either as a competitive insurance market, where some risks remain uninsured, or as a compulsory scheme, where however, the level...... competitive insurance; this situation turns out to be at least as good as either of the alternatives...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Electronic Commerce - Payment Schemes. V Rajaraman. Series Article Volume 6 Issue 2 February 2001 pp 6-13 ... Author Affiliations. V Rajaraman1. IBM Professor of Information Technology JNCASR Bangalore 560 064, India.
DEFF Research Database (Denmark)
Pötz, Katharina Anna; Haas, Rainer; Balzarova, Michaela
2013-01-01
of schemes that can be categorized on focus areas, scales, mechanisms, origins, types and commitment levels. Research limitations/implications – The findings contribute to conceptual and empirical research on existing models to compare and analyse CSR standards. Sampling technique and depth of analysis limit...
Simple monotonic interpolation scheme
International Nuclear Information System (INIS)
Greene, N.M.
1980-01-01
A procedure for presenting tabular data, such as are contained in the ENDF/B files, that is simpler, more general, and potentially much more compact than the present schemes used with ENDF/B is presented. The method has been successfully used for Bondarenko interpolation in a module of the AMPX system. 1 figure, 1 table
TVD schemes in one and two space dimensions
International Nuclear Information System (INIS)
Leveque, R.J.; Goodman, J.B.; New York Univ., NY)
1985-01-01
The recent development of schemes which are second order accurate in smooth regions has made it possible to overcome certain difficulties which used to arise in numerical computations of discontinuous solutions of conservation laws. The present investigation is concerned with scalar conservation laws, taking into account the employment of total variation diminishing (TVD) schemes. The concept of a TVD scheme was introduced by Harten et al. (1976). Harten et al. first constructed schemes which are simultaneously TVD and second order accurate on smooth solutions. In the present paper, a summary is provided of recently conducted work in this area. Attention is given to TVD schemes in two space dimensions, a second order accurate TVD scheme in one dimension, and the entropy condition and spreading of rarefaction waves. 19 references
Modern Schemes for Computation of Transonic Flows in Internal Aerodynamics
Directory of Open Access Journals (Sweden)
J. Fürst
2000-01-01
Full Text Available The work deals with numerical solution of steady transonic flows with applications in internal aerodynamics. The problems are described by the system of 2D or 3D Euler or Navier-Stokes equations. Our group developed during last years several central or upwind TVD finite volume methods for computation of transonic flows through a cascade or in a channel using grids of quadrilateral cells or triangular cells. We also developed other (non TVD schemes e.g. MacCormack scheme or several multistage Runge-Kutta finite volume schemes with applications of some acceleration techniques (multi-grid solution or hierarchical residual averaging. Our aim is to present some comparison of results of flows in internal aerodynamics using TVD schemes or other schemes. One can also compare the influence or artificial viscosity effects especially using TVD schemes.
Numerical simulation of double-diffusive finger convection
Hughes, J.D.; Sanford, W.E.; Vacher, H.L.
2005-01-01
A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double-diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density-dependent, saturated-unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute-transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute-transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High-resolution data from a double-diffusive Hele-Shaw experiment, initially in a density-stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double-diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer. Copyright 2005 by the American Geophysical Union.
Wind-Ramp-Forecast Sensitivity to Closure Parameters in a Boundary-Layer Parametrization Scheme
Jahn, David E.; Takle, Eugene S.; Gallus, William A.
2017-09-01
Wind ramps are relatively large changes in wind speed over a period of a few hours and present a challenge for electric utilities to balance power generation and load. Failures of boundary-layer parametrization schemes to represent physical processes limit the ability of numerical models to forecast wind ramps, especially in a stable boundary layer. Herein, the eight "closure parameters" of a widely used boundary-layer parameterization scheme are subject to sensitivity tests for a set of wind-ramp cases. A marked sensitivity of forecast wind speed to closure-parameter values is observed primarily for three parameters that influence in the closure equations the depth of turbulent mixing, dissipation, and the transfer of kinetic energy from the mean to the turbulent flow. Reducing the value of these parameters independently by 25% or by 50% reduces the overall average in forecast wind-speed errors by at least 24% for the first two parameters and increases average forecast error by at least 63% for the third parameter. Doubling any of these three parameters increases average forecast error by at least 67%. Such forecast sensitivity to closure parameter values provides motivation to explore alternative values in the context of a stable boundary layer.
Chu, Chunlei
2009-01-01
We present two Lax‐Wendroff type high‐order time stepping schemes and apply them to solving the 3D elastic wave equation. The proposed schemes have the same format as the Taylor series expansion based schemes, only with modified temporal extrapolation coefficients. We demonstrate by both theoretical analysis and numerical examples that the modified schemes significantly improve the stability conditions.
Brezinski, C
2012-01-01
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<
MIMO transmit scheme based on morphological perceptron with competitive learning.
Valente, Raul Ambrozio; Abrão, Taufik
2016-08-01
This paper proposes a new multi-input multi-output (MIMO) transmit scheme aided by artificial neural network (ANN). The morphological perceptron with competitive learning (MP/CL) concept is deployed as a decision rule in the MIMO detection stage. The proposed MIMO transmission scheme is able to achieve double spectral efficiency; hence, in each time-slot the receiver decodes two symbols at a time instead one as Alamouti scheme. Other advantage of the proposed transmit scheme with MP/CL-aided detector is its polynomial complexity according to modulation order, while it becomes linear when the data stream length is greater than modulation order. The performance of the proposed scheme is compared to the traditional MIMO schemes, namely Alamouti scheme and maximum-likelihood MIMO (ML-MIMO) detector. Also, the proposed scheme is evaluated in a scenario with variable channel information along the frame. Numerical results have shown that the diversity gain under space-time coding Alamouti scheme is partially lost, which slightly reduces the bit-error rate (BER) performance of the proposed MP/CL-NN MIMO scheme. Copyright © 2016 Elsevier Ltd. All rights reserved.
Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme
Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm
2018-03-01
The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.
Baker, John G.
2009-01-01
Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.
On Converting Secret Sharing Scheme to Visual Secret Sharing Scheme
Directory of Open Access Journals (Sweden)
Wang Daoshun
2010-01-01
Full Text Available Abstract Traditional Secret Sharing (SS schemes reconstruct secret exactly the same as the original one but involve complex computation. Visual Secret Sharing (VSS schemes decode the secret without computation, but each share is m times as big as the original and the quality of the reconstructed secret image is reduced. Probabilistic visual secret sharing (Prob.VSS schemes for a binary image use only one subpixel to share the secret image; however the probability of white pixels in a white area is higher than that in a black area in the reconstructed secret image. SS schemes, VSS schemes, and Prob. VSS schemes have various construction methods and advantages. This paper first presents an approach to convert (transform a -SS scheme to a -VSS scheme for greyscale images. The generation of the shadow images (shares is based on Boolean XOR operation. The secret image can be reconstructed directly by performing Boolean OR operation, as in most conventional VSS schemes. Its pixel expansion is significantly smaller than that of VSS schemes. The quality of the reconstructed images, measured by average contrast, is the same as VSS schemes. Then a novel matrix-concatenation approach is used to extend the greyscale -SS scheme to a more general case of greyscale -VSS scheme.
Energy Technology Data Exchange (ETDEWEB)
Elliott, C.J.; Fisher, H.; Pepin, J. [Los Alamos National Lab., NM (United States); Gillmann, R. [Federal Highway Administration, Washington, DC (United States)
1996-07-01
Traffic classification techniques were evaluated using data from a 1993 investigation of the traffic flow patterns on I-20 in Georgia. First we improved the data by sifting through the data base, checking against the original video for questionable events and removing and/or repairing questionable events. We used this data base to critique the performance quantitatively of a classification method known as Scheme F. As a context for improving the approach, we show in this paper that scheme F can be represented as a McCullogh-Pitts neural network, oar as an equivalent decomposition of the plane. We found that Scheme F, among other things, severely misrepresents the number of vehicles in Class 3 by labeling them as Class 2. After discussing the basic classification problem in terms of what is measured, and what is the desired prediction goal, we set forth desirable characteristics of the classification scheme and describe a recurrent neural network system that partitions the high dimensional space up into bins for each axle separation. the collection of bin numbers, one for each of the axle separations, specifies a region in the axle space called a hyper-bin. All the vehicles counted that have the same set of in numbers are in the same hyper-bin. The probability of the occurrence of a particular class in that hyper- bin is the relative frequency with which that class occurs in that set of bin numbers. This type of algorithm produces classification results that are much more balanced and uniform with respect to Classes 2 and 3 and Class 10. In particular, the cancellation of errors of classification that occurs is for many applications the ideal classification scenario. The neural network results are presented in the form of a primary classification network and a reclassification network, the performance matrices for which are presented.
On usage of CABARET scheme for tracer transport in INM ocean model
International Nuclear Information System (INIS)
Diansky, Nikolay; Kostrykin, Sergey; Gusev, Anatoly; Salnikov, Nikolay
2010-01-01
The contemporary state of ocean numerical modelling sets some requirements for the numerical advection schemes used in ocean general circulation models (OGCMs). The most important requirements are conservation, monotonicity and numerical efficiency including good parallelization properties. Investigation of some advection schemes shows that one of the best schemes satisfying the criteria is CABARET scheme. 3D-modification of the CABARET scheme was used to develop a new transport module (for temperature and salinity) for the Institute of Numerical Mathematics ocean model (INMOM). Testing of this module on some common benchmarks shows a high accuracy in comparison with the second-order advection scheme used in the INMOM. This new module was incorporated in the INMOM and experiments with the modified model showed a better simulation of oceanic circulation than its previous version.
He, Qiaolin
2011-06-01
In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
Scalable Nonlinear Compact Schemes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Debojyoti [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil M. [Univ. of Chicago, IL (United States); Brown, Jed [Univ. of Colorado, Boulder, CO (United States)
2014-04-01
In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.
Asynchronous schemes for CFD at extreme scales
Konduri, Aditya; Donzis, Diego
2013-11-01
Recent advances in computing hardware and software have made simulations an indispensable research tool in understanding fluid flow phenomena in complex conditions at great detail. Due to the nonlinear nature of the governing NS equations, simulations of high Re turbulent flows are computationally very expensive and demand for extreme levels of parallelism. Current large simulations are being done on hundreds of thousands of processing elements (PEs). Benchmarks from these simulations show that communication between PEs take a substantial amount of time, overwhelming the compute time, resulting in substantial waste in compute cycles as PEs remain idle. We investigate a novel approach based on widely used finite-difference schemes in which computations are carried out asynchronously, i.e. synchronization of data among PEs is not enforced and computations proceed regardless of the status of messages. This drastically reduces PE idle time and results in much larger computation rates. We show that while these schemes remain stable, their accuracy is significantly affected. We present new schemes that maintain accuracy under asynchronous conditions and provide a viable path towards exascale computing. Performance of these schemes will be shown for simple models like Burgers' equation.
Li, Wei; Saleeb, Atef F.
1995-01-01
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of
Saleeb, Atef F.; Li, Wei
1995-01-01
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the
Directory of Open Access Journals (Sweden)
Hai Bi
2012-01-01
Full Text Available This paper discusses efficient numerical methods for the Steklov eigenvalue problem and establishes a new multiscale discretization scheme and an adaptive algorithm based on the Rayleigh quotient iterative method. The efficiency of these schemes is analyzed theoretically, and the constants appeared in the error estimates are also analyzed elaborately. Finally, numerical experiments are provided to support the theory.
Quantum identification schemes with entanglements
International Nuclear Information System (INIS)
Mihara, Takashi
2002-01-01
We need secure identification schemes because many situations exist in which a person must be identified. In this paper, we propose three quantum identification schemes with entanglements. First, we propose a quantum one-time pad password scheme. In this scheme, entanglements play the role of a one-time pad password. Next, we propose a quantum identification scheme that requires a trusted authority. Finally, we propose a quantum message authentication scheme that is constructed by combining a different quantum cryptosystem with an ordinary authentication tag
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.; Tang, Qi
2017-08-01
A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. The numerical scheme is verified on a number of difficult benchmark problems.
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.; Tang, Qi
2017-08-01
A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added-mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this first part of a two-part series, the properties of the AMP scheme are motivated and evaluated through the development and analysis of some model problems. The analysis shows when and why the traditional partitioned scheme becomes unstable due to either added-mass or added-damping effects. The analysis also identifies the proper form of the added-damping which depends on the discrete time-step and the grid-spacing normal to the rigid body. The results of the analysis are confirmed with numerical simulations that also demonstrate a second-order accurate implementation of the AMP scheme.
Efficient Scheme for Chemical Flooding Simulation
Directory of Open Access Journals (Sweden)
Braconnier Benjamin
2014-07-01
Full Text Available In this paper, we investigate an efficient implicit scheme for the numerical simulation of chemical enhanced oil recovery technique for oil fields. For the sake of brevity, we only focus on flows with polymer to describe the physical and numerical models. In this framework, we consider a black oil model upgraded with the polymer modeling. We assume the polymer only transported in the water phase or adsorbed on the rock following a Langmuir isotherm. The polymer reduces the water phase mobility which can change drastically the behavior of water oil interfaces. Then, we propose a fractional step technique to resolve implicitly the system. The first step is devoted to the resolution of the black oil subsystem and the second to the polymer mass conservation. In such a way, jacobian matrices coming from the implicit formulation have a moderate size and preserve solvers efficiency. Nevertheless, the coupling between the black-oil subsystem and the polymer is not fully resolved. For efficiency and accuracy comparison, we propose an explicit scheme for the polymer for which large time step is prohibited due to its CFL (Courant-Friedrichs-Levy criterion and consequently approximates accurately the coupling. Numerical experiments with polymer are simulated : a core flood, a 5-spot reservoir with surfactant and ions and a 3D real case. Comparisons are performed between the polymer explicit and implicit scheme. They prove that our polymer implicit scheme is efficient, robust and resolves accurately the coupling physics. The development and the simulations have been performed with the software PumaFlow [PumaFlow (2013 Reference manual, release V600, Beicip Franlab].
A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method
Directory of Open Access Journals (Sweden)
Zhen Chen
2017-03-01
Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
Nakamura, T
1993-01-01
In GR13 we heard many reports on recent. progress as well as future plans of detection of gravitational waves. According to these reports (see the report of the workshop on the detection of gravitational waves by Paik in this volume), it is highly probable that the sensitivity of detectors such as laser interferometers and ultra low temperature resonant bars will reach the level of h ~ 10—21 by 1998. in this level we may expect the detection of the gravitational waves from astrophysical sources such as coalescing binary neutron stars once a year or so. Therefore the progress in numerical relativity is urgently required to predict the wave pattern and amplitude of the gravitational waves from realistic astrophysical sources. The time left for numerical relativists is only six years or so although there are so many difﬁculties in principle as well as in practice.
Set up an Arc Welding Code with Enthalpy Method in Upwind Scheme
Ho, Je-Ee.
2010-05-01
In this study, a numerical code with enthalpy method in upwind scheme is proposed to estimate the distribution of thermal stress in the molten pool, which is primarily determined by the type of the input power and travel speed of heating source. To predict the cracker deficit inside the workpiece, a simulated program satisfying the diagonal domination and Scarborough criterion provides a stable iteration. Meantime, an experimental performance, operated by robot arm "DR-400" to provide a steady and continuous arc welding, was also conducted to verify the simulated result. By surveying the consistence of molten pool bounded by contrast shade and simulated melting contour on the surface of workpiece, the validity of model proposed to predict the thermal cracker has been successfully identified.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Numerical integration of variational equations.
Skokos, Ch; Gerlach, E
2010-09-01
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing well-known properties of chaos indicators such as the Lyapunov characteristic exponents and the generalized alignment indices. We find that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton equations of motion by the repeated action of a symplectic map S , while the corresponding tangent map TS is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.
Chance and stability stable distributions and their applications
Uchaikin, Vladimir V
1999-01-01
An introduction to the theory of stable distributions and their applications. It contains a modern outlook on the mathematical aspects of the theory. The authors explain numerous peculiarities of stable distributions and describe the principle concept of probability theory and function analysis. A significant part of the book is devoted to applications of stable distributions. Another notable feature is the material on the interconnection of stable laws with fractals, chaos and anomalous transport processes.
Two-step rational cononical function in the numerical integration of ...
African Journals Online (AJOL)
By collocation, an explicit nonlinerar two-step scheme is obtained. Numerical examples are provided to demonstrate the performance of the scheme. The results obtained were found to be quite comparable with those by existing schemes. Key Words: Collocation two-step scheme. [Global Jnl Mathematical Sci Vol.2(1) 2003: ...
Numerical experiments for turbulent flows
Trefilík, Jiří; Kozel, Karel; Příhoda, Jaromír
2013-04-01
The aim of the work is to explore the possibilities of modelling transonic flows in the internal and external aerodynamics. Several configurations were analyzed and calculations were performed using both inviscid and viscous models of flow. Viscous turbulent flows have been simulated using either zero equation algebraic Baldwin-Lomax model and two equation k—ω model in its basic version and improved TNT variant. The numerical solution was obtained using Lax-Wendroff scheme in the MacCormack form on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability. Achieved results are compared with experimental data.
Numerical experiments for turbulent flows
Directory of Open Access Journals (Sweden)
Příhoda Jaromír
2013-04-01
Full Text Available The aim of the work is to explore the possibilities of modelling transonic flows in the internal and external aerodynamics. Several configurations were analyzed and calculations were performed using both inviscid and viscous models of flow. Viscous turbulent flows have been simulated using either zero equation algebraic Baldwin-Lomax model and two equation k—ω model in its basic version and improved TNT variant. The numerical solution was obtained using Lax-Wendroff scheme in the MacCormack form on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability. Achieved results are compared with experimental data.
Yasas, F M
1977-01-01
In response to a United Nations resolution, the Mobile Training Scheme (MTS) was set up to provide training to the trainers of national cadres engaged in frontline and supervisory tasks in social welfare and rural development. The training is innovative in its being based on an analysis of field realities. The MTS team consisted of a leader, an expert on teaching methods and materials, and an expert on action research and evaluation. The country's trainers from different departments were sent to villages to work for a short period and to report their problems in fulfilling their roles. From these grass roots experiences, they made an analysis of the job, determining what knowledge, attitude and skills it required. Analysis of daily incidents and problems were used to produce indigenous teaching materials drawn from actual field practice. How to consider the problems encountered through government structures for policy making and decisions was also learned. Tasks of the students were to identify the skills needed for role performance by job analysis, daily diaries and project histories; to analyze the particular community by village profiles; to produce indigenous teaching materials; and to practice the role skills by actual role performance. The MTS scheme was tried in Nepal in 1974-75; 3 training programs trained 25 trainers and 51 frontline workers; indigenous teaching materials were created; technical papers written; and consultations were provided. In Afghanistan the scheme was used in 1975-76; 45 participants completed the training; seminars were held; and an ongoing Council was created. It is hoped that the training program will be expanded to other countries.
Adaptive transmission schemes for MISO spectrum sharing systems
Bouida, Zied
2013-06-01
We propose three adaptive transmission techniques aiming to maximize the capacity of a multiple-input-single-output (MISO) secondary system under the scenario of an underlay cognitive radio network. In the first scheme, namely the best antenna selection (BAS) scheme, the antenna maximizing the capacity of the secondary link is used for transmission. We then propose an orthogonal space time bloc code (OSTBC) transmission scheme using the Alamouti scheme with transmit antenna selection (TAS), namely the TAS/STBC scheme. The performance improvement offered by this scheme comes at the expense of an increased complexity and delay when compared to the BAS scheme. As a compromise between these schemes, we propose a hybrid scheme using BAS when only one antenna verifies the interference condition and TAS/STBC when two or more antennas are illegible for communication. We first derive closed-form expressions of the statistics of the received signal-to-interference-and-noise ratio (SINR) at the secondary receiver (SR). These results are then used to analyze the performance of the proposed techniques in terms of the average spectral efficiency, the average number of transmit antennas, and the average bit error rate (BER). This performance is then illustrated via selected numerical examples. © 2013 IEEE.
Bonus Schemes and Trading Activity
Pikulina, E.S.; Renneboog, L.D.R.; Ter Horst, J.R.; Tobler, P.N.
2013-01-01
Abstract: Little is known about how different bonus schemes affect traders’ propensity to trade and which bonus schemes improve traders’ performance. We study the effects of linear versus threshold (convex) bonus schemes on traders’ behavior. Traders purchase and sell shares in an experimental stock
Numerical and symbolic scientific computing
Langer, Ulrich
2011-01-01
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from
International Nuclear Information System (INIS)
Grashilin, V.A.; Karyshev, Yu.Ya.
1982-01-01
A 6-cycle scheme of step motor is described. The block-diagram and the basic circuit of the step motor control are presented. The step motor control comprises a pulse shaper, electronic commutator and power amplifiers. The step motor supply from 6-cycle electronic commutator provides for higher reliability and accuracy than from 3-cycle commutator. The control of step motor work is realised by the program given by the external source of control signals. Time-dependent diagrams for step motor control are presented. The specifications of the step-motor is given
Receptivity of a TVD Scheme in Incompressible Flow Analysis
Shin, Byeong Rog
A TVD upwind scheme originally designed for compressible flow is applied to the SMAC finite-difference method for incompressible flow analysis. The receptivity and validity of this application are investigated by an evaluation of the accuracy, stability and convergence rate for the SMAC method combined with the TVD scheme. Using this method, three-dimensional developing entry flows through a square-curved duct are calculated and compared with available experimental data as well as some computational results obtained by QUICKs and third-order upwind schemes. Such comparisons show that the numerical method applying the TVD scheme has the highest computational efficiency without a sharp loss of accuracy, resulting in confidence in the application this scheme to incompressible flow computations.
Numerical simulations of magnetic reversal in layered spring magnets.
Energy Technology Data Exchange (ETDEWEB)
Jiang, J.S.; Kaper, H.G.; Leaf, G.K.
2001-01-24
This report summarizes the results of numerical investigations of magnetic reversal in layered spring magnets. A one-dimensional model is used of a film consisting of several atomic layers of soft material on top of several atomic layers of hard material. Each atomic layer is taken to be uniformly magnetized, and spatial inhomogeneities within an atomic layer are neglected. The state of such a system is described by a chain of magnetic spin vectors. Each spin vector behaves like a spinning top driven locally by the effective magnetic field and subject to damping (Landau-Lifshitz-Gilbert equation). A numerical integration scheme for the LLG equation is presented that is unconditionally stable and preserves the magnitude of the magnetization vector at all times. The results of numerical investigations for a bilayer in a rotating in-plane magnetic field show hysteresis with a basic period of 2{pi} at moderate fields and hysteresis with a basic period of {pi} (or any multiple thereof) at strong fields.
Packet reversed packet combining scheme
International Nuclear Information System (INIS)
Bhunia, C.T.
2006-07-01
The packet combining scheme is a well defined simple error correction scheme with erroneous copies at the receiver. It offers higher throughput combined with ARQ protocols in networks than that of basic ARQ protocols. But packet combining scheme fails to correct errors when the errors occur in the same bit locations of two erroneous copies. In the present work, we propose a scheme that will correct error if the errors occur at the same bit location of the erroneous copies. The proposed scheme when combined with ARQ protocol will offer higher throughput. (author)
Gerolymos, G. A.; Sénéchal, D.; Vallet, I.
2009-12-01
We study WENO(2 r - 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving WENO schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405-452], with the mapping ( WENOM) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542-567], which we extend up to WENO17 (r=9). We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent CFL limitation (CFL∈[0.8,1]), for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent pβ in the definition of the Jiang-Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] nonlinear weights be taken as pβ=r, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200-212], instead of pβ=2 (this is valid both for WENO and WENOM reconstructions), although the optimal value of the exponent is probably pβ(r)∈[2,r]. Then, we apply the family of very-high-order reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes III, J. Comput. Phys. 71 (1987) 231-303], with recursive-order-reduction ( ROR) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ROR algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume WENO schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238-260], is free of adjustable parameters, and the corresponding schemes are essentially nonoscillatory, as Δx→0, up to r=9, for all of the test-cases studied. Finally
New advection schemes for free surface flows
International Nuclear Information System (INIS)
Pavan, Sara
2016-01-01
The purpose of this thesis is to build higher order and less diffusive schemes for pollutant transport in shallow water flows or 3D free surface flows. We want robust schemes which respect the main mathematical properties of the advection equation with relatively low numerical diffusion and apply them to environmental industrial applications. Two techniques are tested in this work: a classical finite volume method and a residual distribution technique combined with a finite element method. For both methods we propose a decoupled approach since it is the most advantageous in terms of accuracy and CPU time. Concerning the first technique, a vertex-centred finite volume method is used to solve the augmented shallow water system where the numerical flux is computed through an Harten-Lax-Van Leer-Contact Riemann solver. Starting from this solution, a decoupled approach is formulated and is preferred since it allows to compute with a larger time step the advection of a tracer. This idea was inspired by Audusse, E. and Bristeau, M.O. [13]. The Monotonic Upwind Scheme for Conservation Law, combined with the decoupled approach, is then used for the second order extension in space. The wetting and drying problem is also analysed and a possible solution is presented. In the second case, the shallow water system is entirely solved using the finite element technique and the residual distribution method is applied to the solution of the tracer equation, focusing on the case of time-dependent problems. However, for consistency reasons the resolution of the continuity equation must be considered in the numerical discretization of the tracer. In order to get second order schemes for unsteady cases a predictor-corrector scheme is used in this work. A first order but less diffusive version of the predictor-corrector scheme is also introduced. Moreover, we also present a new locally semi-implicit version of the residual distribution method which, in addition to good properties in
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
Jacques, Ian
1987-01-01
This book is primarily intended for undergraduates in mathematics, the physical sciences and engineering. It introduces students to most of the techniques forming the core component of courses in numerical analysis. The text is divided into eight chapters which are largely self-contained. However, with a subject as intricately woven as mathematics, there is inevitably some interdependence between them. The level of difficulty varies and, although emphasis is firmly placed on the methods themselves rather than their analysis, we have not hesitated to include theoretical material when we consider it to be sufficiently interesting. However, it should be possible to omit those parts that do seem daunting while still being able to follow the worked examples and to tackle the exercises accompanying each section. Familiarity with the basic results of analysis and linear algebra is assumed since these are normally taught in first courses on mathematical methods. For reference purposes a list of theorems used in the t...
A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline.
Zeybek, Halil; Karakoç, S Battal Gazi
2016-01-01
In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.
Carrasco, F. L.; Reula, O. A.
2017-09-01
Force-free electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In this article, we present a full 3D numerical implementation of the FFE evolution around a Kerr black hole. The novelty of our approach is three-folded: (i) We use the "multiblock" technique [1 L. Lehner, O. Reula, and M.Tiglio, Multi-block simulations in general relativity: High-order discretizations, numerical stability and applications, Classical Quantum Gravity 22, 5283 (2005)., 10.1088/0264-9381/22/24/006] to represent a domain with S2×R+ topology within a stable finite-differences scheme. (ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system [2 F. Carrasco and O. Reula, Covariant hyperbolization of force-free electrodynamics, Phys. Rev. D 93, 085013 (2016)., 10.1103/PhysRevD.93.085013]. (iii) We implement stable and constraint-preserving boundary conditions to represent an outer region given by a uniform magnetic field aligned or misaligned respect to the symmetry axis. The construction of appropriate and consistent boundary conditions, both preserving the constraints and physically immersing the system in a uniform magnetic field, has allowed us to obtain long-term stationary solutions representing jets of astrophysical relevance. These numerical solutions are shown to be consistent with previous studies.
A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method
Directory of Open Access Journals (Sweden)
Feng Wu
Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
An energy-stable time-integrator for phase-field models
Vignal, Philippe
2016-12-27
We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.
Explicit TE/TM scheme for particle beam simulations
International Nuclear Information System (INIS)
Dohlus, M.; Zagorodnov, I.
2008-10-01
In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version. It does not have dispersion in the longitudinal direction and the dispersion properties in the transversal plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee's explicit method used in the most popular electrodynamics codes. (orig.)
Stable isotopes labelled compounds
International Nuclear Information System (INIS)
1982-09-01
The catalogue on stable isotopes labelled compounds offers deuterium, nitrogen-15, and multiply labelled compounds. It includes: (1) conditions of sale and delivery, (2) the application of stable isotopes, (3) technical information, (4) product specifications, and (5) the complete delivery programme
Steeneveld, G.J.
2012-01-01
Understanding and prediction of the stable atmospheric boundary layer is a challenging task. Many physical processes are relevant in the stable boundary layer, i.e. turbulence, radiation, land surface coupling, orographic turbulent and gravity wave drag, and land surface heterogeneity. The
Indian Academy of Sciences (India)
IAS Admin
After Maynard-Smith and Price [1] mathematically derived why a given behaviour or strategy was adopted by a certain proportion of the population at a given time, it was shown that a strategy which is currently stable in a population need not be stable in evolutionary time (across generations). Additionally it was sug-.
DEFF Research Database (Denmark)
Fjelde, Tina; Kloch, Allan; Wolfson, David
2001-01-01
We present a novel scheme for all-optical label swapping that relies on logic exclusive-OR (XOR) in an integrated SOA-based Michelson interferometer. The scheme allows simple, efficient and mechanically stable operation, while relaxing the requirements on packet format and simplifying switch...
Transmission usage cost allocation schemes
International Nuclear Information System (INIS)
Abou El Ela, A.A.; El-Sehiemy, R.A.
2009-01-01
This paper presents different suggested transmission usage cost allocation (TCA) schemes to the system individuals. Different independent system operator (ISO) visions are presented using the proportional rata and flow-based TCA methods. There are two proposed flow-based TCA schemes (FTCA). The first FTCA scheme generalizes the equivalent bilateral exchanges (EBE) concepts for lossy networks through two-stage procedure. The second FTCA scheme is based on the modified sensitivity factors (MSF). These factors are developed from the actual measurements of power flows in transmission lines and the power injections at different buses. The proposed schemes exhibit desirable apportioning properties and are easy to implement and understand. Case studies for different loading conditions are carried out to show the capability of the proposed schemes for solving the TCA problem. (author)
Fourth order scheme for wavelet based solution of Black-Scholes equation
Finěk, Václav
2017-12-01
The present paper is devoted to the numerical solution of the Black-Scholes equation for pricing European options. We apply the Crank-Nicolson scheme with Richardson extrapolation for time discretization and Hermite cubic spline wavelets with four vanishing moments for space discretization. This scheme is the fourth order accurate both in time and in space. Computational results indicate that the Crank-Nicolson scheme with Richardson extrapolation significantly decreases the amount of computational work. We also numerically show that optimal convergence rate for the used scheme is obtained without using startup procedure despite the data irregularities in the model.
A Lagrangian Slug Capturing Scheme for Gas-Liquid Flows in Pipes
Energy Technology Data Exchange (ETDEWEB)
Renault, Fabien
2007-06-15
In this thesis a new Lagrangian numerical scheme for the simulation of gas-liquid flows in pipelines is presented. Based on an approximate two-fluid model, this new scheme, called LASSI (Lagrangian Approximate Scheme for Slug Initiation) is dedicated to the modelling of the transition between stratified and slug flow. It is able to capture directly the slug initiation process and to track the motion of every single slug in the pipe without numerical diffusion. It can thus be qualified as a slug capturing and slug tracking scheme
Patrick Honohan
1987-01-01
A Ponzi scheme is an arrangement whereby a promoter offers an investment opportunity with attractive dividends, but where the only basis for the dividends is the future receipts from new investors. The first of these two notes explores some of the analytical properties of a Ponzi scheme, addressing in particular the question whether it is possible for a Ponzi scheme to exist if all the participants are rational. The second note briefly examines the collapse of the PMPA insurance company whos...
Madhulatha, A.; Rajeevan, M.
2018-02-01
Main objective of the present paper is to examine the role of various parameterization schemes in simulating the evolution of mesoscale convective system (MCS) occurred over south-east India. Using the Weather Research and Forecasting (WRF) model, numerical experiments are conducted by considering various planetary boundary layer, microphysics, and cumulus parameterization schemes. Performances of different schemes are evaluated by examining boundary layer, reflectivity, and precipitation features of MCS using ground-based and satellite observations. Among various physical parameterization schemes, Mellor-Yamada-Janjic (MYJ) boundary layer scheme is able to produce deep boundary layer height by simulating warm temperatures necessary for storm initiation; Thompson (THM) microphysics scheme is capable to simulate the reflectivity by reasonable distribution of different hydrometeors during various stages of system; Betts-Miller-Janjic (BMJ) cumulus scheme is able to capture the precipitation by proper representation of convective instability associated with MCS. Present analysis suggests that MYJ, a local turbulent kinetic energy boundary layer scheme, which accounts strong vertical mixing; THM, a six-class hybrid moment microphysics scheme, which considers number concentration along with mixing ratio of rain hydrometeors; and BMJ, a closure cumulus scheme, which adjusts thermodynamic profiles based on climatological profiles might have contributed for better performance of respective model simulations. Numerical simulation carried out using the above combination of schemes is able to capture storm initiation, propagation, surface variations, thermodynamic structure, and precipitation features reasonably well. This study clearly demonstrates that the simulation of MCS characteristics is highly sensitive to the choice of parameterization schemes.
DEFF Research Database (Denmark)
Rotbart, Noy Galil
in a distributed fashion increases. Second, attempting to answer queries on vertices of a graph stored in a distributed fashion can be significantly more complicated. In order to lay theoretical foundations to the first penalty mentioned a large body of work concentrated on labeling schemes. A labeling scheme...... evaluation of fully dynamic labeling schemes. Due to a connection between adjacency labeling schemes and the graph theoretical study of induced universal graphs, we study these in depth and show novel results for bounded degree graphs and power-law graphs. We also survey and make progress on the related...
Finite element or Galerkin type semidiscrete schemes
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
hybrid modulation scheme fo rid modulation scheme fo dulation ...
African Journals Online (AJOL)
eobe
This work proposes a switching technique for ca proposes a switching technique for ca. (SCSPWM) scheme is employed in the generation circulation schemes are presented for this concepts, it is now possible to generate equal ave pts, it is now possible to generate equal ave semiconductor switches. This results in equal ...
User Matching with Relation to the Stable Marriage Problem in Cognitive Radio Networks
Hamza, Doha R.
2017-03-20
We consider a network comprised of multiple primary users (PUs) and multiple secondary users (SUs), where the SUs seek access to a set of orthogonal channels each occupied by one PU. Only one SU is allowed to coexist with a given PU. We propose a distributed matching algorithm to pair the network users, where a Stackelberg game model is assumed for the interaction between the paired PU and SU. The selected secondary is given access in exchange for monetary compensation to the primary. The PU optimizes the interference price it charges to a given SU and the power allocation to maintain communication. The SU optimizes its power demand so as to maximize its utility. Our algorithm provides a unique stable matching. Numerical results indicate the advantage of the proposed algorithm over other reference schemes.
Normal modified stable processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2002-01-01
This paper discusses two classes of distributions, and stochastic processes derived from them: modified stable (MS) laws and normal modified stable (NMS) laws. This extends corresponding results for the generalised inverse Gaussian (GIG) and generalised hyperbolic (GH) or normal generalised inverse...... Gaussian (NGIG) laws. The wider framework thus established provides, in particular, for added flexibility in the modelling of the dynamics of financial time series, of importance especially as regards OU based stochastic volatility models for equities. In the special case of the tempered stable OU process...
Applications of stable isotopes
International Nuclear Information System (INIS)
Letolle, R.; Mariotti, A.; Bariac, T.
1991-06-01
This report reviews the historical background and the properties of stable isotopes, the methods used for their measurement (mass spectrometry and others), the present technics for isotope enrichment and separation, and at last the various present and foreseeable application (in nuclear energy, physical and chemical research, materials industry and research; tracing in industrial, medical and agronomical tests; the use of natural isotope variations for environmental studies, agronomy, natural resources appraising: water, minerals, energy). Some new possibilities in the use of stable isotope are offered. A last chapter gives the present state and forecast development of stable isotope uses in France and Europe
A robust anonymous biometric-based authenticated key agreement scheme for multi-server environments.
Guo, Hua; Wang, Pei; Zhang, Xiyong; Huang, Yuanfei; Ma, Fangchao
2017-01-01
In order to improve the security in remote authentication systems, numerous biometric-based authentication schemes using smart cards have been proposed. Recently, Moon et al. presented an authentication scheme to remedy the flaws of Lu et al.'s scheme, and claimed that their improved protocol supports the required security properties. Unfortunately, we found that Moon et al.'s scheme still has weaknesses. In this paper, we show that Moon et al.'s scheme is vulnerable to insider attack, server spoofing attack, user impersonation attack and guessing attack. Furthermore, we propose a robust anonymous multi-server authentication scheme using public key encryption to remove the aforementioned problems. From the subsequent formal and informal security analysis, we demonstrate that our proposed scheme provides strong mutual authentication and satisfies the desirable security requirements. The functional and performance analysis shows that the improved scheme has the best secure functionality and is computational efficient.
A robust anonymous biometric-based authenticated key agreement scheme for multi-server environments
Huang, Yuanfei; Ma, Fangchao
2017-01-01
In order to improve the security in remote authentication systems, numerous biometric-based authentication schemes using smart cards have been proposed. Recently, Moon et al. presented an authentication scheme to remedy the flaws of Lu et al.’s scheme, and claimed that their improved protocol supports the required security properties. Unfortunately, we found that Moon et al.’s scheme still has weaknesses. In this paper, we show that Moon et al.’s scheme is vulnerable to insider attack, server spoofing attack, user impersonation attack and guessing attack. Furthermore, we propose a robust anonymous multi-server authentication scheme using public key encryption to remove the aforementioned problems. From the subsequent formal and informal security analysis, we demonstrate that our proposed scheme provides strong mutual authentication and satisfies the desirable security requirements. The functional and performance analysis shows that the improved scheme has the best secure functionality and is computational efficient. PMID:29121050
A robust anonymous biometric-based authenticated key agreement scheme for multi-server environments.
Directory of Open Access Journals (Sweden)
Hua Guo
Full Text Available In order to improve the security in remote authentication systems, numerous biometric-based authentication schemes using smart cards have been proposed. Recently, Moon et al. presented an authentication scheme to remedy the flaws of Lu et al.'s scheme, and claimed that their improved protocol supports the required security properties. Unfortunately, we found that Moon et al.'s scheme still has weaknesses. In this paper, we show that Moon et al.'s scheme is vulnerable to insider attack, server spoofing attack, user impersonation attack and guessing attack. Furthermore, we propose a robust anonymous multi-server authentication scheme using public key encryption to remove the aforementioned problems. From the subsequent formal and informal security analysis, we demonstrate that our proposed scheme provides strong mutual authentication and satisfies the desirable security requirements. The functional and performance analysis shows that the improved scheme has the best secure functionality and is computational efficient.
Nguyen-Quang, Trung; Polcher, Jan; Ducharne, Agnès; Arsouze, Thomas
2017-04-01
This study presents an improved version of river routing scheme in the Organising Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) land surface model. The routing scheme in ORCHIDEE is designed to be resolution independent. This is achieved by routing water through sub-grid hydrological transfer units. An approach which also allows to use refined residence times in each transfer unit which also depend on the nature of the water to be routed. In the proposed evolution, the Hydrological data and maps based on SHuttle Elevation Derivatives at multiple Scales (HydroSHEDS) is used to enhance both these aspects. As a seamless near-global hydrological data set, HydroSHEDS is a suitable database for improving the water transfer scheme in ORCHIDEE. The approximately 1 km resolution HydroSHEDS data enables the construction of more adequate transfer units in each LSM grid box. In addition, the slope factor of each transfer unit, which is calculated with new averaging algorithm, improves the time constant of the reservoirs. Moreover, the new routing scheme is designed to function on generalized grids to make it applicable in modern regional and global climate models. We will present an analysis of the optimal transfer unit size which ensures that the results of the routing scheme are independent of the grid at which ORCHIDEE operates. It is found that with transfer units of 10km2 the model results are optimal and numerically stable. For the validation of this enhanced version of the routing scheme, 35-year simulations (1979-2013) were carried out forced by three atmospheric datasets on horizontal resolution of 0.5o and 0.25o. These datasets are: the Watch Forcing ERA-Interim dataset with bias-corrected precipitation using the (1) CRU station based product; (2) GPCCv5 satellite based estimates and (3) the higher resolution version E2OFD. Investigating on monthly and daily timescale at 22 stations of 12 rivers which contribute freshwater to Mediterranean sea shows that the
Accuracy of spectral and finite difference schemes in 2D advection problems
DEFF Research Database (Denmark)
Naulin, V.; Nielsen, A.H.
2003-01-01
In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....
Stable lattice Boltzmann model for Maxwell equations in media
Hauser, A.; Verhey, J. L.
2017-12-01
The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.
Parallel S/sub n/ iteration schemes
International Nuclear Information System (INIS)
Wienke, B.R.; Hiromoto, R.E.
1986-01-01
The iterative, multigroup, discrete ordinates (S/sub n/) technique for solving the linear transport equation enjoys widespread usage and appeal. Serial iteration schemes and numerical algorithms developed over the years provide a timely framework for parallel extension. On the Denelcor HEP, the authors investigate three parallel iteration schemes for solving the one-dimensional S/sub n/ transport equation. The multigroup representation and serial iteration methods are also reviewed. This analysis represents a first attempt to extend serial S/sub n/ algorithms to parallel environments and provides good baseline estimates on ease of parallel implementation, relative algorithm efficiency, comparative speedup, and some future directions. The authors examine ordered and chaotic versions of these strategies, with and without concurrent rebalance and diffusion acceleration. Two strategies efficiently support high degrees of parallelization and appear to be robust parallel iteration techniques. The third strategy is a weaker parallel algorithm. Chaotic iteration, difficult to simulate on serial machines, holds promise and converges faster than ordered versions of the schemes. Actual parallel speedup and efficiency are high and payoff appears substantial
National Research Council Canada - National Science Library
Adler, Robert
1997-01-01
We describe how to take a stable, ARMA, time series through the various stages of model identification, parameter estimation, and diagnostic checking, and accompany the discussion with a goodly number...
Numerical methods in astrophysics an introduction
Bodenheimer, Peter; Rozyczka, Michal; Plewa, Tomasz; Yorke, Harold W; Yorke, Harold W
2006-01-01
Basic Equations The Boltzmann Equation Conservation Laws of Hydrodynamics The Validity of the Continuous Medium Approximation Eulerian and Lagrangian Formulation of Hydrodynamics Viscosity and Navier-Stokes Equations Radiation Transfer Conducting and Magnetized Media Numerical Approximations to Partial Differential Equations Numerical Modeling with Finite-Difference Equations Difference Quotient Discrete Representation of Variables, Functions, and Derivatives Stability of Finite-Difference Methods Physical Meaning of Stability Criterion A Useful Implicit Scheme Diffusion
Numerical experiment with upstream boundary conditions
Huml, Jaroslav; Kozel, Karel
2012-04-01
The work deals with a numerical solution of subsonic and transonic flows described by the system of Euler equations in 2D and 3D flows in a channel. Authors used Lax-Wendroff and the multistage Runge-Kutta scheme to numerically solve the flows in a 2D G AMM channel and an extended 3D channel. Authors compare the results achieved by two different upstream boundary conditions in 2D and also in 3D transonic channel flows.
Introducing a moisture scheme to a nonhydrostatic sigma coordinate model
CSIR Research Space (South Africa)
Bopape, Mary-Jane M
2011-09-01
Full Text Available and precipitation in mid-latitude cyclones. VII: A model for the ?seeder-feeder? process in warm-frontal rainbands. Journal of the Atmospheric Sciences, 40, 1185-1206. Stensrud DJ, 2007: Parameterization schemes. Keys to understanding numerical weather...
Kou, Jisheng
2018-02-25
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager\\'s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.
Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method
Parsani, Matteo
2012-01-01
Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.
Progress with multigrid schemes for hypersonic flow problems
International Nuclear Information System (INIS)
Radespiel, R.; Swanson, R.C.
1995-01-01
Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 X 10 6 and Mach numbers up to 25. 32 refs., 31 figs., 1 tab
Efficient scheme for parametric fitting of data in arbitrary dimensions.
Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching
2008-07-01
We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.
Nonoscillatory shock capturing scheme using flux limited dissipation
International Nuclear Information System (INIS)
Jameson, A.
1985-01-01
A method for modifying the third order dissipative terms by the introduction of flux limiters is proposed. The first order dissipative terms can then be eliminated entirely, and in the case of a scalar conservation law the scheme is converted into a total variation diminishing scheme provided that an appropriate value is chosen for the dissipative coefficient. Particular attention is given to: (1) the treatment of the scalar conservation law; (2) the treatment of the Euler equations for inviscid compressible flow; (3) the boundary conditions; and (4) multistage time stepping and multigrid schemes. Numerical results for transonic flows suggest that a central difference scheme augmented by flux limited dissipative terms can lead to an effective nonoscillatory shock capturing method. 20 references
Support schemes and market design in international offshore grids
DEFF Research Database (Denmark)
Schröder, Sascha Thorsten
2013-01-01
International offshore grids can combine the grid connection of offshore wind parks with the possibility for international power trading in the future. This paper investigates the choice of support scheme and power market design in international offshore grids and derives resulting incentives...... support. For a stable investment framework in the near future, a tendering/feed-in tariff may be the best choice. It avoids exposing wind farms to balancing with multiple countries. In the long run, also other support scheme options may be of interest....
Gao, Min
2014-09-01
In this paper, we develop an efficient numerical method for the two phase moving contact line problem with variable density, viscosity, and slip length. The physical model is based on a phase field approach, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition [1,2,5]. To overcome the difficulties due to large density and viscosity ratio, the Navier-Stokes equations are solved by a splitting method based on a pressure Poisson equation [11], while the Cahn-Hilliard equation is solved by a convex splitting method. We show that the method is stable under certain conditions. The linearized schemes are easy to implement and introduce only mild CFL time constraint. Numerical tests are carried out to verify the accuracy, stability and efficiency of the schemes. The method allows us to simulate the interface problems with extremely small interface thickness. Three dimensional simulations are included to validate the efficiency of the method. © 2014 Elsevier Inc.
An improved anonymous authentication scheme for roaming in ubiquitous networks.
Lee, Hakjun; Lee, Donghoon; Moon, Jongho; Jung, Jaewook; Kang, Dongwoo; Kim, Hyoungshick; Won, Dongho
2018-01-01
With the evolution of communication technology and the exponential increase of mobile devices, the ubiquitous networking allows people to use our data and computing resources anytime and everywhere. However, numerous security concerns and complicated requirements arise as these ubiquitous networks are deployed throughout people's lives. To meet the challenge, the user authentication schemes in ubiquitous networks should ensure the essential security properties for the preservation of the privacy with low computational cost. In 2017, Chaudhry et al. proposed a password-based authentication scheme for the roaming in ubiquitous networks to enhance the security. Unfortunately, we found that their scheme remains insecure in its protection of the user privacy. In this paper, we prove that Chaudhry et al.'s scheme is vulnerable to the stolen-mobile device and user impersonation attacks, and its drawbacks comprise the absence of the incorrect login-input detection, the incorrectness of the password change phase, and the absence of the revocation provision. Moreover, we suggest a possible way to fix the security flaw in Chaudhry et al's scheme by using the biometric-based authentication for which the bio-hash is applied in the implementation of a three-factor authentication. We prove the security of the proposed scheme with the random oracle model and formally verify its security properties using a tool named ProVerif, and analyze it in terms of the computational and communication cost. The analysis result shows that the proposed scheme is suitable for resource-constrained ubiquitous environments.
Improved Atmospheric Stable Boundary Layer Formulations for Navy Seasonal Forecasting
2012-09-30
Long-term goals are to develop methods, descriptions and parameterizations that will alleviate long-standing problems in basically all large-scale numerical atmospheric models in dealing with statically stable and/or very stable conditions, and to implement these for Navy extended forecasting
Tukey max-stable processes for spatial extremes
Xu, Ganggang
2016-09-21
We propose a new type of max-stable process that we call the Tukey max-stable process for spatial extremes. It brings additional flexibility to modeling dependence structures among spatial extremes. The statistical properties of the Tukey max-stable process are demonstrated theoretically and numerically. Simulation studies and an application to Swiss rainfall data indicate the effectiveness of the proposed process. © 2016 Elsevier B.V.
Basic numerical methods. [of unsteady and transonic flow
Steger, Joseph L.; Van Dalsem, William R.
1989-01-01
Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.
An Energy-Work Relationship Integration Scheme for Nonconservative Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Fu Jingli
2008-01-01
Full Text Available This letter focuses on studying a new energy-work relationship numerical integration scheme of nonconservative Hamiltonian systems. The signal-stage, multistage, and parallel composition numerical integration schemes are presented for this system. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multistage scheme of order 2 which its order of accuracy is 2n. The connection, which is discrete analog of usual case, between the change of energy and work of nonconservative force is obtained for nonconservative Hamiltonian systems.This letter also shows that the more the stages of the schemes are, the less the error rate of the scheme is for nonconservative Hamiltonian systems. Finally, an applied example is discussed to illustrate these results.
Stable isogeometric analysis of trimmed geometries
Marussig, Benjamin; Zechner, Jürgen; Beer, Gernot; Fries, Thomas-Peter
2017-04-01
We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.
High-Order Entropy Stable Formulations for Computational Fluid Dynamics
Carpenter, Mark H.; Fisher, Travis C.
2013-01-01
A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
A Robust Trust Establishment Scheme for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Farruh Ishmanov
2015-03-01
Full Text Available Security techniques like cryptography and authentication can fail to protect a network once a node is compromised. Hence, trust establishment continuously monitors and evaluates node behavior to detect malicious and compromised nodes. However, just like other security schemes, trust establishment is also vulnerable to attack. Moreover, malicious nodes might misbehave intelligently to trick trust establishment schemes. Unfortunately, attack-resistance and robustness issues with trust establishment schemes have not received much attention from the research community. Considering the vulnerability of trust establishment to different attacks and the unique features of sensor nodes in wireless sensor networks, we propose a lightweight and robust trust establishment scheme. The proposed trust scheme is lightweight thanks to a simple trust estimation method. The comprehensiveness and flexibility of the proposed trust estimation scheme make it robust against different types of attack and misbehavior. Performance evaluation under different types of misbehavior and on-off attacks shows that the detection rate of the proposed trust mechanism is higher and more stable compared to other trust mechanisms.
Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime
International Nuclear Information System (INIS)
Zumbusch, G
2009-01-01
Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection.
A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2013-01-01
Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.
Spectral scheme for spacetime physics
International Nuclear Information System (INIS)
Seriu, Masafumi
2002-01-01
Based on the spectral representation of spatial geometry, we construct an analysis scheme for spacetime physics and cosmology, which enables us to compare two or more universes with each other. In this scheme the spectral distance plays a central role, which is the measure of closeness between two geometries defined in terms of the spectra. We apply this scheme for analyzing the averaging problem in cosmology; we explicitly investigate the time evolution of the spectra, distance between two nearby spatial geometries, simulating the relation between the real Universe and its model. We then formulate the criteria for a model to be a suitable one
Coordinated renewable energy support schemes
DEFF Research Database (Denmark)
Morthorst, P.E.; Jensen, S.G.
2006-01-01
This paper illustrates the effect that can be observed when support schemes for renewable energy are regionalised. Two theoretical examples are used to explain interactive effects on, e.g., the price of power, conditions for conventional power producers, and changes in import and export of power...... RES-E support schemes already has a common liberalised power market. In this case the introduction of a common support scheme for renewable technologies will lead to more efficient sitings of renewable plants, improving economic and environmental performance of the total power system...
Parsani, Matteo
2013-04-10
Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.
Calcium stable isotope geochemistry
Energy Technology Data Exchange (ETDEWEB)
Gausonne, Nikolaus [Muenster Univ. (Germany). Inst. fuer Mineralogie; Schmitt, Anne-Desiree [Strasbourg Univ. (France). LHyGeS/EOST; Heuser, Alexander [Bonn Univ. (Germany). Steinmann-Inst. fuer Geologie, Mineralogie und Palaeontologie; Wombacher, Frank [Koeln Univ. (Germany). Inst. fuer Geologie und Mineralogie; Dietzel, Martin [Technische Univ. Graz (Austria). Inst. fuer Angewandte Geowissenschaften; Tipper, Edward [Cambridge Univ. (United Kingdom). Dept. of Earth Sciences; Schiller, Martin [Copenhagen Univ. (Denmark). Natural History Museum of Denmark
2016-08-01
This book provides an overview of the fundamentals and reference values for Ca stable isotope research, as well as current analytical methodologies including detailed instructions for sample preparation and isotope analysis. As such, it introduces readers to the different fields of application, including low-temperature mineral precipitation and biomineralisation, Earth surface processes and global cycling, high-temperature processes and cosmochemistry, and lastly human studies and biomedical applications. The current state of the art in these major areas is discussed, and open questions and possible future directions are identified. In terms of its depth and coverage, the current work extends and complements the previous reviews of Ca stable isotope geochemistry, addressing the needs of graduate students and advanced researchers who want to familiarize themselves with Ca stable isotope research.
TE/TM alternating direction scheme for wake field calculation in 3D
International Nuclear Information System (INIS)
Zagorodnov, Igor; Weiland, Thomas
2006-01-01
In the future, accelerators with very short bunches will be used. It demands developing new numerical approaches for long-time calculation of electromagnetic fields in the vicinity of relativistic bunches. The conventional FDTD scheme, used in MAFIA, ABCI and other wake and PIC codes, suffers from numerical grid dispersion and staircase approximation problem. As an effective cure of the dispersion problem, a numerical scheme without dispersion in longitudinal direction can be used as it was shown by Novokhatski et al. [Transition dynamics of the wake fields of ultrashort bunches, TESLA Report 2000-03, DESY, 2000] and Zagorodnov et al. [J. Comput. Phys. 191 (2003) 525]. In this paper, a new economical conservative scheme for short-range wake field calculation in 3D is presented. As numerical examples show, the new scheme is much more accurate on long-time scale than the conventional FDTD approach
TE/TM alternating direction scheme for wake field calculation in 3D
Energy Technology Data Exchange (ETDEWEB)
Zagorodnov, Igor [Institut fuer Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt, Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)]. E-mail: zagor@temf.de; Weiland, Thomas [Institut fuer Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt, Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)
2006-03-01
In the future, accelerators with very short bunches will be used. It demands developing new numerical approaches for long-time calculation of electromagnetic fields in the vicinity of relativistic bunches. The conventional FDTD scheme, used in MAFIA, ABCI and other wake and PIC codes, suffers from numerical grid dispersion and staircase approximation problem. As an effective cure of the dispersion problem, a numerical scheme without dispersion in longitudinal direction can be used as it was shown by Novokhatski et al. [Transition dynamics of the wake fields of ultrashort bunches, TESLA Report 2000-03, DESY, 2000] and Zagorodnov et al. [J. Comput. Phys. 191 (2003) 525]. In this paper, a new economical conservative scheme for short-range wake field calculation in 3D is presented. As numerical examples show, the new scheme is much more accurate on long-time scale than the conventional FDTD approach.
Correct numerical simulation of a two-phase coolant
Kroshilin, A. E.; Kroshilin, V. E.
2016-02-01
Different models used in calculating flows of a two-phase coolant are analyzed. A system of differential equations describing the flow is presented; the hyperbolicity and stability of stationary solutions of the system is studied. The correctness of the Cauchy problem is considered. The models' ability to describe the following flows is analyzed: stable bubble and gas-droplet flows; stable flow with a level such that the bubble and gas-droplet flows are observed under and above it, respectively; and propagation of a perturbation of the phase concentration for the bubble and gas-droplet media. The solution of the problem about the breakdown of an arbitrary discontinuity has been constructed. Characteristic times of the development of an instability at different parameters of the flow are presented. Conditions at which the instability does not make it possible to perform the calculation are determined. The Riemann invariants for the nonlinear problem under consideration have been constructed. Numerical calculations have been performed for different conditions. The influence of viscosity on the structure of the discontinuity front is studied. Advantages of divergent equations are demonstrated. It is proven that a model used in almost all known investigating thermohydraulic programs, both in Russia and abroad, has significant disadvantages; in particular, it can lead to unstable solutions, which makes it necessary to introduce smoothing mechanisms and a very small step for describing regimes with a level. This does not allow one to use efficient numerical schemes for calculating the flow of two-phase currents. A possible model free from the abovementioned disadvantages is proposed.
A Class of Convergent Rational Runge-Kutta Schemes for solution ...
African Journals Online (AJOL)
In this paper, a class of convergent implicit Rational Runge-Kutta schemes using Taylor and binomial series expansion, are developed, analysed and computerized to solve ODEs. Numerical results arising from the new schemes compare favourably with the existing Euler's method. Furthermore, the results show that the ...
International Nuclear Information System (INIS)
Fedon-Magnaud, C.; Hennart, J.P.; Lautard, J.J.
1983-03-01
An unified formulation of non conforming finite elements with quadrature formula and simple nodal scheme is presented. The theoretical convergence is obtained for the previous scheme when the mesh is refined. Numerical tests are provided in order to bear out the theorical results
Numerical solution of atmospheric boundary layer flow
Energy Technology Data Exchange (ETDEWEB)
Benes, L.; Kozel, K. [Czech Technical Univ. (Czech Republic). Dept. of Technical Mathematics; Sladek, I. [Czech Technical Univ. (Czech Republic). Dept. of Mathematics
2000-07-01
The work deals with numerical solution of the 3D viscous turbulent steady flows in the atmospheric boundary layer including pollution propagation. The theoretical model consists of a system of Navier-Stokes equations for incompressible flows (continuity and momentum equations) and two equations for concentration and potential temperature in conservative form. Turbulent flow is considered using an algebraic model of turbulence. Numerical solution is based on artificial compressibility method. Numerically is realized using by the finite volume method and multistage Runge-Kutta scheme. The work presents 3D flow for high Re{proportional_to}10{sup 7}-10{sup 8} over a hill or a system of hills. (orig.)
Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness
Directory of Open Access Journals (Sweden)
Tong Zhang
2014-01-01
stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.
Good governance for pension schemes
Thornton, Paul
2011-01-01
Regulatory and market developments have transformed the way in which UK private sector pension schemes operate. This has increased demands on trustees and advisors and the trusteeship governance model must evolve in order to remain fit for purpose. This volume brings together leading practitioners to provide an overview of what today constitutes good governance for pension schemes, from both a legal and a practical perspective. It provides the reader with an appreciation of the distinctive characteristics of UK occupational pension schemes, how they sit within the capital markets and their social and fiduciary responsibilities. Providing a holistic analysis of pension risk, both from the trustee and the corporate perspective, the essays cover the crucial role of the employer covenant, financing and investment risk, developments in longevity risk hedging and insurance de-risking, and best practice scheme administration.
A Novel Iris Segmentation Scheme
Directory of Open Access Journals (Sweden)
Chen-Chung Liu
2014-01-01
Full Text Available One of the key steps in the iris recognition system is the accurate iris segmentation from its surrounding noises including pupil, sclera, eyelashes, and eyebrows of a captured eye-image. This paper presents a novel iris segmentation scheme which utilizes the orientation matching transform to outline the outer and inner iris boundaries initially. It then employs Delogne-Kåsa circle fitting (instead of the traditional Hough transform to further eliminate the outlier points to extract a more precise iris area from an eye-image. In the extracted iris region, the proposed scheme further utilizes the differences in the intensity and positional characteristics of the iris, eyelid, and eyelashes to detect and delete these noises. The scheme is then applied on iris image database, UBIRIS.v1. The experimental results show that the presented scheme provides a more effective and efficient iris segmentation than other conventional methods.
Modified exponential based differential quadrature scheme to solve convection diffusion equation
Arora, Geeta; Kataria, Pooja
2017-07-01
This paper proffers differential quadrature scheme to obtain approximate solution of one dimensional advection diffusion equation with Dirichlet's boundary conditions. The scheme uses modified exponential cubic spline basis functions to obtain the numerical results. The method uses less computational effort and produces more accurate results. In the numerical problems, L∞ and L2 errors show the relative performance of the method for different time levels. The results shown by the method are in good approximation with the exact solution.
2012-09-03
Numerical Solution of Polynomial Systems by Homotopy Con- tinuation Methods in Handbook of Numerical Analysis , Volume XI, Spe- cial Volume: Foundations of...A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws Wenrui Hao∗ Jonathan D. Hauenstein† Chi...robustness of the new method . Keywords homotopy continuation, hyperbolic conservation laws, WENO scheme, steady state problems. ∗Department of Applied and
Breeding schemes in reindeer husbandry
Directory of Open Access Journals (Sweden)
Lars Rönnegård
2003-04-01
Full Text Available The objective of the paper was to investigate annual genetic gain from selection (G, and the influence of selection on the inbreeding effective population size (Ne, for different possible breeding schemes within a reindeer herding district. The breeding schemes were analysed for different proportions of the population within a herding district included in the selection programme. Two different breeding schemes were analysed: an open nucleus scheme where males mix and mate between owner flocks, and a closed nucleus scheme where the males in non-selected owner flocks are culled to maximise G in the whole population. The theory of expected long-term genetic contributions was used and maternal effects were included in the analyses. Realistic parameter values were used for the population, modelled with 5000 reindeer in the population and a sex ratio of 14 adult females per male. The standard deviation of calf weights was 4.1 kg. Four different situations were explored and the results showed: 1. When the population was randomly culled, Ne equalled 2400. 2. When the whole population was selected on calf weights, Ne equalled 1700 and the total annual genetic gain (direct + maternal in calf weight was 0.42 kg. 3. For the open nucleus scheme, G increased monotonically from 0 to 0.42 kg as the proportion of the population included in the selection programme increased from 0 to 1.0, and Ne decreased correspondingly from 2400 to 1700. 4. In the closed nucleus scheme the lowest value of Ne was 1300. For a given proportion of the population included in the selection programme, the difference in G between a closed nucleus scheme and an open one was up to 0.13 kg. We conclude that for mass selection based on calf weights in herding districts with 2000 animals or more, there are no risks of inbreeding effects caused by selection.
Small-scale classification schemes
DEFF Research Database (Denmark)
Hertzum, Morten
2004-01-01
. While coordination mechanisms focus on how classification schemes enable cooperation among people pursuing a common goal, boundary objects embrace the implicit consequences of classification schemes in situations involving conflicting goals. Moreover, the requirements specification focused on functional...... requirements and provided little information about why these requirements were considered relevant. This stands in contrast to the discussions at the project meetings where the software engineers made frequent use of both abstract goal descriptions and concrete examples to make sense of the requirements...
Design and Analysis of a Dynamic Mobility Management Scheme for Wireless Mesh Network
Directory of Open Access Journals (Sweden)
Abhishek Majumder
2013-01-01
Full Text Available Seamless mobility management of the mesh clients (MCs in wireless mesh network (WMN has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO, mesh mobility management (M3, and wireless mesh mobility management (WMM have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC’s session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M3, and WMM with respect to total cost.
Design and analysis of a dynamic mobility management scheme for wireless mesh network.
Majumder, Abhishek; Roy, Sudipta
2013-01-01
Seamless mobility management of the mesh clients (MCs) in wireless mesh network (WMN) has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO), mesh mobility management (M(3)), and wireless mesh mobility management (WMM) have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR) based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC's session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M(3), and WMM with respect to total cost.
Computing Evans functions numerically via boundary-value problems
Barker, Blake; Nguyen, Rose; Sandstede, Björn; Ventura, Nathaniel; Wahl, Colin
2018-03-01
The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.
Modified SIMPLE algorithm for the numerical analysis of incompressible flows with free surface
International Nuclear Information System (INIS)
Mok, Jin Ho; Hong, Chun Pyo; Lee, Jin Ho
2005-01-01
While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipment or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented for the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... Home; Journals; Resonance – Journal of Science Education; Volume 21; Issue 9. Evolutionary Stable Strategy: Application of Nash Equilibrium in Biology. General ... Using some examples of classical games, we show how evolutionary game theory can help understand behavioural decisions of animals.
Kearney, M. Kate
2013-01-01
The concordance genus of a knot is the least genus of any knot in its concordance class. Although difficult to compute, it is a useful invariant that highlights the distinction between the three-genus and four-genus. In this paper we define and discuss the stable concordance genus of a knot, which describes the behavior of the concordance genus under connected sum.
Manifolds admitting stable forms
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van; Panák, Martin; Vanžura, Jiří
2008-01-01
Roč. 49, č. 1 (2008), s. 101-11 ISSN 0010-2628 R&D Projects: GA ČR(CZ) GP201/05/P088 Institutional research plan: CEZ:AV0Z10190503 Keywords : stable forms * automorphism groups Subject RIV: BA - General Mathematics
International Nuclear Information System (INIS)
Ishida, T.
1992-01-01
The research has been in four general areas: (1) correlation of isotope effects with molecular forces and molecular structures, (2) correlation of zero-point energy and its isotope effects with molecular structure and molecular forces, (3) vapor pressure isotope effects, and (4) fractionation of stable isotopes. 73 refs, 38 figs, 29 tabs
Interactive Stable Ray Tracing
DEFF Research Database (Denmark)
Dal Corso, Alessandro; Salvi, Marco; Kolb, Craig
2017-01-01
Interactive ray tracing applications running on commodity hardware can suffer from objectionable temporal artifacts due to a low sample count. We introduce stable ray tracing, a technique that improves temporal stability without the over-blurring and ghosting artifacts typical of temporal post-pr...
Directory of Open Access Journals (Sweden)
Behnaz Tolue
2018-07-01
Full Text Available In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1\\cap H_2\
A Multiserver Biometric Authentication Scheme for TMIS using Elliptic Curve Cryptography.
Chaudhry, Shehzad Ashraf; Khan, Muhammad Tawab; Khan, Muhammad Khurram; Shon, Taeshik
2016-11-01
Recently several authentication schemes are proposed for telecare medicine information system (TMIS). Many of such schemes are proved to have weaknesses against known attacks. Furthermore, numerous such schemes cannot be used in real time scenarios. Because they assume a single server for authentication across the globe. Very recently, Amin et al. (J. Med. Syst. 39(11):180, 2015) designed an authentication scheme for secure communication between a patient and a medical practitioner using a trusted central medical server. They claimed their scheme to extend all security requirements and emphasized the efficiency of their scheme. However, the analysis in this article proves that the scheme designed by Amin et al. is vulnerable to stolen smart card and stolen verifier attacks. Furthermore, their scheme is having scalability issues along with inefficient password change and password recovery phases. Then we propose an improved scheme. The proposed scheme is more practical, secure and lightweight than Amin et al.'s scheme. The security of proposed scheme is proved using the popular automated tool ProVerif.
A literature survey on numerical heat transfer
Shih, T. M.
1982-12-01
Technical papers in the area of numerical heat transfer published from 1977 through 1981 are reviewed. The journals surveyed include: (1) ASME Journal of Heat Transfer, (2) International Journal of Heat and Mass Transfer, (3) AIAA Journal, (4) Numerical Heat Transfer, (5) Computers and Fluids, (6) International Journal for Numerical Methods in Engineering, (7) SIAM Journal of Numerical Analysis, and (8) Journal of Computational Physics. This survey excludes experimental work in heat transfer and numerical schemes that are not applied to equations governing heat transfer phenomena. The research work is categorized into the following areas: (A) conduction, (B) boundary-layer flows, (C) momentum and heat transfer in cavities, (D) turbulent flows, (E) convection around cylinders and spheres or within annuli, (F) numerical convective instability, (G) radiation, (H) combustion, (I) plumes, jets, and wakes, (J) heat transfer in porous media, (K) boiling, condensation, and two-phase flows, (L) developing and fully developed channel flows, (M) combined heat and mass transfer, (N) applications, (O) comparison and properties of numerical schemes, and (P) body-fitted coordinates and nonuniform grids.
Comparison of several numerical methods for internal transonic flow problems
Energy Technology Data Exchange (ETDEWEB)
Dobes, J.; Fort, J.; Fuerst, J.; Halama, J.; Kozel, K. [Karlova Univ., Prague (Czech Republic). Dept. of Technical Mathematics
2001-07-01
This contribution summarizes results of several numerical methods developed at our department. Presented methods are based on central TVD schemes, upwind TVD schemes with or without Riemann solver, ENO schemes and Lax-Wendroff type schemes. The results of 2D methods, computed on either structured quadrilateral grids or unstructured grids composed of triangles and quadrilaterals, are compared on 2D axial and radial turbine cascade and 2D axial compressor cascade. A comparison of results, obtained on structured hexahedral grids, is shown for 3D axial turbine cascade of Skoda Pilsen enterprise. (orig.)
Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature
Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)
2000-01-01
This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.
Balsara, Dinshaw S.; Garain, Sudip; Taflove, Allen; Montecinos, Gino
2018-02-01
schemes. The computer algebra system scripts for generating ADER time update schemes for any general PDE with stiff source terms are also given in the electronic supplements to this paper. Second, third and fourth order accurate schemes for numerically solving Maxwell's equations in material media are presented in this paper. Several stringent tests are also presented to show that the method works and meets its design goals even when material permittivity and permeability vary by an order of magnitude over just a few zones. Furthermore, since the method is unconditionally stable and sub-cell-resolving in the presence of stiff source terms (i.e. for problems involving giant variations in conductivity over just a few zones), it can accurately handle such problems without any reduction in timestep. We also show that increasing the order of accuracy offers distinct advantages for resolving sub-cell variations in material properties. Most importantly, we show that when the accuracy requirements are stringent the higher order schemes offer the shortest time to solution. This makes a compelling case for the use of higher order, sub-cell resolving schemes in CED.
An Efficient and Robust Numerical Solution of the Full-Order Multiscale Model of Lithium-Ion Battery
Directory of Open Access Journals (Sweden)
Michal Beneš
2018-01-01
Full Text Available We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the finite difference discretization of the diffusion equations combined with an original iterative scheme for solving the integral formulation of the laws of electrochemical interactions. We demonstrate that our implementation is fast and stable over the expected lifetime of the cell. In contrast to some simplified models, it provides physically consistent results for a wide range of applied currents including high loads. The algorithm forms a solid basis for simulations of cells and battery packs in hybrid electric vehicles, with possible straightforward extensions by aging and heat effects.
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
A secure communication scheme using projective chaos synchronization
International Nuclear Information System (INIS)
Li Zhigang; Xu Daolin
2004-01-01
Most secure communication schemes using chaotic dynamics are based on identical synchronization. In this paper, we show the possibility of secure communication using projective synchronization (PS). The unpredictability of the scaling factor in projective synchronization can additionally enhance the security of communication. It is also showed that the scaling factor can be employed to improve the robustness against noise contamination. The feasibility of the communication scheme in high-dimensional chaotic systems, such as the hyperchaotic Roessler system, is demonstrated. Numerical results show the success in transmitting a sound signal through chaotic systems
A novel approach for numerical computation of Burgers’ equation in (1 + 1 and (2 + 1 dimensions
Directory of Open Access Journals (Sweden)
Brajesh Kumar Singh
2016-12-01
Full Text Available This paper proposes a new scheme termed as modified extended cubic B-Spline differential quadrature (mECDQ method for time dependent partial differential equations. Specially, the numerical computation of the Burgers’ equation is obtained using mECDQ method. First of all the modified extended cubic B-splines are used as a set of basis function in DQ to evaluate the weighting coefficients. The mECDQ method converts the initial boundary value system of Burgers’ equation into a initial value system of ordinary differential equations (ODEs. The resulting system is solved by using an optimal five stage four order strong stability preserving Runge–Kutta method (SSP-RK54. The accuracy and efficiency of the method is illustrated by considering five test problems. The proposed results are compared with the exact solutions in terms of L2 and L∞ error norms and the existing results. The mECDQ scheme produces better results than the results due to almost all the existing schemes. The stability analysis of the scheme is also carried out using the matrix stability analysis method for various grid points. This shows that mECDQ scheme is conditionally stable.
High resolution finite volume scheme for the quantum hydrodynamic equations
Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu
2009-03-01
The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were
High resolution finite volume scheme for the quantum hydrodynamic equations
International Nuclear Information System (INIS)
Lin, C.-T.; Yeh, J.-Y.; Chen, J.-Y.
2009-01-01
The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12 . The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4 . To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were
Numerical simulation of steady and unsteady flows through plane cascades
Fořt, J.; Huněk, M.; Kozel, K.; Lain, J.; Šejna, M.; Vavřincová, M.
This paper of a few co-authors presents some works of the group of the Department of Technical Mathematics, Faculty of Mechanical Eng., TU Prague, which deals with numerical methods in fluid dynamics. We present numerical methods for a solution of different physical and mathematical models of flow through plane cascades. We use the Mac Cormack's scheme, Ron — Ho — Ni's scheme and Runge — Kutta schemes on H — type structured grid and upwind schemes on an unstructured triangular grid. This methods are used for simulation of steady or unsteady inviscid flow and for simulation of viscous laminar flow. We deal with comparison of different methods mutually and with experimental data and with comparison of different physical and mathematical models of flow used for numerical simulation.
Numerical solution of the stochastic parabolic equation with the dependent operator coefficient
Energy Technology Data Exchange (ETDEWEB)
Ashyralyev, Allaberen [Department of Elementary Mathematics Education, Fatih University, 34500, Istanbul (Turkey); Department of Mathematics, ITTU, Ashgabat (Turkmenistan); Okur, Ulker [Institute for Stochastics and Applications, Department of Mathematics, University of Stuttgart, 70569, Stuttgart (Germany)
2015-09-18
In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.
Numerical Methods for the Design and Analysis of Photonic Crystal Fibres
DEFF Research Database (Denmark)
Roberts, John
2008-01-01
The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted.......The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted....
Auction dynamics: A volume constrained MBO scheme
Jacobs, Matt; Merkurjev, Ekaterina; Esedoǧlu, Selim
2018-02-01
We show how auction algorithms, originally developed for the assignment problem, can be utilized in Merriman, Bence, and Osher's threshold dynamics scheme to simulate multi-phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases. The resulting algorithms are highly efficient and robust, and can be used in simulations ranging from minimal partition problems in Euclidean space to semi-supervised machine learning via clustering on graphs. In the case of the latter application, numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state-of-the-art methods, while requiring a fraction of the computation time.
Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Johnson, J.L.; Dalhed, H.E.; Greene, J.M.
1978-07-01
Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given
Yee, H. C.; Sweby, P. K.
1995-01-01
The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.
Yee, H. C.; Sweby, P. K.
1995-01-01
The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.
Extended lattice Boltzmann scheme for droplet combustion.
Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas
2017-05-01
The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.
A subgrid parameterization scheme for precipitation
Directory of Open Access Journals (Sweden)
S. Turner
2012-04-01
Full Text Available With increasing computing power, the horizontal resolution of numerical weather prediction (NWP models is improving and today reaches 1 to 5 km. Nevertheless, clouds and precipitation formation are still subgrid scale processes for most cloud types, such as cumulus and stratocumulus. Subgrid scale parameterizations for water vapor condensation have been in use for many years and are based on a prescribed probability density function (PDF of relative humidity spatial variability within the model grid box, thus providing a diagnosis of the cloud fraction. A similar scheme is developed and tested here. It is based on a prescribed PDF of cloud water variability and a threshold value of liquid water content for droplet collection to derive a rain fraction within the model grid. Precipitation of rainwater raises additional concerns relative to the overlap of cloud and rain fractions, however. The scheme is developed following an analysis of data collected during field campaigns in stratocumulus (DYCOMS-II and fair weather cumulus (RICO and tested in a 1-D framework against large eddy simulations of these observed cases. The new parameterization is then implemented in a 3-D NWP model with a horizontal resolution of 2.5 km to simulate real cases of precipitating cloud systems over France.
The same number of optimized parameters scheme for determining intermolecular interaction energies
DEFF Research Database (Denmark)
Kristensen, Kasper; Ettenhuber, Patrick; Eriksen, Janus Juul
2015-01-01
We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave...... as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP...
A well-balanced scheme for Ten-Moment Gaussian closure equations with source term
Meena, Asha Kumari; Kumar, Harish
2018-02-01
In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.
International Nuclear Information System (INIS)
Tibari, Elghali; Taous, Fouad; Marah, Hamid
2014-01-01
This report presents results related to stable isotopes analysis carried out at the CNESTEN DASTE in Rabat (Morocco), on behalf of Senegal. These analyzes cover 127 samples. These results demonstrate that Oxygen-18 and Deuterium in water analysis were performed by infrared Laser spectroscopy using a LGR / DLT-100 with Autosampler. Also, the results are expressed in δ values (‰) relative to V-SMOW to ± 0.3 ‰ for oxygen-18 and ± 1 ‰ for deuterium.
International Nuclear Information System (INIS)
Zhang Yun-Peng; Duan Hai-Bin; Zhang Xiang-Yin
2011-01-01
A novel distributed control scheme to generate stable flocking motion for a group of agents is proposed. In this control scheme, a molecular potential field model is applied as the potential field function because of its smoothness and unique shape. The approach of distributed receding horizon control is adopted to drive each agent to find its optimal control input to lower its potential at every step. Experimental results show that this proposed control scheme can ensure that all agents eventually converge to a stable flocking formation with a common velocity and the collisions can also be avoided at the same time. (general)
Forensic Stable Isotope Biogeochemistry
Cerling, Thure E.; Barnette, Janet E.; Bowen, Gabriel J.; Chesson, Lesley A.; Ehleringer, James R.; Remien, Christopher H.; Shea, Patrick; Tipple, Brett J.; West, Jason B.
2016-06-01
Stable isotopes are being used for forensic science studies, with applications to both natural and manufactured products. In this review we discuss how scientific evidence can be used in the legal context and where the scientific progress of hypothesis revisions can be in tension with the legal expectations of widely used methods for measurements. Although this review is written in the context of US law, many of the considerations of scientific reproducibility and acceptance of relevant scientific data span other legal systems that might apply different legal principles and therefore reach different conclusions. Stable isotopes are used in legal situations for comparing samples for authenticity or evidentiary considerations, in understanding trade patterns of illegal materials, and in understanding the origins of unknown decedents. Isotope evidence is particularly useful when considered in the broad framework of physiochemical processes and in recognizing regional to global patterns found in many materials, including foods and food products, drugs, and humans. Stable isotopes considered in the larger spatial context add an important dimension to forensic science.
Numerical approach for a relaxed minimization problem arising in tomographic reconstruction
Directory of Open Access Journals (Sweden)
Ali Srour
2013-05-01
Full Text Available The purpose of this article is to develop a numerical scheme for a system of optimality conditions for a smooth minimization problem that arises in tomographic reconstruction of binary axially symmetric objects. The density function of the object with the Lagrange multipliers is seen as a saddle point of an associated Lagrangian, then we use the Usawa scheme mixed with descent gradient method to give the corresponding numerical scheme.
A New time Integration Scheme for Cahn-hilliard Equations
Schaefer, R.
2015-06-01
In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.
A Hybrid Combination Scheme for Cooperative Spectrum Sensing in Cognitive Radio Networks
Directory of Open Access Journals (Sweden)
Changhua Yao
2014-01-01
Full Text Available We propose a novel hybrid combination scheme in cooperative spectrum sensing (CSS, which utilizes the diversity of reporting channels to achieve better throughput performance. Secondary users (SUs with good reporting channel quality transmit quantized local observation statistics to fusion center (FC, while others report their local decisions. FC makes the final decision by carrying out hybrid combination. We derive the closed-form expressions of throughput and detection performance as a function of the number of SUs which report local observation statistics. The simulation and numerical results show that the hybrid combination scheme can achieve better throughput performance than hard combination scheme and soft combination scheme.
An intelligent robotics control scheme
Orlando, N. E.
1984-01-01
The problem of robot control is viewed at the level of communicating high-level commands produced by intelligent algorithms to the actuator/sensor controllers. Four topics are considered in the design of an integrated control and communications scheme for an intelligent robotic system: the use of abstraction spaces, hierarchical versus heterarchical control, distributed processing, and the interleaving of the steps of plan creation and plan execution. A scheme is presented for an n-level distributed hierarchical/heterarchical control system that effectively interleaves intelligent planning, execution, and sensory feedback. A three-level version of this scheme has been successfully implemented in the Intelligent Systems Research Lab at NASA Langley Research Center. This implementation forms the control structure for DAISIE (Distributed Artificially Intelligent System for Interacting with the Environment), a testbed system integrating AI software with robotics hardware.
One-qubit fingerprinting schemes
International Nuclear Information System (INIS)
Beaudrap, J. Niel de
2004-01-01
Fingerprinting is a technique in communication complexity in which two parties (Alice and Bob) with large data sets send short messages to a third party (a referee), who attempts to compute some function of the larger data sets. For the equality function, the referee attempts to determine whether Alice's data and Bob's data are the same. In this paper, we consider the extreme scenario of performing fingerprinting where Alice and Bob both send either one bit (classically) or one qubit (in the quantum regime) messages to the referee for the equality problem. Restrictive bounds are demonstrated for the error probability of one-bit fingerprinting schemes, and show that it is easy to construct one-qubit fingerprinting schemes which can outperform any one-bit fingerprinting scheme. The author hopes that this analysis will provide results useful for performing physical experiments, which may help to advance implementations for more general quantum communication protocols
Modulation Schemes for Wireless Access
Directory of Open Access Journals (Sweden)
F. Vejrazka
2000-12-01
Full Text Available Four modulation schemes, namely minimum shift keying (MSK, Gaussianminimum shift keying (GMSK, multiamplitude minimum shift keying(MAMSK and ÃÂ€/4 differential quadrature phase shift keying (ÃÂ€/4-QPSKare described and their applicability to wireless access is discussedin the paper. Low complexity receiver structures based on differentialdetection are analysed to estimate the performance of the modulationschemes in the additive Gaussian noise and the Rayleigh and Riceenvelope fast fading channel. The bandwidth efficiency is calculated toevaluate the modulation schemes. The results show that the MAMSK schemegives the greatest bandwidth efficiency, but its performance in theRayleigh channel is rather poor. In contrast, the MSK scheme is lessbandwidth efficient, but it is more resistant to Rayleigh fading. Theperformance of ÃÂ€/4-QPSK signal is considerably improved by appropriateprefiltering.
Simple scheme for gauge mediation
International Nuclear Information System (INIS)
Murayama, Hitoshi; Nomura, Yasunori
2007-01-01
We present a simple scheme for constructing models that achieve successful gauge mediation of supersymmetry breaking. In addition to our previous work [H. Murayama and Y. Nomura, Phys. Rev. Lett. 98, 151803 (2007)] that proposed drastically simplified models using metastable vacua of supersymmetry breaking in vectorlike theories, we show there are many other successful models using various types of supersymmetry-breaking mechanisms that rely on enhanced low-energy U(1) R symmetries. In models where supersymmetry is broken by elementary singlets, one needs to assume U(1) R violating effects are accidentally small, while in models where composite fields break supersymmetry, emergence of approximate low-energy U(1) R symmetries can be understood simply on dimensional grounds. Even though the scheme still requires somewhat small parameters to sufficiently suppress gravity mediation, we discuss their possible origins due to dimensional transmutation. The scheme accommodates a wide range of the gravitino mass to avoid cosmological problems
Stable channel of reclaimed tidal lowland
Syarifudin, Achmad; Imanuddin, Momon S.; Moerwanto, Arie S.; Suryadi, F. X.
2017-11-01
This study aimed to develop models of the Operation and Maintenance in the reclaimed tidal marsh area to get a stable channel. The research location is reclaimed tidal delta area Telang I Primary 8 representing land typology A/B and a survey conducted in 13 South Secondary Schemes following existing tertiary Telang I. MIKE - 11 computer models used used to analyze the movement of sediment in the channel in both the Primary channel 8, SPD, SDU and tertiary channels in block 13 South. Calibration model with multiple channels in the field of physical parameters has been performed to obtain results close to the results of measurement modeling sediment movement in the channel. The integration models of MIKE - 11 models with various scenarios are used to model the operation and maintenance of the channel in the tidal marsh area to get a stable channel. According to the scheme P8 - 13S, OM models obtained 75 percent, in which the secondary channel (SPD/SDU) and built flap gate in tertiary channel, get a well prototype model of the stable channel (equilibriums), where the average erosion on P8 at a distance of 3,200 m in the amount of 4,472,049 m3 and the mean sedimentation in the SPD of 963,836 m3 and mean of sedimentation in the tertiary channel of 3,508,213 m3. Similarly, on average erosion P8 by 4,135,649 m3 and the mean sedimentation in the SDU of 681,304 m3 and the mean sedimentation in the tertiary channel of 3,454,345 m3.
A reduced feedback proportional fair multiuser scheduling scheme
Shaqfeh, Mohammad
2011-12-01
Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed and ordered scheduling mechanism. A slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we propose a novel proportional fair multiuser switched-diversity scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the per-user feedback thresholds. We demonstrate by numerical examples that our reduced feedback proportional fair scheduler operates within 0.3 bits/sec/Hz from the achievable rates by the conventional full feedback proportional fair scheduler in Rayleigh fading conditions. © 2011 IEEE.
A General Symbolic PDE Solver Generator: Beyond Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
Testing stable boundary layer parameterizations against the BASE:ALFA measurements
Bonafè, G.; Tampieri, F.; di Giuseppe, F.; Caporaso, L.
2010-09-01
The Po valley in the Northern Italy is a large plain in a semi-closed basin surrounded by complex orography; the Alps to the North and Apennines to the South-East, and closed to the east by the Adriatic sea. As a flatland basin shielded by mountains, calm wind is very frequent and strong temperature inversions are often observed near the ground, during the night and in the winter period the occurrence of a extremely stable boundary layer is common. A complete set of surface and atmospheric measurements have been collected during a four month observational program carried out at San Pietro Capofiume meteo station, in the middle of the Po Valley. The long term dataset has been collected in the contest of the project BASE:ALFA with the main aim of creating a data pool of micro-meteorological /soil data to test and validate numerical weather prediction PBL schemes. The measurement periods span summer, winter and spring and allows to analyse a wide range of PBL stability conditions. Different parameterizations of first and second order moments of velocity and temperature are tested against the collected data. A particular focus is given to stable boundary layer and the values of its height obtained from Nieuwstadt 1984 and Zilitinkievich et al 2005 formulas will be provided and compared against radiosounding profile estimates.
Bao, Kai
2012-10-01
In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..
Radiation transport in numerical astrophysics
International Nuclear Information System (INIS)
Lund, C.M.
1983-02-01
In this article, we discuss some of the numerical techniques developed by Jim Wilson and co-workers for the calculation of time-dependent radiation flow. Difference equations for multifrequency transport are given for both a discrete-angle representation of radiation transport and a Fick's law-like representation. These methods have the important property that they correctly describe both the streaming and diffusion limits of transport theory in problems where the mean free path divided by characteristic distances varies from much less than one to much greater than one. They are also stable for timesteps comparable to the changes in physical variables, rather than being limited by stability requirements
Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics
Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter
2018-01-01
This paper presents a high order hybrid discontinuous Galerkin/finite volume scheme for solving the equations of the magnetohydrodynamics (MHD) and of the relativistic hydrodynamics (SRHD) on quadrilateral meshes. In this approach, for the spatial discretization, an arbitrary high order discontinuous Galerkin spectral element (DG) method is combined with a finite volume (FV) scheme in order to simulate complex flow problems involving strong shocks. Regarding the time discretization, a fourth order strong stability preserving Runge-Kutta method is used. In the proposed hybrid scheme, a shock indicator is computed at the beginning of each Runge-Kutta stage in order to flag those elements containing shock waves or discontinuities. Subsequently, the DG solution in these troubled elements and in the current time step is projected onto a subdomain composed of finite volume subcells. Right after, the DG operator is applied to those unflagged elements, which, in principle, are oscillation-free, meanwhile the troubled elements are evolved with a robust second/third order FV operator. With this approach we are able to numerically simulate very challenging problems in the context of MHD and SRHD in one, and two space dimensions and with very high order polynomials. We make convergence tests and show a comprehensive one- and two dimensional testbench for both equation systems, focusing in problems with strong shocks. The presented hybrid approach shows that numerical schemes of very high order of accuracy are able to simulate these complex flow problems in an efficient and robust manner.
Numerical Solution of the Modified Equal Width Wave Equation
Directory of Open Access Journals (Sweden)
Seydi Battal Gazi Karakoç
2012-01-01
Full Text Available Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws 2 and ∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.
An integration scheme for stiff solid-gas reactor models
Directory of Open Access Journals (Sweden)
Bjarne A. Foss
2001-04-01
Full Text Available Many dynamic models encounter numerical integration problems because of a large span in the dynamic modes. In this paper we develop a numerical integration scheme for systems that include a gas phase, and solid and liquid phases, such as a gas-solid reactor. The method is based on neglecting fast dynamic modes and exploiting the structure of the algebraic equations. The integration method is suitable for a large class of industrially relevant systems. The methodology has proven remarkably efficient. It has in practice performed excellent and been a key factor for the success of the industrial simulator for electrochemical furnaces for ferro-alloy production.
Efficient adaptive fuzzy control scheme
Papp, Z.; Driessen, B.J.F.
1995-01-01
The paper presents an adaptive nonlinear (state-) feedback control structure, where the nonlinearities are implemented as smooth fuzzy mappings defined as rule sets. The fine tuning and adaption of the controller is realized by an indirect adaptive scheme, which modifies the parameters of the fuzzy
New practicable Siberian Snake schemes
International Nuclear Information System (INIS)
Steffen, K.
1983-07-01
Siberian Snake schemes can be inserted in ring accelerators for making the spin tune almost independent of energy. Two such schemes are here suggested which lend particularly well to practical application over a wide energy range. Being composed of horizontal and vertical bending magnets, the proposed snakes are designed to have a small maximum beam excursion in one plane. By applying in this plane a bending correction that varies with energy, they can be operated at fixed geometry in the other plane where most of the bending occurs, thus avoiding complicated magnet motion or excessively large magnet apertures that would otherwise be needed for large energy variations. The first of the proposed schemes employs a pair of standard-type Siberian Snakes, i.e. of the usual 1st and 2nd kind which rotate the spin about the longitudinal and the transverse horizontal axis, respectively. The second scheme employs a pair of novel-type snakes which rotate the spin about either one of the horizontal axes that are at 45 0 to the beam direction. In obvious reference to these axes, they are called left-pointed and right-pointed snakes. (orig.)
Symmetry-preserving finite element schemes: An introductory investigation
Bihlo, Alexander; Valiquette, Francis
2018-01-01
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our constructions can be extended to (1+1)-dimensional evolutionary partial differential equations, using Burgers' equation as an example. Numerical simulations verify that the symmetry-preserving finite element schemes constructed converge at the expected rate and tha...
Constructing space difference schemes which satisfy a cell entropy inequality
Merriam, Marshal L.
1989-01-01
A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.
Stability of sinusoidal responses of marginally stable bandpass sigma delta modulators
Ho, Charlotte Yuk-Fan; Ling, Bingo Wing-Kuen; Reiss, Joshua
2006-01-01
In this paper, we analyze the stability of the sinusoidal responses of second order interpolative marginally stable bandpass sigma delta modulators (SDMs) with the sum of the numerator and denominator polynomials equal to one and explore new results on the more general second order interpolative marginally stable bandpass SDMs. These results can be further extended to the high order interpolative marginally stable bandpass SDMs.
Numerical Contour Integration for Loop Integrals
Kurihara, Y.; Kaneko, T.
2005-01-01
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculations of the standard model. Examples of 3- and 4-point diagrams in 1-loop integrals and 2- and 3-point ...
A potential enstrophy and energy conserving scheme for the shallow water equations
Arakawa, A.; Lamb, V. R.
1981-01-01
To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.
Balsara, Dinshaw S.; Taflove, Allen; Garain, Sudip; Montecinos, Gino
2017-11-01
While classic finite-difference time-domain (FDTD) solutions of Maxwell's equations have served the computational electrodynamics (CED) community very well, formulations based on Godunov methodology have begun to show advantages. We argue that the formulations presented so far are such that FDTD schemes and Godunov-based schemes each have their own unique advantages. However, there is currently not a single formulation that systematically integrates the strengths of both these major strains of development. While an early glimpse of such a formulation was offered in Balsara et al. [16], that paper focused on electrodynamics in plasma. Here, we present a synthesis that integrates the strengths of both FDTD and Godunov-based schemes into a robust single formulation for CED in material media. Three advances make this synthesis possible. First, from the FDTD method, we retain (but somewhat modify) a spatial staggering strategy for the primal variables. This provides a beneficial constraint preservation for the electric displacement and magnetic induction vector fields via reconstruction methods that were initially developed in some of the first author's papers for numerical magnetohydrodynamics (MHD). Second, from the Godunov method, we retain the idea of upwinding, except that this idea, too, has to be significantly modified to use the multi-dimensionally upwinded Riemann solvers developed by the first author. Third, we draw upon recent advances in arbitrary derivatives in space and time (ADER) time-stepping by the first author and his colleagues. We use the ADER predictor step to endow our method with sub-cell resolving capabilities so that the method can be stiffly stable and resolve significant sub-cell variation in the material properties within a zone. Overall, in this paper, we report a new scheme for numerically solving Maxwell's equations in material media, with special attention paid to a second-order-accurate formulation. Several numerical examples are
Auzinger, Winfried
2016-07-28
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
A nine-point finite difference scheme for one-dimensional wave equation
Szyszka, Barbara
2017-07-01
The paper is devoted to an implicit finite difference method (FDM) for solving initial-boundary value problems (IBVP) for one-dimensional wave equation. The second-order derivatives in the wave equation have been approximated at the four intermediate points, as a consequence, an implicit nine-point difference scheme has been obtained. Von Neumann stability analysis has been conducted and we have demonstrated, that the presented difference scheme is unconditionally stable.
ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.
2018-03-01
We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.
An improved anonymous authentication scheme for roaming in ubiquitous networks
Lee, Hakjun; Lee, Donghoon; Moon, Jongho; Jung, Jaewook; Kang, Dongwoo; Kim, Hyoungshick
2018-01-01
With the evolution of communication technology and the exponential increase of mobile devices, the ubiquitous networking allows people to use our data and computing resources anytime and everywhere. However, numerous security concerns and complicated requirements arise as these ubiquitous networks are deployed throughout people’s lives. To meet the challenge, the user authentication schemes in ubiquitous networks should ensure the essential security properties for the preservation of the privacy with low computational cost. In 2017, Chaudhry et al. proposed a password-based authentication scheme for the roaming in ubiquitous networks to enhance the security. Unfortunately, we found that their scheme remains insecure in its protection of the user privacy. In this paper, we prove that Chaudhry et al.’s scheme is vulnerable to the stolen-mobile device and user impersonation attacks, and its drawbacks comprise the absence of the incorrect login-input detection, the incorrectness of the password change phase, and the absence of the revocation provision. Moreover, we suggest a possible way to fix the security flaw in Chaudhry et al’s scheme by using the biometric-based authentication for which the bio-hash is applied in the implementation of a three-factor authentication. We prove the security of the proposed scheme with the random oracle model and formally verify its security properties using a tool named ProVerif, and analyze it in terms of the computational and communication cost. The analysis result shows that the proposed scheme is suitable for resource-constrained ubiquitous environments. PMID:29505575
Numerical solutions of the Vlasov equation
International Nuclear Information System (INIS)
Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi
1985-01-01
A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)
Compact tokamak reactors part 2 (numerical results)
International Nuclear Information System (INIS)
Wiley, J.C.; Wootton, A.J.; Ross, D.W.
1996-01-01
The authors describe a numerical optimization scheme for fusion reactors. The particular application described is to find the smallest copper coil spherical tokamak, although the numerical scheme is sufficiently general to allow many other problems to be solved. The solution to the steady state energy balance is found by first selecting the fixed variables. The range of all remaining variables is then selected, except for the temperature. Within the specified ranges, the temperature which satisfies the power balance is then found. Tests are applied to determine that remaining constraints are satisfied, and the acceptable results then stored. Results are presented for a range of auxiliary current drive efficiencies and different scaling relationships; for the range of variables chosen the machine encompassing volume increases or remains approximately unchanged as the aspect ratio is reduced
Compact tokamak reactors part 2 (numerical results)
Energy Technology Data Exchange (ETDEWEB)
Wiley, J.C.; Wootton, A.J.; Ross, D.W.
1996-10-21
The authors describe a numerical optimization scheme for fusion reactors. The particular application described is to find the smallest copper coil spherical tokamak, although the numerical scheme is sufficiently general to allow many other problems to be solved. The solution to the steady state energy balance is found by first selecting the fixed variables. The range of all remaining variables is then selected, except for the temperature. Within the specified ranges, the temperature which satisfies the power balance is then found. Tests are applied to determine that remaining constraints are satisfied, and the acceptable results then stored. Results are presented for a range of auxiliary current drive efficiencies and different scaling relationships; for the range of variables chosen the machine encompassing volume increases or remains approximately unchanged as the aspect ratio is reduced.
Numerical Optimization in Microfluidics
DEFF Research Database (Denmark)
Jensen, Kristian Ejlebjærg
2017-01-01
Numerical modelling can illuminate the working mechanism and limitations of microfluidic devices. Such insights are useful in their own right, but one can take advantage of numerical modelling in a systematic way using numerical optimization. In this chapter we will discuss when and how numerical...... optimization is best used....
An efficient shock-capturing scheme for simulating compressible homogeneous mixture flow
International Nuclear Information System (INIS)
Dang, Son Tung; Ha, Cong Tu; Park, Warn Gyu; Jung, Chul Min
2016-01-01
This work is devoted to the development of a procedure for the numerical solution of Navier-Stokes equations for cavitating flows with and without ventilation based on a compressible, multiphase, homogeneous mixture model. The governing equations are discretized on a general structured grid using a high-resolution shock-capturing scheme in conjunction with appropriate limiters to prevent the generation of spurious solutions near shock waves or discontinuities. Two well-known limiters are examined, and a new limiter is proposed to enhance the accuracy and stability of the numerical scheme. A sensitivity analysis is first conducted to determine the relative influences of various model parameters on the solution. These parameters are adopted for the computation of water flows over a hemispherical body, conical body and a divergent/convergent nozzle. Finally, numerical calculations of ventilated supercavitating flows over a hemispherical cylinder body with a hot propulsive jet are conducted to verify the capabilities of the numerical scheme
Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows
Wang, Wei; Yee, H. C.; Sjogreen, Bjorn; Magin, Thierry; Shu, Chi-Wang
2009-01-01
The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.
Chertock, A.
2012-02-02
Aquatic bacteria like Bacillus subtilis are heavier than water yet they are able to swim up an oxygen gradient and concentrate in a layer below the water surface, which will undergo Rayleigh-Taylor-type instabilities for sufficiently high concentrations. In the literature, a simplified chemotaxis-fluid system has been proposed as a model for bio-convection in modestly diluted cell suspensions. It couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier-Stokes equations subject to a gravitational force proportional to the relative surplus of the cell density compared to the water density. In this paper, we derive a high-resolution vorticity-based hybrid finite-volume finite-difference scheme, which allows us to investigate the nonlinear dynamics of a two-dimensional chemotaxis-fluid system with boundary conditions matching an experiment of Hillesdon et al. (Bull. Math. Biol., vol. 57, 1995, pp. 299-344). We present selected numerical examples, which illustrate (i) the formation of sinking plumes, (ii) the possible merging of neighbouring plumes and (iii) the convergence towards numerically stable stationary plumes. The examples with stable stationary plumes show how the surface-directed oxytaxis continuously feeds cells into a high-concentration layer near the surface, from where the fluid flow (recurring upwards in the space between the plumes) transports the cells into the plumes, where then gravity makes the cells sink and constitutes the driving force in maintaining the fluid convection and, thus, in shaping the plumes into (numerically) stable stationary states. Our numerical method is fully capable of solving the coupled chemotaxis-fluid system and enabling a full exploration of its dynamics, which cannot be done in a linearised framework. © 2012 Cambridge University Press.
Yan, Y.; Barth, A.; Beckers, J. M.; Brankart, J. M.; Brasseur, P.; Candille, G.
2017-07-01
In this paper, three incremental analysis update schemes (IAU 0, IAU 50 and IAU 100) are compared in the same assimilation experiments with a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. The difference between the three IAU schemes lies on the position of the increment update window. The relevance of each IAU scheme is evaluated through analyses on both thermohaline and dynamical variables. The validation of the assimilation results is performed according to both deterministic and probabilistic metrics against different sources of observations. For deterministic validation, the ensemble mean and the ensemble spread are compared to the observations. For probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centred random variable (RCRV) score. The obtained results show that 1) the IAU 50 scheme has the same performance as the IAU 100 scheme 2) the IAU 50/100 schemes outperform the IAU 0 scheme in error covariance propagation for thermohaline variables in relatively stable region, while the IAU 0 scheme outperforms the IAU 50/100 schemes in dynamical variables estimation in dynamically active region 3) in case with sufficient number of observations and good error specification, the impact of IAU schemes is negligible. The differences between the IAU 0 scheme and the IAU 50/100 schemes are mainly due to different model integration time and different instability (density inversion, large vertical velocity, etc.) induced by the increment update. The longer model integration time with the IAU 50/100 schemes, especially the free model integration, on one hand, allows for better re-establishment of the equilibrium model state, on the other hand, smooths the strong gradients in dynamically active region.
Marginally Stable Nuclear Burning
Strohmayer, Tod E.; Altamirano, D.
2012-01-01
Thermonuclear X-ray bursts result from unstable nuclear burning of the material accreted on neutron stars in some low mass X-ray binaries (LMXBs). Theory predicts that close to the boundary of stability oscillatory burning can occur. This marginally stable regime has so far been identified in only a small number of sources. We present Rossi X-ray Timing Explorer (RXTE) observations of the bursting, high- inclination LMXB 4U 1323-619 that reveal for the first time in this source the signature of marginally stable burning. The source was observed during two successive RXTE orbits for approximately 5 ksec beginning at 10:14:01 UTC on March 28, 2011. Significant mHz quasi- periodic oscillations (QPO) at a frequency of 8.1 mHz are detected for approximately 1600 s from the beginning of the observation until the occurrence of a thermonuclear X-ray burst at 10:42:22 UTC. The mHz oscillations are not detected following the X-ray burst. The average fractional rms amplitude of the mHz QPOs is 6.4% (3 - 20 keV), and the amplitude increases to about 8% below 10 keV.This phenomenology is strikingly similar to that seen in the LMXB 4U 1636-53. Indeed, the frequency of the mHz QPOs in 4U 1323-619 prior to the X-ray burst is very similar to the transition frequency between mHz QPO and bursts found in 4U 1636-53 by Altamirano et al. (2008). These results strongly suggest that the observed QPOs in 4U 1323-619 are, like those in 4U 1636-53, due to marginally stable nuclear burning. We also explore the dependence of the energy spectrum on the oscillation phase, and we place the present observations within the context of the spectral evolution of the accretion-powered flux from the source.
Numerical experiment with upstream boundary conditions
Directory of Open Access Journals (Sweden)
Huml Jaroslav
2012-04-01
Full Text Available The work deals with a numerical solution of subsonic and transonic ﬂows described by the system of Euler equations in 2D and 3D ﬂows in a channel. Authors used Lax-Wendroff and the multistage Runge-Kutta scheme to numerically solve the ﬂows in a 2D G AMM channel and an extended 3D channel. Authors compare the results achieved by two different upstream boundary conditions in 2D and also in 3D transonic channel ﬂows.