Approximation and stability of three-dimensional natural convection flows in a porous medium

International Nuclear Information System (INIS)

Janotto, Marie-Laurence

1991-01-01

The equations of the three-dimensional natural convection in a porous medium within a differentially heated horizontal walls cavity are solved by a pseudo-spectral method. First we will present the evolution of the two main modes according to two models of convection. A few asymptotic properties connected to the small and large eddies are set up and numerically validated. A new approximate inertial manifold is then proposed. The numerical scheme used is an exponential fitting algorithm the convergence of which is proved. We will present the physical mechanism at the origin of the un-stationary three-dimensional convection at high Rayleigh numbers. (author) [fr

A two-dimensional model for the analysis of radioactive waste contamination in soils: the integral transform method

Energy Technology Data Exchange (ETDEWEB)

Leal, M.A.; Ruperti Junior, N.J. [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil). Coordenacao de Rejeitos Radioativos; Cotta, R.M. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Lab. de Transmissao e Tecnologia do Calor

1997-12-31

A two-dimensional model for the flow and mass transfer of radioactive waste in porous media is investigated. The flow equations are modeled under steady-state Darcy regime assumptions, subjected to discrete boundary source terms. The mass transfer of the contaminant is modeled through the transient convection-diffusion equation, allowing for variable dispersivity coefficients and boundary source functions. The Generalized Integral Transform Technique (GITT) is utilized to provide the proposed hybrid numerical-analytical solution . (author) 12 refs., 3 figs.

The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

Two-dimensional wave propagation in layered periodic media

KAUST Repository

Quezada de Luna, Manuel

2014-09-16

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using highorder homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coeffi cient equations.

Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

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Liping Gao

2017-01-01

Full Text Available In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Science.gov (United States)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

International Nuclear Information System (INIS)

Indekeu, Joseph O; Smets, Ruben

2017-01-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

Numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities

International Nuclear Information System (INIS)

Milioli, F.E.

1985-01-01

In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt

Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

Directory of Open Access Journals (Sweden)

Svetlana S. Vlasova

2016-09-01

Full Text Available The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in the two-dimensional layer with the square heating of a free surface in Stokes's approach is found. The linearization of the Oberbeck–Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.

Two-dimensional nonlinear equations of supersymmetric gauge theories

International Nuclear Information System (INIS)

Savel'ev, M.V.

1985-01-01

Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations

A perturbational h4 exponential finite difference scheme for the convective diffusion equation

International Nuclear Information System (INIS)

Chen, G.Q.; Gao, Z.; Yang, Z.F.

1993-01-01

A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic

Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

International Nuclear Information System (INIS)

Kataoka, Isao; Tomiyama, Akio

2004-01-01

The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

Two dimensional generalizations of the Newcomb equation

International Nuclear Information System (INIS)

Dewar, R.L.; Pletzer, A.

1989-11-01

The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs

Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

International Nuclear Information System (INIS)

Lewandowski, Jerome L.V.

2005-01-01

A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details

TURBO: a computer program for two-dimensional incompressible fluid flow analysis using a two-equations turbulence model

International Nuclear Information System (INIS)

Botelho, D.A.; Moreira, M.L.

1991-06-01

The Reynolds turbulent transport equations for an incompressible fluid are integrated on a bi-dimensional staggered grid, for velocity and pressure, using the SIMPLER method. With the resulting algebraic relations it was developed the TURBO program, which final objectives are the thermal stratification and natural convection analysis of nuclear reactor pools. This program was tested in problems applications with analytic or experimental solutions previously known. (author)

The investigation for (2+1)-dimensional Eckhaus-type extension of the dispersive long wave equation

International Nuclear Information System (INIS)

Yan Zhenya

2004-01-01

The (2+1)-dimensional Eckhaus-type extension of the dispersive long wave (EEDLW) equation is investigated, which was obtained in the appropriate approximation from the basic equations of hydrodynamics. Though it has no Painleve property, we gain an auto-Baecklund transformation (aBT) by truncating the Laurent series expansion at O(w 0 ). In particular, the special one of the aBT establishes a relationship between the EEDLW equation and a set of three linear partial differential equations involving the well-known heat equation. Finally many types of new exact solutions of the EEDLW equation are found from the obtained aBT and some proper ansaetze, which may be useful to explain some physical phenomena

Extreme value statistics for two-dimensional convective penetration in a pre-main sequence star

Science.gov (United States)

Pratt, J.; Baraffe, I.; Goffrey, T.; Constantino, T.; Viallet, M.; Popov, M. V.; Walder, R.; Folini, D.

2017-08-01

Context. In the interior of stars, a convectively unstable zone typically borders a zone that is stable to convection. Convective motions can penetrate the boundary between these zones, creating a layer characterized by intermittent convective mixing, and gradual erosion of the density and temperature stratification. Aims: We examine a penetration layer formed between a central radiative zone and a large convection zone in the deep interior of a young low-mass star. Using the Multidimensional Stellar Implicit Code (MUSIC) to simulate two-dimensional compressible stellar convection in a spherical geometry over long times, we produce statistics that characterize the extent and impact of convective penetration in this layer. Methods: We apply extreme value theory to the maximal extent of convective penetration at any time. We compare statistical results from simulations which treat non-local convection, throughout a large portion of the stellar radius, with simulations designed to treat local convection in a small region surrounding the penetration layer. For each of these situations, we compare simulations of different resolution, which have different velocity magnitudes. We also compare statistical results between simulations that radiate energy at a constant rate to those that allow energy to radiate from the stellar surface according to the local surface temperature. Results: Based on the frequency and depth of penetrating convective structures, we observe two distinct layers that form between the convection zone and the stable radiative zone. We show that the probability density function of the maximal depth of convective penetration at any time corresponds closely in space with the radial position where internal waves are excited. We find that the maximal penetration depth can be modeled by a Weibull distribution with a small shape parameter. Using these results, and building on established scalings for diffusion enhanced by large-scale convective motions, we

Wave dispersion relations in two-dimensional Yukawa systems

International Nuclear Information System (INIS)

Liu Yanhong; Liu Bin; Chen Yanping; Yang Size; Wang Long; Wang Xiaogang

2003-01-01

Collective modes in a two-dimensional Yukawa system are investigated by molecular dynamics simulation in a wide range of coupling parameter Γ and screening strength κ. The dispersion relations and sound speeds of the transverse and longitudinal waves obtained for hexagonal lattice are in agreement with the theoretical results. The negative dispersion of the longitudinal wave is demonstrated. Frequency gaps are found on the dispersion curves of the transverse wave due to scattering of the waves on lattice defects for proper values of Γ. The common frequency of transverse and longitudinal waves drops dramatically with the increasing screening strength κ

A solution of the dispersion-convection equation of radial tracer transportation by the finite element variational method

International Nuclear Information System (INIS)

Hubert, J.

1979-01-01

The variational finite element method (of the Rayleigh-Ritz type) has been applied to solve the standard diffusion-convection equation of radial flow in a dispersive medium. It was shown that the imposing of the boundary condition ΔC/Δx = 0 (=null concentration gradient) introduced great errors in computation results. To remedy it this condition was imposed at the free end of the artifical domain. Its other end joined to the downstream boundary of the investigated domain. The results of calculations compared with the known analytical solutions of the parallel flow show their good accuracy. The method was used to discuss the applicability of the approximate analytical solutions of the radial flow. (author)

Control Operator for the Two-Dimensional Energized Wave Equation

Directory of Open Access Journals (Sweden)

Sunday Augustus REJU

2006-07-01

Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

A two-dimensional embedded-boundary method for convection problems with moving boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2010-01-01

htmlabstractIn this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes

Velocity and Dispersion for a Two-Dimensional Random Walk

International Nuclear Information System (INIS)

Li Jinghui

2009-01-01

In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem. (general)

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

Science.gov (United States)

Wen, Baole; Chini, Gregory P.; Kerswell, Rich R.; Doering, Charles R.

2015-10-01

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu˜PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L =2 √{2 },Nu≤0.106 Pr0Ra5/12 , which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

Science.gov (United States)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Dispersion in two dimensional channels—the Fick-Jacobs approximation revisited

Science.gov (United States)

Mangeat, M.; Guérin, T.; Dean, D. S.

2017-12-01

We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs’ approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we derive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition, a perturbation theory can be developed in \\varepsilon = h_0/L where h 0 is the characteristic channel height and L the period. This perturbation theory confirms the results of Kalinay and Percus (2006 Phys. Rev. E 74 041203), based on the reduction, to one dimensional diffusion are exact at least to {{ O}}(\\varepsilon^6) . Furthermore, we show how the Kalinay and Percus pseudo-linear approximation can be straightforwardly recovered. The approach proposed here can also be exploited to yield exact results in the limit \\varepsilon \\to ∞ , we show that here the diffusion constant remains finite and show how the result can be obtained with a simple physical argument. Moreover, we show that the correction to the effective diffusion constant is of order 1/\\varepsilon and remarkably has some universal characteristics. Numerically we compare the analytic results obtained with exact numerical calculations for a number of interesting channel geometries.

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

Energy Technology Data Exchange (ETDEWEB)

Li, K., E-mail: likai@imech.ac.cn [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100190 (China); Xun, B.; Hu, W. R. [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)

2016-05-15

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

International Nuclear Information System (INIS)

Li, K.; Xun, B.; Hu, W. R.

2016-01-01

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.

Influence of convective conditions on three dimensional mixed convective hydromagnetic boundary layer flow of Casson nanofluid

Energy Technology Data Exchange (ETDEWEB)

Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)

2016-10-15

The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.

Dynamics of two-dimensional solitary vortices in a low-β plasma with convective motion

International Nuclear Information System (INIS)

Makino, Mitsuhiro; Kamimura, Tetsuo; Taniuti, Tosiya.

1980-12-01

Numerical studies of the Hasegawa-Mima equation, derived in the context of drift waves but equivalent to the quasigeostrophic vortex potential equation for Rossby waves, show the stable properties of solitary vortices which are two dimensional, localized, steady and translating solutions of this same equation. A solitary vortex can propagate only in the direction (x-direction) perpendicular to the density gradient. When this solitary vortex solution is inclined at some angle with respect to the x-axis, its propagation direction oscillates in the x and y plane. In two dimensional collisions, i.e. head-on collision and overtaking, solitary vortices interact two-dimensionally and recover their initial shapes at the end of both types of collisions. (author)

Validation of a two-dimensional pollutant dispersion model in an isolated street canyon

Energy Technology Data Exchange (ETDEWEB)

Chan, T.L.; Dong, G.; Leung, C.W.; Cheung, C.S. [The Hong Kong Polytechnic University, Kowloon (Hong Kong). Research Centre for Combustion and Pollution Control, Department of Mechanical Engineering; Hung, W.T. [The Hong Kong Polytechnic University, Kowloon (Hong Kong). Department of Civil and Structural Engineering

2002-07-01

A two-dimensional numerical model based on Reynolds-averaged Navier-Stokes equations coupled with a series of standard, Renormalization Group (RNG) and realizable k-{epsilon} turbulence models was developed to simulate the fluid-flow development and pollutant dispersion within an isolated street canyon using the FLUENT code. In the present study, the validation of the numerical model was evaluated using an extensive experimental database obtained from the atmospheric boundary layer wind tunnel at the Meteorological Institute of Hamburg University, Germany (J. Wind Eng. Ind. Aerodyn. 62 (1996) 37). Among the studied turbulence models, the RNG k-{epsilon} turbulence model was found to be the most optimum turbulence model coupled with the two-dimensional street canyon model developed in the present study. Both the calculated and measured dimensionless pollutant concentrations have been shown to be less dependent on the variation of wind speed and source strength conditions for the studied street canyon aspect ratio of the B/H=1 case. However, the street canyon configuration has significant influence on the pollutant dispersion. The wider street and lower height of the buildings are favorable to pollutant dilution within the street canyon. The fluid-flow development has demonstrated that the rotative vortex or vortices generated within the urban street canyon can transport the pollutants from a line source to the wall surfaces of the buildings. (author)

Recognition of Equations Using a Two-Dimensional Stochastic Context-Free Grammar

Science.gov (United States)

Chou, Philip A.

1989-11-01

We propose using two-dimensional stochastic context-free grammars for image recognition, in a manner analogous to using hidden Markov models for speech recognition. The value of the approach is demonstrated in a system that recognizes printed, noisy equations. The system uses a two-dimensional probabilistic version of the Cocke-Younger-Kasami parsing algorithm to find the most likely parse of the observed image, and then traverses the corresponding parse tree in accordance with translation formats associated with each production rule, to produce eqn I troff commands for the imaged equation. In addition, it uses two-dimensional versions of the Inside/Outside and Baum re-estimation algorithms for learning the parameters of the grammar from a training set of examples. Parsing the image of a simple noisy equation currently takes about one second of cpu time on an Alliant FX/80.

Stabilizing local boundary conditions for two-dimensional shallow water equations

KAUST Repository

Dia, Ben Mansour; Oppelstrup, Jesper

2018-01-01

In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary

A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence

Science.gov (United States)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2018-03-01

We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional extensions. The two dimensional lattice equation we present is linearizable in both directions, and has the Laurent and the coprimeness properties. Moreover, its reduction produces a generalized family of the Heideman-Hogan recurrence. Higher order examples of two dimensional linearizable lattice equations related to the Dana Scott recurrence are also discussed.

Thermal and solutal stratification in mixed convection three-dimensional flow of an Oldroyd-B nanofluid

Directory of Open Access Journals (Sweden)

Tasawar Hayat

Full Text Available This paper investigates the double stratified effects in mixed convection three-dimensional flow of an Oldroyd-B nanofluid. The flow is due to a bidirectional stretching surface. Mathematical analysis is carried out using the temperature and concentration stratification effects. Brownian motion, thermophoresis and chemical reaction effects are also considered. The governing nonlinear boundary layer equations are first converted into the dimensionless ordinary differential equations and then solved for the convergent series solutions of velocity, temperature and nanoparticles concentration. Convergence analysis of the obtained series solutions is also checked and verified. Effects of various emerging parameters are studied in details. Numerical values of local Nusselt and Sherwood numbers are tabulated and analyzed. It is noticed that the impact of mixed convection parameter on temperature and nanoparticles concentration is quite similar. Both temperature and nanoparticles concentration are reduced for larger mixed convection parameter. Keywords: Three-dimensional flow, Oldroyd-B fluid, Nanoparticles, Mixed convection, Thermal and solutal stratification, Chemically reactive species

Unsteady three-dimensional behavior of natural convection in horizontal annulus

International Nuclear Information System (INIS)

Ohya, Toshizo; Miki, Yasutomi; Morita, Kouji; Fukuda, Kenji; Hasegawa, Shu

1988-01-01

An numerical analysis has been performed on unsteady three-dimensional natural convection in a concentric horizontal annulus filled with air. The explicit leap-frog scheme is used for integrating three-dimensional time-dependent equations and the fast Fourier transform (FFT) for solving the Poisson equations for pressure. An oscillatory flow is found to occur at high Rayleigh numbers, which agree qualitatively with the experimental observation made by Bishop et al. An experiment is also conducted to measure temperature fluctuations; a comparison between periods of fluctuations obtained numerically and experimentally shows a good agreement. Numerical calculations yield various statistical parameters of turbulence at higher Rayleigh numbers, which wait experimental verificaions, however. (author)

Heat transfer in a one-dimensional mixed convection loop

International Nuclear Information System (INIS)

Kim, Min Joon; Lee, Yong Bum; Kim, Yong Kyun; Kim, Jong Man; Nam, Ho Yun

1999-01-01

Effects of non-uniform heating in the core and additional forced circulation during decay heat removal operation are studied with a simplified mixed convection loop. The heat transfer coefficient is calculated analytically and measured experimentally. The analytic solution obtained from a one-dimensional heat equation is found to agree well with the experimental results. The effects of the non-uniform heating and the forced circulation are discussed

Risk methodology for geologic disposal of radioactive waste: The distributed velocity method of solving the convective-dispersion equation

Energy Technology Data Exchange (ETDEWEB)

Campbell, James E; Longsine, Dennis E [Sandia National Laboratories, Albuquerque, New Mexico (United States); Reeves, Mark [INTERA Environmental Consultants, Inc. Houston, TX (United States)

1980-06-01

A new method is proposed for treating convective-dispersive transport. The motivation for developing this technique arises from the demands of performing a risk assessment for a nuclear waste repository. These demands include computational efficiency over a relatively large range of Peclet numbers and the ability to handle chains of decaying radionuclides with rather extreme contrasts in both solution velocities and half lives. To the extent it has been tested to date, the Distributed Velocity Method (DVM) appears to satisfy these demands. Included in this paper are the mathematical theory, numerical implementation, an error analysis employing statistical sampling and regression analysis techniques, and comparisons of DVM with other methods for convective-dispersive transport. (author)

Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation

Science.gov (United States)

Cardoso, Wesley B.; Salasnich, Luca; Malomed, Boris A.

2017-05-01

We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self-focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad stability areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

Two dimensional modelling of flood flows and suspended sediment transport: the case of Brenta River

Science.gov (United States)

D'Alpaos, L.; Martini, P.; Carniello, L.

2003-04-01

The paper deals with numerical modelling of flood waves and suspended sediment in plain river basins. The two dimensional depth integrated momentum and continuity equations, modified to take into account of the bottom irregularities that strongly affect the hydrodynamic and the continuity in partially dry areas (for example, during the first stages of a plain flooding and in tidal flows), are solved with a standard Galerkin finite element method using a semi-implicit numerical scheme and considering the role both of the small channel network and the regulation dispositive on the flooding wave propagation. Transport of suspended sediment and bed evolution are coupled with the flood propagation through the convection-dispersion equation and the Exner's equation. Results of a real case study are presented in which the effects of extreme flood of Brenta River (Italy) are examinated. The flooded areas (urban and rural areas) are identified and a mitigation solution based on a diversion channel flowing into Venice Lagoon is proposed. We show that this solution strongly reduces the flood risk in the downstream areas and can provide an important sediment source to the Venice Lagoon. Finally, preliminary results of the sediment dispersion in the Venice Lagoon are presented.

Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media

KAUST Repository

Luna, Manuel

2011-05-01

Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

Science.gov (United States)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

International Nuclear Information System (INIS)

Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

2002-01-01

In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

Science.gov (United States)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

Science.gov (United States)

Ablowitz, Mark; Biondini, Gino; Wang, Qiao

2017-09-01

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

Electromagnetic wave propagation over an inhomogeneous flat earth (two-dimensional integral equation formulation)

International Nuclear Information System (INIS)

de Jong, G.

1975-01-01

With the aid of a two-dimensional integral equation formulation, the ground wave propagation of electromagnetic waves transmitted by a vertical electric dipole over an inhomogeneous flat earth is investigated. For the configuration in which a ground wave is propagating across an ''island'' on a flat earth, the modulus and argument of the attenuation function have been computed. The results for the two-dimensional treatment are significantly more accurate in detail than the calculations using a one-dimensional integral equation

Explicit solutions of two nonlinear dispersive equations with variable coefficients

International Nuclear Information System (INIS)

Lai Shaoyong; Lv Xiumei; Wu Yonghong

2008-01-01

A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa-Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions

A two-column formalism for time-dependent modelling of stellar convection. I. Description of the method

Science.gov (United States)

Stökl, A.

2008-11-01

Context: In spite of all the advances in multi-dimensional hydrodynamics, investigations of stellar evolution and stellar pulsations still depend on one-dimensional computations. This paper devises an alternative to the mixing-length theory or turbulence models usually adopted in modelling convective transport in such studies. Aims: The present work attempts to develop a time-dependent description of convection, which reflects the essential physics of convection and that is only moderately dependent on numerical parameters and far less time consuming than existing multi-dimensional hydrodynamics computations. Methods: Assuming that the most extensive convective patterns generate the majority of convective transport, the convective velocity field is described using two parallel, radial columns to represent up- and downstream flows. Horizontal exchange, in the form of fluid flow and radiation, over their connecting interface couples the two columns and allows a simple circulating motion. The main parameters of this convective description have straightforward geometrical meanings, namely the diameter of the columns (corresponding to the size of the convective cells) and the ratio of the cross-section between up- and downdrafts. For this geometrical setup, the time-dependent solution of the equations of radiation hydrodynamics is computed from an implicit scheme that has the advantage of being unaffected by the Courant-Friedrichs-Lewy time-step limit. This implementation is part of the TAPIR-Code (short for The adaptive, implicit RHD-Code). Results: To demonstrate the approach, results for convection zones in Cepheids are presented. The convective energy transport and convective velocities agree with expectations for Cepheids and the scheme reproduces both the kinetic energy flux and convective overshoot. A study of the parameter influence shows that the type of solution derived for these stars is in fact fairly robust with respect to the constitutive numerical

Two-dimensional behavior of solitons in a low-β plasma with convective motion

International Nuclear Information System (INIS)

Makino, Mitsuhiro; Kamimura, Tetsuo; Sato, Tetsuya.

1981-01-01

The initial value problem of the Hasegawa-Mima (HM) equation, which describes the propagation of drift waves in a low beta magnetized plasma, is numerically studied. Solitons are formed from an initial sinusoidal wave. For a wide range of initial conditions, the number of solitons and the recurrence time agree well with those obtained from the KdV eq. reduced from the HM eq. by Nozaki et al. As a result of nonlinear interactions among different solitons, their peak positions shift in the direction normal to the zeroth order convective motion in a regular but different fashion. When we start from a sinusoidal wave, the peaks of the generated soliton train line up on a line at an angle with respect to the convective direction. Two-deimensional collisions of different solitons are examined. (author)

Introduction to nonlinear dispersive equations

CERN Document Server

Linares, Felipe

2015-01-01

This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

Reactimeter dispersion equation

OpenAIRE

A.G. Yuferov

2016-01-01

The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

A block-iterative nodal integral method for forced convection problems

International Nuclear Information System (INIS)

Decker, W.J.; Dorning, J.J.

1992-01-01

A new efficient iterative nodal integral method for the time-dependent two- and three-dimensional incompressible Navier-Stokes equations has been developed. Using the approach introduced by Azmy and Droning to develop nodal mehtods with high accuracy on coarse spatial grids for two-dimensional steady-state problems and extended to coarse two-dimensional space-time grids by Wilson et al. for thermal convection problems, we have developed a new iterative nodal integral method for the time-dependent Navier-Stokes equations for mechanically forced convection. A new, extremely efficient block iterative scheme is employed to invert the Jacobian within each of the Newton-Raphson iterations used to solve the final nonlinear discrete-variable equations. By taking advantage of the special structure of the Jacobian, this scheme greatly reduces memory requirements. The accuracy of the overall method is illustrated by appliying it to the time-dependent version of the classic two-dimensional driven cavity problem of computational fluid dynamics

Heat transfer through natural convection in a porous saturated medium between two vertical cylinders

Energy Technology Data Exchange (ETDEWEB)

Hasnaoui, M. [Faculte des Sciences Semlalia, Marrakech (Morocco); Vasseur, P.; Bilgen, E.; Robillard, L. [Ecole Polytechnique, Montreal, PQ (Canada)

1993-12-31

A numerical and analytical study of two dimensional, laminar and near steady convection in a vertical porous annular region. The mathematical model was established, basing on Darcy-Oberbeck-Boussinesq equations. The analytical resolution is in the limit where the width of the porous layer is small compared to the cylinders height and it is based on the hypothesis of the parallel flow. (Authors). 4 refs., 4 figs.

Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

KAUST Repository

Zhang, Zhendong

2016-07-26

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yong Chen; Qi Wang

2005-01-01

In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained

Wave-equation dispersion inversion

KAUST Repository

Li, Jing

2016-12-08

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

1998-01-01

The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...

Methods for the solution of the two-dimensional radiation-transfer equation

International Nuclear Information System (INIS)

Weaver, R.; Mihalas, D.; Olson, G.

1982-01-01

We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed

On integrability of a noncommutative q-difference two-dimensional Toda lattice equation

Energy Technology Data Exchange (ETDEWEB)

Li, C.X., E-mail: trisha_li2001@163.com [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Department of Mathematics, College of Charleston, Charleston, SC 29401 (United States); Nimmo, J.J.C., E-mail: jonathan.nimmo@glasgow.ac.uk [School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Shen, Shoufeng, E-mail: mathssf@zjut.edu.cn [Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023 (China)

2015-12-18

In our previous work (C.X. Li and J.J.C. Nimmo, 2009 [18]), we presented a generalized type of Darboux transformations in terms of a twisted derivation in a unified form. The twisted derivation includes ordinary derivatives, forward difference operators, super derivatives and q-difference operators as its special cases. This result not only enables one to recover the known Darboux transformations and quasideterminant solutions to the noncommutative KP equation, the non-Abelian two-dimensional Toda lattice equation, the non-Abelian Hirota–Miwa equation and the super KdV equation, but also inspires us to investigate quasideterminant solutions to q-difference soliton equations. In this paper, we first construct the bilinear Bäcklund transformations for the known bilinear q-difference two-dimensional Toda lattice equation (q-2DTL) and then derive a Lax pair whose compatibility gives a formally different nonlinear q-2DTL equation and finally obtain its quasideterminant solutions by iterating its Darboux transformations. - Highlights: • Examples are given to illustrate the extensive applications of twisted derivations. • Bilinear Bäcklund transformation is constructed for the known q-2DTL equation. • Lax pair is obtained for an equivalent q-2DTL equation. • Quasideterminant solutions are found for the nc q-2DTL equation.

Energy dispersion of charged particles decelerated in a two-dimensional electrostatic field of the type x1/n

International Nuclear Information System (INIS)

Zashkvara, V.V.; Bok, A.A.

1992-01-01

Two components of the spatial dispersion of particles with respect to kinetic energy can be distinguished of the motion of charged particle beams in electrostatic mirros with a two-dimensional field φ(x,y) ans xz symmetry plane. The first is the longitudinal dispersion, which is along the z axis perpendicular to the field; the second is the transverse dispersion, along the x axis parallel to the field vector in the plane of symmetry. The longitudinal dispersion is a basic characteristic of electrostatic mirrors used as energy analyzers. It has been shown that for first-order angular focusing, the longitudinal dispersion, divided by the focal length, is independent of the structure of the two-dimensional field and is a function only of the angle at which the charged particle beam enters the mirror. The transverse dispersion stems from the energy dependence of the penetration depth of the beam as it is decelerated, and it plays an important role when the energy of a charged particle beam is analyzed by the filtering principle, making use of the property of an electrostatic mirror to transmit or reflect charged particles with kinetic energy in a specified interval. This type of dispersion in electrostatic mirrors with two-dimensional fields has not been analyzed systematically. In the present note the authors consider a particular type of two-dimensional electrostatic field which is characterized by a large transverse dispersion, many times larger than in existing electrostatic reflecting filters employing planar and cylindrical fields

Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Palacios, Sergio L.

2004-01-01

We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

Two-dimensional nonlinear string-type equations and their exact integration

International Nuclear Information System (INIS)

Leznov, A.N.; Saveliev, M.V.

1982-01-01

On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions

Solutions of Navier-Stokes Equation with Coriolis Force

Directory of Open Access Journals (Sweden)

Sunggeun Lee

2017-01-01

Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.

Discrete formulation for two-dimensional multigroup neutron diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid

2003-02-01

The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.

Discrete formulation for two-dimensional multigroup neutron diffusion equations

International Nuclear Information System (INIS)

Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid

2003-01-01

The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method

Horizontal structures of velocity and temperature boundary layers in two-dimensional numerical turbulent Rayleigh-Bénard convection

NARCIS (Netherlands)

Zhou, Quan; Sugiyama, K.; Stevens, Richard Johannes Antonius Maria; Grossmann, Siegfried; Lohse, Detlef; Xia, K.

2011-01-01

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-Bénard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra = 108 and the Prandtl

Solution of the two-dimensional space-time reactor kinetics equation by a locally one-dimensional method

International Nuclear Information System (INIS)

Chen, G.S.; Christenson, J.M.

1985-01-01

In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program

Combined effect of thermal dispersion and variable viscosity of non-darcy convection heat transfer in a fluidsaturated porous medium

KAUST Repository

El-Amin, Mohamed

2013-01-01

In this paper, the effects of thermal dispersion and variable viscosity on the non-Darcy free, mixed, and forced convection heat transfer along a vertical flat plate embedded in a fluid-saturated porous medium are investigated. Forchheimer extension is employed in the flow equation to express the non-Darcy model. The fluid viscosity varies as an inverse linear function of temperature. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. Similarity solutions of the governing equations, for an isothermally heated plate, are obtained. Effects of the physical parameters, which govern the problem, on the rate of heat transfer in terms of Nusselt number, the slip velocity, and the boundary layer thickness, for the two cases Darcy and non-Darcy, are shown on graphs or entered in tables. © 2013 by Begell House, Inc.

Approximate solutions for the two-dimensional integral transport equation. The critically mixed methods of resolution

International Nuclear Information System (INIS)

Sanchez, Richard.

1980-11-01

This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr

Three-dimensional numerical simulation of natural convection under the influence of magnetic fields

International Nuclear Information System (INIS)

Moessner, R.

1996-04-01

This report deals with the influence of strong magnetic fields on three-dimensional natural convection. First the dimensionless basic equations are derived in cartesian coordinates. This equations are solved numerically in rectangular domains with a Finite-Difference-Method. The following calculations investigate the flow in an electrically insulated cube which is heated and cooled at side walls. It is possible to perform systematic computations for the variation of the direction of the magnetic field and thermal boundary conditions. (orig.)

Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations

Directory of Open Access Journals (Sweden)

Umer Saeed

2014-01-01

Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

Direct simulation of turbulent Rayleigh-Benard convection in liquid sodium

International Nuclear Information System (INIS)

Woerner, M.

1994-11-01

The numerical results are analysed to investigate both the structures and mechanisms of convection and the statistical features of turbulence in natural convection of liquid metals. The simulations are performed with the finite volume code TURBIT which is extended by a semi-implicit time integration scheme for the energy equation. Due to the implicit treatment of thermal diffusion the computational time for simulation of natural convection in liquid metals is reduced by about one order of magnitude, as compared to the original fully explicit code version. Results for Rayleigh-Benard convection in liquid sodium with Prandtl number Pr=0.006 are given for four different Rayleigh numbers: Ra=3 000, Ra=6 000, Ra=12 000, and Ra=24 000. At the Rayleigh number Ra=3 000 the inertial convection is identified. It is characterized by large two-dimensional vortices, which rotate like a solid body. These vortices are also observed in the simulations for Ra=6 000, Ra=12 000 and Ra=24 000, but, they only exist in certain regions and for short time intervals. The appearance of these two-dimensional structures in three-dimensional, time-dependent and turbulent convection is explained by the relative importance of the non-linear terms in the momentum and energy equation, which is totally different in both equations, and by the coupling of these equations by the buoyancy and the convective term. In order to improve and validate statistical turbulence model for application to natural convection in liquid metals, budgets of turbulence kinetic energy, turbulent heat flux and temperature variance are calculated from the numerical results. For several unknown correlations closure assumptions used in standard turbulence models are analyzed and model coefficients are determined. (orig./HP) [de

Natural convection and dispersion in a tilted fracture

International Nuclear Information System (INIS)

Woods, A.W.; Linz, S.J.

1992-01-01

In many geophysical situations, fluid is contained in long narrow fractures embedded within an impermeable medium of different thermal conductivity; and there may be a uniform vertical temperature gradient imposed upon the system. We show that whenever the slot is tilted to the vertical, convection develops in the fluid, even if the background temperature increases with height. Using typical values for the physical properties of a water-filled fracture, we show that the Earth's geothermal gradient produces a convective flow in a fracture; this has an associated dispersion coefficient D T ∼10 2 -10 3 D in fractures about a centimetre wide. We show that this shear dispersion could transport radioactive material, of half-life 10 4 years, tens of metres along the fracture within one half-life; without this dispersion, the material would only diffuse a few metres along the fracture within one half-life. (author)

Solution of the two- dimensional heat equation for a rectangular plate

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Nurcan BAYKUŞ SAVAŞANERİL

2015-11-01

Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.

Travelling wave solutions and proper solutions to the two-dimensional Burgers-Korteweg-de Vries equation

International Nuclear Information System (INIS)

Feng Zhaosheng

2003-01-01

In this paper, we study the two-dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analysing an equivalent two-dimensional autonomous system, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded travelling wave solution. Then by using a direct method, a travelling solitary wave solution to the 2D-BKdV equation is expressed explicitly, which appears to be more efficient than the existing methods proposed in the literature. At the end of the paper, the asymptotic behaviour of the proper solutions of the 2D-BKdV equation is established by applying the qualitative theory of differential equations

Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

International Nuclear Information System (INIS)

Gligoric, G.; Hadzievski, Lj.; Maluckov, A.; Salasnich, L.; Malomed, B. A.

2009-01-01

The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schroedinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce 'model 1' (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. 'Model 2,' which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2--in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

Formulation of Low Peclet Number Based Grid Expansion Factor for the Solution of the Convection Diffusion Equation

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A. Abdullah

2018-04-01

Full Text Available Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.

Improved scheme for parametrization of convection in the Met Office's Numerical Atmospheric-dispersion Modelling Environment (NAME)

Science.gov (United States)

Meneguz, Elena; Thomson, David; Witham, Claire; Kusmierczyk-Michulec, Jolanta

2015-04-01

NAME is a Lagrangian atmospheric dispersion model used by the Met Office to predict the dispersion of both natural and man-made contaminants in the atmosphere, e.g. volcanic ash, radioactive particles and chemical species. Atmospheric convection is responsible for transport and mixing of air resulting in a large exchange of heat and energy above the boundary layer. Although convection can transport material through the whole troposphere, convective clouds have a small horizontal length scale (of the order of few kilometres). Therefore, for large-scale transport the horizontal scale on which the convection exists is below the global NWP resolution used as input to NAME and convection must be parametrized. Prior to the work presented here, the enhanced vertical mixing generated by non-resolved convection was reproduced by randomly redistributing Lagrangian particles between the cloud base and cloud top with probability equal to 1/25th of the NWP predicted convective cloud fraction. Such a scheme is essentially diffusive and it does not make optimal use of all the information provided by the driving meteorological model. To make up for these shortcomings and make the parametrization more physically based, the convection scheme has been recently revised. The resulting version, presented in this paper, is now based on the balance equation between upward, entrainment and detrainment fluxes. In particular, upward mass fluxes are calculated with empirical formulas derived from Cloud Resolving Models and using the NWP convective precipitation diagnostic as closure. The fluxes are used to estimate how many particles entrain, move upward and detrain. Lastly, the scheme is completed by applying a compensating subsidence flux. The performance of the updated convection scheme is benchmarked against available observational data of passive tracers. In particular, radioxenon is a noble gas that can undergo significant long range transport: this study makes use of observations of

Analytic energies and wave functions of the two-dimensional Schrodinger equation: ground state of two-dimensional quartic potential and classification of solutions

Czech Academy of Sciences Publication Activity Database

Tichý, V.; Kuběna, Aleš Antonín; Skála, L.

2012-01-01

Roč. 90, č. 6 (2012), s. 503-513 ISSN 0008-4204 Institutional support: RVO:67985556 Keywords : Schroninger equation * partial differential equation * analytic solution * anharmonic oscilator * double-well Subject RIV: BE - Theoretical Physics Impact factor: 0.902, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kubena-analytic energies and wave functions of the two-dimensional schrodinger equation.pdf

Stabilizing local boundary conditions for two-dimensional shallow water equations

KAUST Repository

Dia, Ben Mansour

2018-03-27

In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

Science.gov (United States)

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Wave dispersion relation of two-dimensional plasma crystals in a magnetic field

International Nuclear Information System (INIS)

Uchida, G.; Konopka, U.; Morfill, G.

2004-01-01

The wave dispersion relation in a two-dimensional strongly coupled plasma crystal is studied by theoretical analysis and molecular dynamics simulation taking into account a constant magnetic field parallel to the crystal normal. The expression for the wave dispersion relation clearly shows that high-frequency and low-frequency branches exist as a result of the coupling of longitudinal and transverse modes due to the Lorenz force acting on the dust particles. The high-frequency and the low-frequency branches are found to belong to right-hand and left-hand polarized waves, respectively

Wave-equation dispersion inversion

KAUST Repository

Li, Jing; Feng, Zongcai; Schuster, Gerard T.

2016-01-01

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

A New Auto-Baecklund Transformation and Two-Soliton Solution for (3+1)-Dimensional Jimbo-Miwa Equation

International Nuclear Information System (INIS)

Liu Chunping; Zhou Ling

2011-01-01

By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Baecklund transformation (BT) for (3+1)-Dimensional Jimbo-Miwa (JM) equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the (3+1)-Dimensional JM equation is obtained. (general)

Approximate analytical solution of two-dimensional multigroup P-3 equations

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1981-01-01

Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)

Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

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Reza Abazari

2013-01-01

Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.

Family of two-dimensional Born-Infeld equations and a system of conservation laws

International Nuclear Information System (INIS)

Koiv, M.; Rosenhaus, V.

1979-01-01

Lower-order conserved quantities, the ''currents'', for two-dimensional Lorentz-invariant Born-Infeld equation are considered. The currents are divided into pairs, which contain a class (basic currents) leading to the family equations. The basic currents determine the transformations between the solutions of the Born-Infeld eqution family. The equations belonging to the family are fully hodograph-invariant, partly hodograph-invariant, and effectively linear, i.e. non-linear equations with linear image of hodograph transformation

Approximate analytical solution of two-dimensional multigroup P-3 equations

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1981-01-01

Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

Science.gov (United States)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schroedinger equation via ∂-macron-dressing method

International Nuclear Information System (INIS)

Dubrovsky, V.G.; Formusatik, I.B.

2003-01-01

The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular

Vapour-liquid equilibrium properties for two- and three-dimensional Lennard-Jones fluids from equations of state

International Nuclear Information System (INIS)

Mulero, A.; Cuadros, F; Faundez, C.A.

1999-01-01

Vapour-liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour-liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state. Copyright (1999) CSIRO Australia

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

Science.gov (United States)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

International Nuclear Information System (INIS)

Butt, Imran A; Wattis, Jonathan A D

2006-01-01

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2 + 1)-dimensional cubic nonlinear Schroedinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalized (2 + 1)-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does not go to zero with the amplitude; we find that the energy threshold is maximized by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

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Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

Study of mixed convection in sodium pool

International Nuclear Information System (INIS)

Wang Zhou; Chen Yan

1995-01-01

The mixed convection phenomena in the sodium pool of fast reactor have been studied systematically by the two dimensional modeling method. A generalized concept of circumferential line in the cylindrical coordinates was proposed to overcome the three dimensional effect induced by the pool geometry in an analysis of two dimensional modeling. A method of sub-step in time was developed for solving the turbulent equations. The treatments on the boundary condition for the auxiliary velocity field have been proposed, and the explanation of allowing the flow function method to be used in the flow field in presence of a mass source term was given. As examples of verification, the experiments were conducted with water flow in a rectangular cavity. The results from theoretical analysis were applied to the numerical computation for the mixed convection in the cavity. The mechanism of stratified flow in the cavity was studied. A numerical calculation was carried out for the mixed convection in hot plenum of a typical fast reactor

Dispersion modeling of atmospheric contaminants in the Angra Nuclear Power Plant using LES and a new model for the CBL growth

International Nuclear Information System (INIS)

Moreira, Davidson M.; Goulart, Antonio G.; Soares, Pedro M.; Vilhena, Marco T.

2009-01-01

In the present work we report a comparison between experimental data and GILTT approach to simulate radioactive contaminant dispersion in the Atmospheric Boundary Layer using micrometeorological parameters generated by LES (Large Eddy Simulation) in the area around the Angra dos Reis Nuclear Power Plant. Furthermore, starting from the evolution equation for the turbulent energy density spectrum (EDS), we develop a new model for the growth of the turbulence in Convective Boundary Layer (CBL). We apply dimensional analysis to parameterize the unknown inertial transport and convective source term in the dynamic equation for the three-dimensional (3-D) spectrum. The non linear integro-differential equation is solved by Adomian decomposition method. The one-dimensional vertical spectrum is derived from the 3-D spectrum, employing a weight function. This allows us to select the magnitude of the vertical spectral component for the construction of the growing 3-D. Using the micrometeorological parameters generated by LES, for the first time, we employ the vertical component of the energy spectrum to calculate the eddy diffusivity (required in dispersion models). This new eddy diffusivity is used in the simulations of the ground-level concentrations considering experimental data of the Nuclear Power Plant. (author)

Convergence of numerical schemes suitable for two dimensional nonlinear convection: application to the coupling of modes in a plasma

International Nuclear Information System (INIS)

Boukadida, T.

1988-01-01

The compatibility between accuracy and stability of the quasilinear equations is studied. Three stuations are analyzed: the discontinuous P-1 approximation of the first order quasilinear equation, the two dimensional version of the Lax-Friedrichs scheme and the coupling of modes in a plasma. For the one dimensional case, the proposed scheme matches the available data. In the two dimensional case, tests to show the explosion condition are performed. This investigation can be applied in laser-matter interactions, nonlinear optics and in many fields of physics [fr

One-dimensional model of oxygen transport impedance accounting for convection perpendicular to the electrode

Energy Technology Data Exchange (ETDEWEB)

Mainka, J. [Laboratorio Nacional de Computacao Cientifica (LNCC), CMC 6097, Av. Getulio Vargas 333, 25651-075 Petropolis, RJ, Caixa Postal 95113 (Brazil); Maranzana, G.; Thomas, A.; Dillet, J.; Didierjean, S.; Lottin, O. [Laboratoire d' Energetique et de Mecanique Theorique et Appliquee (LEMTA), Universite de Lorraine, 2, avenue de la Foret de Haye, 54504 Vandoeuvre-les-Nancy (France); LEMTA, CNRS, 2, avenue de la Foret de Haye, 54504 Vandoeuvre-les-Nancy (France)

2012-10-15

A one-dimensional (1D) model of oxygen transport in the diffusion media of proton exchange membrane fuel cells (PEMFC) is presented, which considers convection perpendicular to the electrode in addition to diffusion. The resulting analytical expression of the convecto-diffusive impedance is obtained using a convection-diffusion equation instead of a diffusion equation in the case of classical Warburg impedance. The main hypothesis of the model is that the convective flux is generated by the evacuation of water produced at the cathode which flows through the porous media in vapor phase. This allows the expression of the convective flux velocity as a function of the current density and of the water transport coefficient {alpha} (the fraction of water being evacuated at the cathode outlet). The resulting 1D oxygen transport impedance neglects processes occurring in the direction parallel to the electrode that could have a significant impact on the cell impedance, like gas consumption or concentration oscillations induced by the measuring signal. However, it enables us to estimate the impact of convection perpendicular to the electrode on PEMFC impedance spectra and to determine in which conditions the approximation of a purely diffusive oxygen transport is valid. Experimental observations confirm the numerical results. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Turbulent equipartitions in two dimensional drift convection

International Nuclear Information System (INIS)

Isichenko, M.B.; Yankov, V.V.

1995-01-01

Unlike the thermodynamic equipartition of energy in conservative systems, turbulent equipartitions (TEP) describe strongly non-equilibrium systems such as turbulent plasmas. In turbulent systems, energy is no longer a good invariant, but one can utilize the conservation of other quantities, such as adiabatic invariants, frozen-in magnetic flux, entropy, or combination thereof, in order to derive new, turbulent quasi-equilibria. These TEP equilibria assume various forms, but in general they sustain spatially inhomogeneous distributions of the usual thermodynamic quantities such as density or temperature. This mechanism explains the effects of particle and energy pinch in tokamaks. The analysis of the relaxed states caused by turbulent mixing is based on the existence of Lagrangian invariants (quantities constant along fluid-particle or other orbits). A turbulent equipartition corresponds to the spatially uniform distribution of relevant Lagrangian invariants. The existence of such turbulent equilibria is demonstrated in the simple model of two dimensional electrostatically turbulent plasma in an inhomogeneous magnetic field. The turbulence is prescribed, and the turbulent transport is assumed to be much stronger than the classical collisional transport. The simplicity of the model makes it possible to derive the equations describing the relaxation to the TEP state in several limits

An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Wang Qi; Chen Yong; Zhang Hongqing

2005-01-01

With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

A computational procedure for finding multiple solutions of convective heat transfer equations

International Nuclear Information System (INIS)

Mishra, S; DebRoy, T

2005-01-01

In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations

Self-consistent theory of three-dimensional convection in the geomagnetic tail

International Nuclear Information System (INIS)

Birn, J.; Schindler, K.

1983-01-01

The self-consistent theory of time-dependent convection in the earth's magnetotail of Schindler and Birn (1982) is extended to three dimensions to include more realistic tail geometry and three-dimensional flow. We confirm that a steady state solution implies unrealistic tail geometry or large particle or energy losses that are unrealistic during quiet times and conclude therefore that as in the 2-dimensional case the magnetotail becomes time-dependent for typical convection electric fields. Explicit solutions are derived, even analytically, for the three-dimensional flow and the electric and magnetic field in a realistic tail geometry, and quantitative examples are presented. Consequences of time-dependent convection are demonstrated considering two idealized cases of magnetosphere response to solar wind changes: (1) uniform compression as the likely consequence of increasing (static, dynamic or magnetic) solar wind pressure; and (2) compression only in the z direction perpendicular to the plasma sheet as the probable consequence of a dawn to dusk external electric field (E/sub y/>0), corresponding to a southward interplanetary magnetic field component (B/sub z/ 0 with geomagnetic activity. Several other features, already present in the 2-dimensional theory, are confirmed

Comparison of preconditioned generalized conjugate gradient methods to two-dimensional neutron and photon transport equation

International Nuclear Information System (INIS)

Chen, G.S.

1997-01-01

We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)

Transition from boiling to two-phase forced convection

International Nuclear Information System (INIS)

Maroti, L.

1985-01-01

The paper presents a method for the prediction of the boundary points of the transition region between fully developed boiling and two-phase forced convection. It is shown that the concept for the determination of the onset of fully developed boiling can also be applied for the calculation of the point where the heat transfer is effected again by the forced convection. Similarly, the criterion for the onset of nucleate boiling can be used for the definition of the point where boiling is completely suppressed and pure two-phase forced convection starts. To calculate the heat transfer coefficient for the transition region, an equation is proposed that applies the boundary points and a relaxation function ensuring the smooth transition of the heat transfer coefficient at the boundaries

Unstable mixed convective transport in groundwater

International Nuclear Information System (INIS)

Schincariol, R.A.; Schwartz, F.W.

1990-01-01

This study is an experimental investigation of variable density groundwater flow in homogeneous and lenticular porous media. A solution of 500 mg/l Rhodamine WT dye served as the carrier for various concentrations of solute (NaCl) introduced into a two-dimensional flow tank at concentrations ranging from 1000 to 100,000 mg/l. At the scale of the experiments, mass transport depends upon both forced and free convection. In addition, density differences as low as 0.008 g/cm 3 (1000 mg/l NaCl) between a plume of dense water and ambient groundwater in homogeneous medium produces gravitational instabilities at realistic groundwater velocities. These instabilities are manifest by lobe-shaped protuberances that formed first along the bottom edge of the plume and later within the plume. As the density difference increases to 0.0015 g/cm 3 (2000 mg/l NaCl), 0.0037 g/cm 3 (5000 mg/l NaCl) or higher, this unstable mixing due to convective dispersion significantly alters the spreading process, resulting in a large degree of vertical spreading of the plume. In a lenticular medium the combination of convective dispersion and nonuniform flow due to heterogeneities results in relatively large dispersion. Scale considerations indicate that convective dispersion may provide an important component of mixing at the field scale. (Author) (30 refs., 12 figs., 3 tabs.)

One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

Science.gov (United States)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

Dispersion characteristics of two-dimensional unmagnetized dielectric plasma photonic crystal

International Nuclear Information System (INIS)

Li-Mei, Qi; Zi-Qiang, Yang; Feng, Lan; Xi, Gao; Da-Zhi, Li

2010-01-01

This paper studies dispersion characteristics of the transverse magnetic (TM) mode for two-dimensional unmagnetized dielectric plasma photonic crystal by a modified plane wave method. First, the cutoff behaviour is made clear by using the Maxwell–Garnett effective medium theory, and the influences of dielectric filling factor and dielectric constant on effective plasma frequency are analysed. Moreover, the occurence of large gaps in dielectric plasma photonic crystal is demonstrated by comparing the skin depth with the lattice constant, and the influence of plasma frequency on the first three gaps is also studied. Finally, by using the particle-in-cell simulation method, a transmission curve in the Γ – X direction is obtained in dielectric plasma photonic crystal, which is in accordance with the dispersion curves calculated by the modified plane wave method, and the large gap between the transmission points of 27 GHz and 47 GHz is explained by comparing the electric field patterns in particle-in-cell simulation

Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions

Directory of Open Access Journals (Sweden)

Jose Luiz Boldrini

2003-11-01

Full Text Available We study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.

Diffraction of a plane wave on two-dimensional conductive structures and a surface wave

Science.gov (United States)

Davidovich, Mikhael V.

2018-04-01

We consider the structures type of two-dimensional electron gas in the form of a thin conductive, in particular, graphene films described by tensor conductivity, which are isolated or located on the dielectric layers. The dispersion equation for hybrid modes, as well as scattering parameters. We show that free wave (eigenwaves) problem follow from the problem of diffraction when linking the amplitude of the current of the linear equations are unsolvable, i.e., the determinant of this system is zero. As a particular case the dispersion equation follow from the conditions of matching (with zero reflection coefficient).

Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations

Energy Technology Data Exchange (ETDEWEB)

Ohnuki, Akira; Akimoto, Hajime [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kamo, Hideki

1996-11-01

In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A {kappa}-{epsilon} turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)

Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations

International Nuclear Information System (INIS)

Ohnuki, Akira; Akimoto, Hajime; Kamo, Hideki.

1996-11-01

In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A κ-ε turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)

Backlund transformations and three-dimensional lattice equations

NARCIS (Netherlands)

Nijhoff, F.W.; Capel, H.W.; Wiersma, G.L.; Quispel, G.R.W.

1984-01-01

A (nonlocal) linear integral equation is studied, which allows for Bäcklund transformations in the measure. The compatibility of three of these transformations leads to an integrable nonlinear three-dimensional lattice equation. In appropriate continuum limits the two-dimensional Toda-lattice

Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1997-01-01

The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

An acoustic-convective splitting-based approach for the Kapila two-phase flow model

Energy Technology Data Exchange (ETDEWEB)

Eikelder, M.F.P. ten, E-mail: m.f.p.teneikelder@tudelft.nl [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Daude, F. [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); IMSIA, UMR EDF-CNRS-CEA-ENSTA 9219, Université Paris Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau (France); Koren, B.; Tijsseling, A.S. [Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

2017-02-15

In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.

Dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals

International Nuclear Information System (INIS)

Hojo, Hitoshi; Mase, Atsushi

2004-01-01

The dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals is studied. The plasma photonic crystal is a periodic array composed of alternating thin plasma and dielectric material. The dispersion relation is obtained by solving a Maxwell wave equation using a method analogous to Kronig-Penny's problem in quantum mechanics, and it is found that the frequency gap and cut-off appear in the dispersion relation. The frequency gap is shown to become larger with the increase of the plasma density as well as plasma width. (author)

Steady, three-dimensional, internally heated convection

International Nuclear Information System (INIS)

Schubert, G.; Glatzmaier, G.A.; Travis, B.

1993-01-01

Numerical calculations have been carried out of steady, symmetric, three-dimensional modes of convection in internally heated, infinite Prandtl number, Boussinesq fluids at a Rayleigh number of 1.4x10 4 in a spherical shell with inner/outer radius of 0.55 and in a 3x3x1 rectangular box. Multiple patterns of convection occur in both geometries. In the Cartesian geometry the patterns are dominated by cylindrical cold downflows and a broad hot upwelling. In the spherical geometry the patterns consist of cylindrical cold downwellings centered either at the vertices of a tetrahedron or the centers of the faces of a cube. The cold downflow cylinders are immersed in a background of upwelling within which there are cylindrical hot concentrations (plumes) and hot halos around the downflows. The forced hot upflow return plumes of internally heated spherical convection are fundamentally different from the buoyancy-driven plumes of heated from below convection

Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method

International Nuclear Information System (INIS)

Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.

2007-01-01

In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple

Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

International Nuclear Information System (INIS)

Berthe, P.M.

2013-01-01

In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

Dynamics in discrete two-dimensional nonlinear Schrödinger equations in the presence of point defects

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim

1996-01-01

The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...... of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped...... narrow spikes. The influence of the point impurities on this dynamics is also investigated....

Analysis and Application of High Resolution Numerical Perturbation Algorithm for Convective-Diffusion Equation

International Nuclear Information System (INIS)

Gao Zhi; Shen Yi-Qing

2012-01-01

The high resolution numerical perturbation (NP) algorithm is analyzed and tested using various convective-diffusion equations. The NP algorithm is constructed by splitting the second order central difference schemes of both convective and diffusion terms of the convective-diffusion equation into upstream and downstream parts, then the perturbation reconstruction functions of the convective coefficient are determined using the power-series of grid interval and eliminating the truncated errors of the modified differential equation. The important nature, i.e. the upwind dominance nature, which is the basis to ensuring that the NP schemes are stable and essentially oscillation free, is firstly presented and verified. Various numerical cases show that the NP schemes are efficient, robust, and more accurate than the original second order central scheme

Travelling wave solutions of two-dimensional Korteweg-de Vries-Burgers and Kadomtsev-Petviashvili equations

International Nuclear Information System (INIS)

Estevez, P G; Kuru, S; Negro, J; Nieto, L M

2006-01-01

The travelling wave solutions of the two-dimensional Korteweg-de Vries-Burgers and Kadomtsev-Petviashvili equations are studied from two complementary points of view. The first one is an adaptation of the factorization technique that provides particular as well as general solutions. The second one applies the Painleve analysis to both equations, throwing light on some aspects of the first method and giving an explanation to some restriction on the coefficients, as well as the relation between factorizations and integrals of motion

Long-range transmission of pollutants simulated by a two-dimensional pseudospectral dispersion model

International Nuclear Information System (INIS)

Prahm, L.P.; Christensen, O.

1977-01-01

The pseudospectral dispersion model (Christensen and Prahm, 1976) is adapted for simulation of the long-range transmission of sulphur pollutants in the European region, covering an area of about 4000 km x 4000 km. Regional ''background'' concentrations of sulphur oxides are found to be highly dependent on distant sources and to correlate poorly with local source strength during the considered three- and four-day episodes. The simulation is based on emission data, given in squares of about 50 km x 50 km and on synoptic wind fields derived from observed wind velocities of the 850 mb level and the surface level. The two-dimensional model includes a constant vertical mixing depth. Appropriate values for the deposition and the transformation rates of SO 2 and SO/sup 4 are used. The concentration of pollutants computed from the two-dimensional pseudospectral dispersion model reflects the variable meteorological conditions. Computed concentrations are compared with measurements, giving spatial correlations between 0.4 and 0.8 for more than 400 ground-based 24 h mean values, and a spatial correlation of 0.9 for eight aircraft samples averaged over approx.30 min. A discussion of the influence of different sources of error in the model simulation is given. The high numerical accuracy of the pseudospectral model is combined with a modest consumption of CPU computer time. This study is the first application of the pseudospectral dispersion model which compares computed concentrations with measured field data. The model has possible applications as a tool for assessment of the impact of both national and international emission regulation strategies

Solution of Schroedinger Equation for Two-Dimensional Complex Quartic Potentials

International Nuclear Information System (INIS)

Singh, Ram Mehar; Chand, Fakir; Mishra, S. C.

2009-01-01

We investigate the quasi-exact solutions of the Schroedinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x 1 + ip 3 , y = x 2 + ip 4 , p x = p 1 + ix 3 , p y = p 2 + ix 4 . Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out. (general)

Dispersion equations for field-aligned cyclotron waves in axisymmetric magnetospheric plasmas

Directory of Open Access Journals (Sweden)

N. I. Grishanov

2006-03-01

Full Text Available In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.

Modeling mantle convection in the spherical annulus

Science.gov (United States)

Hernlund, John W.; Tackley, Paul J.

2008-12-01

Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.

Thermal investigation of an infrared reflow oven with a convection fan

International Nuclear Information System (INIS)

Kim, Mi Ro; Choi, Young Ki; Lee, Jung Hee; Lee, Gyu Bong; Chung, Il Yong; Kim, Jung Duck

1998-01-01

A two-dimensional numerical model for an infrared reflow soldering with a convection fan is used by modifying the Eftychiou's numerical modeling. The two-dimensional tunnel model which predicts convective conditions within the reflow oven are solved using the finite volume method with the SIMPLER algorithm. The card model solves the transient two-dimensional heat conduction equation in conjunction with a radiative heat transfer analysis. We also performed an experiment to validate the numerical modeling. The numerical result shows excellent agreement with experimental data. Based on the capability of this model, parametric simulations are performed to determine the thermal response of the solder to variations in the oven operating conditions and heat transfer conditions. This study shows that radiation and conveyor velocity are important factors in the preheat region

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Directory of Open Access Journals (Sweden)

Elmira Ashpazzadeh

2018-04-01

Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection.

Science.gov (United States)

van der Poel, Erwin P; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, Detlef

2014-07-01

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10(8) and 10(11) the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra ≥ 10(10). Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions

International Nuclear Information System (INIS)

Ohtani, Nobuo

1976-01-01

A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)

An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

International Nuclear Information System (INIS)

Fujita, Y.

2001-01-01

In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

A numerical three-dimensional ocean general circulation and radionuclides dispersion model

International Nuclear Information System (INIS)

Chartier, M.; Marti, O.

1988-01-01

The dispersion of radioactive waste disposed of in the deep-sea or transferred from the atmosphere is a complex hydrodynamic problem concerned by space scales as large as the world ocean. The recent development in the high-speed computers has led to significant progress in ocean modelling and now allows a thorough improvement in the accuracy of the simulations of the nuclides dispersion in the sea. A three-dimensional ocean general circulation model has been recently developed in France for research and engineering purposes. The model solves the primitive equation of the ocean hydrodynamics and the advection-diffusion equation for any dissolved tracer. The code has been fully vectorized and multitasked on 1 to 4 processors of the CRAY-2

Solution of two-dimensional equations of neutron transport in 4P0-approximation of spherical harmonics method

International Nuclear Information System (INIS)

Polivanskij, V.P.

1989-01-01

The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs

On a method of construction of exact solutions for equations of two-dimensional hydrodynamics of incompressible liquids

International Nuclear Information System (INIS)

Yurov, A.V.; Yurova, A.A.

2006-01-01

The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru

A regularization of the Burgers equation using a filtered convective velocity

International Nuclear Information System (INIS)

Norgard, Greg; Mohseni, Kamran

2008-01-01

This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations

Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

International Nuclear Information System (INIS)

Takeshi, Y.; Keisuke, K.

1983-01-01

The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method

Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method

International Nuclear Information System (INIS)

Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.

2010-01-01

The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.

Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

KAUST Repository

Vignal, Philippe

2015-06-01

In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

The simulation of two-dimensional migration patterns - a novel approach

International Nuclear Information System (INIS)

Villar, Heldio Pereira

1997-01-01

A novel approach to the problem of simulation of two-dimensional migration of solutes in saturated soils is presented. In this approach, the two-dimensional advection-dispersion equation is solved by finite-differences in a stepwise fashion, by employing the one-dimensional solution first in the direction of flow and then perpendicularly, using the same time increment in both cases. As the results of this numerical model were to be verified against experimental results obtained by radioactive tracer experiments, an attenuation factor, to account for the contribution of the gamma rays emitted by the whole plume of tracer to the readings of the adopted radiation detectors, was introduced into the model. The comparison between experimental and simulated concentration contours showed good agreement, thus establishing the feasibility of the approach proposed herein. (author)

Natural convection of nanofluids over a convectively heated vertical plate embedded in a porous medium

Energy Technology Data Exchange (ETDEWEB)

Ghalambaz, M.; Noghrehabadi, A.; Ghanbarzadeh, A., E-mail: m.ghalambaz@gmail.com, E-mail: ghanbarzadeh.a@scu.ac.ir [Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz (Iran, Islamic Republic of)

2014-04-15

In this paper, the natural convective flow of nanofluids over a convectively heated vertical plate in a saturated Darcy porous medium is studied numerically. The governing equations are transformed into a set of ordinary differential equations by using appropriate similarity variables, and they are numerically solved using the fourth-order Runge-Kutta method associated with the Gauss-Newton method. The effects of parametric variation of the Brownian motion parameter (Nb), thermophoresis parameter (Nt) and the convective heating parameter (Nc) on the boundary layer profiles are investigated. Furthermore, the variation of the reduced Nusselt number and reduced Sherwood number, as important parameters of heat and mass transfer, as a function of the Brownian motion, thermophoresis and convective heating parameters is discussed in detail. The results show that the thickness of the concentration profiles is much lower than the temperature and velocity profiles. For low values of the convective heating parameter (Nc), as the Brownian motion parameter increases, the non-dimensional wall temperature increases. However, for high values of Nc, the effect of the Brownian motion parameter on the non-dimensional wall temperature is not significant. As the Brownian motion parameter increases, the reduced Sherwood number increases and the reduced Nusselt number decreases. (author)

The numerical simulation of convection delayed dominated diffusion equation

Directory of Open Access Journals (Sweden)

Mohan Kumar P. Murali

2016-01-01

Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.

ADI as a preconditioning for solving the convection-diffusion equation

International Nuclear Information System (INIS)

Chin, R.C.Y.; Manteuffel, T.A.; De Pillis, J.

1984-01-01

The authors examine a splitting of the operator obtained from a steady convection-diffusion equation with variable coefficients in which the convection term dominates. The operator is split into a dominant and subdominant parts consistent with the inherent directional property of the partial differential equation. The equations involving the dominant parts should be easily solved. The authors accelerate the convergence of this splitting or the outer iteration by a Chebyshev semi-iterative method. When the dominant part has constant coefficients, it can be easily solved using alternating direction implicit (ADI) methods. This is called the inner iteration. The optimal parameters for a stationary two-parameter ADI method are obtained when the eigenvalues become complex. This corresponds to either the horizontal or the vertical half-grid Reynolds number larger than unity. The Chebyshev semi-iterative method is used to accelerate the convergence of the inner ADI iteration. A two-fold increase in speed is obtained when the ADI iteration matrix has real eigenvalues, and the increase is less significant when the eigenvalues are complex. If either the horizontal or the vertical half-grid Reynolds number is equal to one, the spectral radius of the optimal ADI iterative matrix is zero. However, a high degree of nilpotency impairs rapid convergence. This problem is removed by introducing a more implicit iterative method called ADI/Gauss-Seidel (ADI/GS). ADI/GS resolves the nilpotency and, thus, converges more rapidly for half-grid Reynolds number near 1. Finally, these methods are compared with several well-known schemes on test problems. 23 references, 5 figures

A collective variable approach and stabilization for dispersion-managed optical solitons in the quintic complex Ginzburg-Landau equation as perturbations of the nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C

2006-01-01

With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods

A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

KAUST Repository

Allen, Rebecca

2013-01-01

The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently

Deferred correction approach on generic transport equation

International Nuclear Information System (INIS)

Shah, I.A.; Ali, M.

2004-01-01

In this study, a two dimensional Steady Convection-Diffusion was solved, using Deferred correction approach, and results were compared with standard spatial discretization schemes. Numerical investigations were carried out based on the velocity and flow direction, for various diffusivity coefficients covering a range from diffusive to convective flows. The results show that the Deferred Ted Correction Approach gives more accurate and stable results in relation to UDS and CDs discretization of convective terms. Deferred Correction Approach caters for the wiggles for convective flows in case of central difference discretization of the equation and also caters for the dissipative error generated by the first order upwind discretization of convective fluxes. (author)

Skeletonized wave equation of surface wave dispersion inversion

KAUST Repository

Li, Jing; Schuster, Gerard T.

2016-01-01

We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel

A family of analytical solutions of a nonlinear diffusion-convection equation

Science.gov (United States)

Hayek, Mohamed

2018-01-01

Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.

Study of two-dimensional interchange turbulence

International Nuclear Information System (INIS)

Sugama, Hideo; Wakatani, Masahiro.

1990-04-01

An eddy viscosity model describing enstrophy transfer in two-dimensional turbulence is presented. This model is similar to that of Canuto et al. and provides an equation for the energy spectral function F(k) as a function of the energy input rate to the system per unit wavenumber, γ s (k). In the enstrophy-transfer inertial range, F(k)∝ k -3 is predicted by the model. The eddy viscosity model is applied to the interchange turbulence of a plasma in shearless magnetic field. Numerical simulation of the two-dimensional interchange turbulence demonstrates that the energy spectrum in the high wavenumber region is well described by this model. The turbulent transport driven by the interchange turbulence is expressed in terms of the Nusselt number Nu, the Rayleigh number Ra and Prantl number Pr in the same manner as that of thermal convection problem. When we use the linear growth rate for γ s (k), our theoretical model predicts that Nu ∝ (Ra·Pr) 1/2 for a constant background pressure gradient and Nu ∝ (Ra·Pr) 1/3 for a self-consistent background pressure profile with the stress-free slip boundary conditions. The latter agrees with our numerical result showing Nu ∝ Ra 1/3 . (author)

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Skeletonized wave equation of surface wave dispersion inversion

KAUST Repository

Li, Jing

2016-09-06

We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube

International Nuclear Information System (INIS)

Nigmatulin, R.I.

1995-01-01

The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered

Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube

Energy Technology Data Exchange (ETDEWEB)

Nigmatulin, R.I.

1995-09-01

The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered.

Investigation of the use of Prandtl/Navier--Stokes equation procedures for two-dimensional incompressible flows

International Nuclear Information System (INIS)

Anderson, C.R.; Reider, M.B.

1994-01-01

The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown

Solving the two-dimensional stationary transport equation with the aid of the nodal method

International Nuclear Information System (INIS)

Mesina, M.

1976-07-01

In this document the two-dimensional stationary transport equation for the geometry of a fuel assembly or for a system of square boxes has been formulated as an algebraic eigenvalue problem, and the solution was achieved with the computer code NODE 2 which was developed for this purpose. (orig.) [de

An integrable (2+1)-dimensional Toda equation with two discrete variables

International Nuclear Information System (INIS)

Cao Cewen; Cao Jianli

2007-01-01

An integrable (2+1)-dimensional Toda equation with two discrete variables is presented from the compatible condition of a Lax triad composed of the ZS-AKNS (Zakharov, Shabat; Ablowitz, Kaup, Newell, Segur) eigenvalue problem and two discrete spectral problems. Through the nonlinearization technique, the Lax triad is transformed into a Hamiltonian system and two symplectic maps, respectively, which are integrable in the Liouville sense, sharing the same set of integrals, functionally independent and involutive with each other. In the Jacobi variety of the associated algebraic curve, both the continuous and the discrete flows are straightened out by the Abel-Jacobi coordinates, and are integrated by quadratures. An explicit algebraic-geometric solution in the original variable is obtained by the Riemann-Jacobi inversion

The simulation of two-dimensional migration patterns - a novel approach

Energy Technology Data Exchange (ETDEWEB)

Villar, Heldio Pereira [Universidade de Pernambuco, Recife, PE (Brazil). Escola Politecnica]|[Centro Regional de Ciencias Nucleares, Recife, PE (Brazil)

1997-12-31

A novel approach to the problem of simulation of two-dimensional migration of solutes in saturated soils is presented. In this approach, the two-dimensional advection-dispersion equation is solved by finite-differences in a stepwise fashion, by employing the one-dimensional solution first in the direction of flow and then perpendicularly, using the same time increment in both cases. As the results of this numerical model were to be verified against experimental results obtained by radioactive tracer experiments, an attenuation factor, to account for the contribution of the gamma rays emitted by the whole plume of tracer to the readings of the adopted radiation detectors, was introduced into the model. The comparison between experimental and simulated concentration contours showed good agreement, thus establishing the feasibility of the approach proposed herein. (author) 6 refs., 6 figs.

Dispersion and damping of two-dimensional dust acoustic waves: theory and simulation

International Nuclear Information System (INIS)

Upadhyaya, Nitin; Miskovic, Z L; Hou, L-J

2010-01-01

A two-dimensional generalized hydrodynamics (GH) model is developed to study the full spectrum of both longitudinal and transverse dust acoustic waves (DAW) in strongly coupled complex (dusty) plasmas, with memory-function-formalism being implemented to enforce high-frequency sum rules. Results are compared with earlier theories (such as quasi-localized charge approximation and its extended version) and with a self-consistent Brownian dynamics simulation. It is found that the GH approach provides a good account, not only of dispersion relations, but also of damping rates of the DAW modes in a wide range of coupling strengths, an issue hitherto not fully addressed for dusty plasmas.

Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

KAUST Repository

Icardi, Matteo

2014-07-31

In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed. © 2014 American Physical Society.

Mathematical modeling of disperse two-phase flows

CERN Document Server

Morel, Christophe

2015-01-01

This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, a...

Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

Directory of Open Access Journals (Sweden)

Musa Danjuma SHEHU

2008-06-01

Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

New continual analogs of two-dimensional Toda lattices related with nonlinear integro-differential equations

International Nuclear Information System (INIS)

Savel'ev, M.V.

1988-01-01

Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the corresponding class of the initial discrete system solutions is discussed. The latter takes place, in particular, for the kernel coinciding with the causal function

An upscaled two-equation model of transport in porous media through unsteady-state closure of volume averaged formulations

Science.gov (United States)

Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.

2012-04-01

We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell

Analytical solutions for one-dimensional advection–dispersion ...

Indian Academy of Sciences (India)

We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0.

A Fibonacci collocation method for solving a class of Fredholm–Volterra integral equations in two-dimensional spaces

Directory of Open Access Journals (Sweden)

Farshid Mirzaee

2014-06-01

Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.

A Fokker-Planck-Landau collision equation solver on two-dimensional velocity grid and its application to particle-in-cell simulation

Energy Technology Data Exchange (ETDEWEB)

Yoon, E. S.; Chang, C. S., E-mail: cschang@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Korea Advanced Institute of Science and Technology, Yuseong-gu, DaeJeon 305-701 (Korea, Republic of)

2014-03-15

An approximate two-dimensional solver of the nonlinear Fokker-Planck-Landau collision operator has been developed using the assumption that the particle probability distribution function is independent of gyroangle in the limit of strong magnetic field. The isotropic one-dimensional scheme developed for nonlinear Fokker-Planck-Landau equation by Buet and Cordier [J. Comput. Phys. 179, 43 (2002)] and for linear Fokker-Planck-Landau equation by Chang and Cooper [J. Comput. Phys. 6, 1 (1970)] have been modified and extended to two-dimensional nonlinear equation. In addition, a method is suggested to apply the new velocity-grid based collision solver to Lagrangian particle-in-cell simulation by adjusting the weights of marker particles and is applied to a five dimensional particle-in-cell code to calculate the neoclassical ion thermal conductivity in a tokamak plasma. Error verifications show practical aspects of the present scheme for both grid-based and particle-based kinetic codes.

Reduction of infinite dimensional equations

Directory of Open Access Journals (Sweden)

Zhongding Li

2006-02-01

Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

Application of Gaussian cubature to model two-dimensional population balances

Directory of Open Access Journals (Sweden)

Bałdyga Jerzy

2017-09-01

Full Text Available In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

Transitional dispersive scenarios driven by mesoscale flows on complex terrain under strong dry convective conditions

Directory of Open Access Journals (Sweden)

J. L. Palau

2009-01-01

Full Text Available By experimentation and modelling, this paper analyses the atmospheric dispersion of the SO₂ emissions from a power plant on complex terrain under strong convective conditions, describing the main dispersion features as an ensemble of "stationary dispersive scenarios" and reformulating some "classical" dispersive concepts to deal with the systematically monitored summer dispersive scenarios in inland Spain. The results and discussions presented arise from a statistically representative study of the physical processes associated with the multimodal distribution of pollutants aloft and around a 343-m-tall chimney under strong dry convective conditions in the Iberian Peninsula. This paper analyses the importance of the identification and physical implications of transitional periods for air quality applications. The indetermination of a transversal plume to the preferred transport direction during these transitional periods implies a small (or null physical significance of the classical definition of horizontal standard deviation of the concentration distribution.

RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry

International Nuclear Information System (INIS)

Valle, Edmundo del; Mund, Ernest H.

2004-01-01

This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature

Two parameters Lie group analysis and numerical solution of unsteady free convective flow of non-Newtonian fluid

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M.J. Uddin

2016-09-01

Full Text Available The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate for methanol are higher (lower than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate factor of Newtonian fluid is higher (lower than the dilatant fluid.

Osmotic dehydration and convective drying of coconut slices: Experimental determination and description using one-dimensional diffusion model

Directory of Open Access Journals (Sweden)

Wilton Pereira da Silva

2014-06-01

Full Text Available Mass migrations in coconut slices during osmotic dehydration and drying are described using a diffusion model with boundary condition of the third kind. The osmotic dehydration experiment was performed at 35°Brix (water and sucrose and 40 °C. The convective drying experiments were performed at 50, 60 and 70 °C. The one-dimensional solution of the diffusion equation for an infinite slab was coupled with an optimizer to determine the effective mass diffusivities D and convective mass transfer coefficients h of the five processes studied. The analyses of the obtained results indicate that there is a good agreement between each experimental dataset and the corresponding simulation using D and h determined by optimization.

Construction and analysis of lattice Boltzmann methods applied to a 1D convection-diffusion equation

International Nuclear Information System (INIS)

Dellacherie, Stephane

2014-01-01

To solve the 1D (linear) convection-diffusion equation, we construct and we analyze two LBM schemes built on the D1Q2 lattice. We obtain these LBM schemes by showing that the 1D convection-diffusion equation is the fluid limit of a discrete velocity kinetic system. Then, we show in the periodic case that these LBM schemes are equivalent to a finite difference type scheme named LFCCDF scheme. This allows us, firstly, to prove the convergence in L∞ of these schemes, and to obtain discrete maximum principles for any time step in the case of the 1D diffusion equation with different boundary conditions. Secondly, this allows us to obtain most of these results for the Du Fort-Frankel scheme for a particular choice of the first iterate. We also underline that these LBM schemes can be applied to the (linear) advection equation and we obtain a stability result in L∞ under a classical CFL condition. Moreover, by proposing a probabilistic interpretation of these LBM schemes, we also obtain Monte-Carlo algorithms which approach the 1D (linear) diffusion equation. At last, we present numerical applications justifying these results. (authors)

The effect of near-surface convection on oscillation frequencies of stars

Science.gov (United States)

Hanasoge, Shravan

2015-08-01

Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modelled frequencies, a phenomenon referred to as the “surface term”. The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modelling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelength (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary 3-D flows, can be reduced to an effective “quiet-Sun” wave equation with altered sound speed, Brünt-Väisäla frequency and Lamb frequency. We derive the modified wave equation and relations for the appropriate averaging of three dimensional flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from three dimensional numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies, and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging.

Science.gov (United States)

Park, Jae-Hyeung; Kim, Hak-Rin; Kim, Yunhee; Kim, Joohwan; Hong, Jisoo; Lee, Sin-Doo; Lee, Byoungho

2004-12-01

A depth-enhanced three-dimensional-two-dimensional convertible display that uses a polymer-dispersed liquid crystal based on the principle of integral imaging is proposed. In the proposed method, a lens array is located behind a transmission-type display panel to form an array of point-light sources, and a polymer-dispersed liquid crystal is electrically controlled to pass or to scatter light coming from these point-light sources. Therefore, three-dimensional-two-dimensional conversion is accomplished electrically without any mechanical movement. Moreover, the nonimaging structure of the proposed method increases the expressible depth range considerably. We explain the method of operation and present experimental results.

Transition to the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection

Science.gov (United States)

Zhu, Xiaojue; Mathai, Varghese; Stevens, Richard J. A. M.; Verzicco, Roberto; Lohse, Detlef

2018-04-01

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962), 10.1063/1.1706533]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to 1 014 for Prandtl number Pr =1 , for the first time in numerical simulations we find the transition to the ultimate regime, namely, at Ra*=1013 . We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling Nu ˜Ra1 /3 [Proc. R. Soc. A 225, 196 (1954), 10.1098/rspa.1954.0197]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely, within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu ˜Ra0.38 , corresponding to the effective scaling in the ultimate regime.

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Institute of Scientific and Technical Information of China (English)

Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN

2017-01-01

Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Martin, D.U.; Yuen, H.C.; Saffman, P.G.

1980-01-01

The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)

Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation

CERN Document Server

Serdyukova, S I

2000-01-01

For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-k

dimensional Jaulent–Miodek equations

Indian Academy of Sciences (India)

(2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...

One-dimensional reduction of the three-dimenstional Gross-Pitaevskii equation with two- and three-body interactions

International Nuclear Information System (INIS)

Cardoso, W. B.; Avelar, A. T.; Bazeia, D.

2011-01-01

We deal with the three-dimensional Gross-Pitaevskii equation which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation,controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.

Local multiplicative Schwarz algorithms for convection-diffusion equations

Science.gov (United States)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Panel summary report

International Nuclear Information System (INIS)

Gutjahr, A.L.; Kincaid, C.T.; Mercer, J.W.; Murarka, I.P.; Siegel, M.D.; Wierenga, P.J.

1987-01-01

The objective of this report is to summarize the various modeling approaches that were used to simulate solute transport in a variably saturated emission. In particular, the technical strengths and weaknesses of each approach are discussed, and conclusions and recommendations for future studies are made. Five models are considered: (1) one-dimensional analytical and semianalytical solutions of the classical deterministic convection-dispersion equation (van Genuchten, Parker, and Kool, this report ); (2) one-dimensional simulation using a continuous-time Markov process (Knighton and Wagenet, this report); (3) one-dimensional simulation using the time domain method and the frequency domain method (Duffy and Al-Hassan, this report); (4) one-dimensional numerical approach that combines a solution of the classical deterministic convection-dispersion equation with a chemical equilibrium speciation model (Cederberg, this report); and (5) three-dimensional numerical solution of the classical deterministic convection-dispersion equation (Huyakorn, Jones, Parker, Wadsworth, and White, this report). As part of the discussion, the input data and modeling results are summarized. The models were used in a data analysis mode, as opposed to a predictive mode. Thus, the following discussion will concentrate on the data analysis aspects of model use. Also, all the approaches were similar in that they were based on a convection-dispersion model of solute transport. Each discussion addresses the modeling approaches in the order listed above

A generalized advection dispersion equation

Indian Academy of Sciences (India)

This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.

Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation

Science.gov (United States)

Charalampidis, E. G.; Kevrekidis, P. G.; Farrell, P. E.

2018-01-01

In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two-dimensional nonlinear Schrödinger equation with a parabolic trap and repulsive interactions. Despite the fact that this system has been studied extensively, we discover a wide variety of previously unknown branches of solutions. We analyze the stability of the newly discovered branches and discuss the bifurcations that relate them to known solutions both in the near linear (Cartesian, as well as polar) and in the highly nonlinear regimes. While deflated continuation is not guaranteed to compute the full bifurcation diagram, this analysis is a potent demonstration that the algorithm can discover new nonlinear states and provide insights into the energy landscape of complex high-dimensional Hamiltonian dynamical systems.

Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

International Nuclear Information System (INIS)

Ravi Kanth, A.S.V.; Aruna, K.

2009-01-01

In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

Equivalence of two-dimensional gravities

International Nuclear Information System (INIS)

Mohammedi, N.

1990-01-01

The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given

On the methods for determining the transverse dispersion coefficient in river mixing

Science.gov (United States)

Baek, Kyong Oh; Seo, Il Won

2016-04-01

In this study, the strengths and weaknesses of existing methods for determining the dispersion coefficient in the two-dimensional river mixing model were assessed based on hydraulic and tracer data sets acquired from experiments conducted on either laboratory channels or natural rivers. From the results of this study, it can be concluded that, when the longitudinal dispersion coefficient as well as the transverse dispersion coefficients must be determined in the transient concentration situation, the two-dimensional routing procedures, 2D RP and 2D STRP, can be employed to calculate dispersion coefficients among the observation methods. For the steady concentration situation, the STRP can be applied to calculate the transverse dispersion coefficient. When the tracer data are not available, either theoretical or empirical equations by the estimation method can be used to calculate the dispersion coefficient using the geometric and hydraulic data sets. Application of the theoretical and empirical equations to the laboratory channel showed that equations by Baek and Seo [[3], 2011] predicted reasonable values while equations by Fischer [23] and Boxwall and Guymer (2003) overestimated by factors of ten to one hundred. Among existing empirical equations, those by Jeon et al. [28] and Baek and Seo [6] gave the agreeable values of the transverse dispersion coefficient for most cases of natural rivers. Further, the theoretical equation by Baek and Seo [5] has the potential to be broadly applied to both laboratory and natural channels.

Equilibrium: two-dimensional configurations

International Nuclear Information System (INIS)

Anon.

1987-01-01

In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7

Analytic solution of the two-dimensional Fokker-Planck equation governing stochastic ion heating by a lower hybrid wave

International Nuclear Information System (INIS)

Malescio, G.

1981-04-01

The two-dimensional Fokker-Planck equation describing the ion motion in a coherent lower hybrid wave above the stochasticity threshold is analytically solved. An expression is given for the steady state power dissipation

Critical behavior in two-dimensional quantum gravity and equations of motion of the string

International Nuclear Information System (INIS)

Das, S.R.; Dhar, A.; Wadia, S.R.

1990-01-01

The authors show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. The authors discuss an example of such a trajectory in the space containing the c ≤ 1 minimal models. The authors also discuss the connection between this work and the recent attempts to construct non-pertubative string theories based on matrix models

Picard-Fuchs equations of dimensionally regulated Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Zayadeh, Raphael

2013-12-15

This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is

Picard-Fuchs equations of dimensionally regulated Feynman integrals

International Nuclear Information System (INIS)

Zayadeh, Raphael

2013-12-01

This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is the two

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

Science.gov (United States)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

Science.gov (United States)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Directory of Open Access Journals (Sweden)

Djordjevich Alexandar

2017-12-01

Full Text Available The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity. Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.

Computational simulation of two-dimensional transient natural convection in volumetrically heated square enclosure

International Nuclear Information System (INIS)

Vieira, Camila Braga; Jian Su

2010-01-01

Natural convection is a physical phenomenon that has been investigated in nuclear engineering so as to provide information about heat transfer in severe accident conditions involving nuclear reactors. This research reported transient natural convection of fluids with uniformly distributed volumetrically heat generation in square cavity with isothermal side walls and adiabatic top/bottom walls. Two Prandtl numbers were considered, 0:0321 and 0:71. Direct numerical simulations were applied in order to obtain results about the velocities of the fluid in directions x and y. These results were used in Fast Fourier Transform, which showed the periodic, quasi-chaotic and chaotic behavior of transient laminar flow. (author)

Baicklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation

Institute of Scientific and Technical Information of China (English)

张解放; 吴锋民

2002-01-01

We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.

New method for solving three-dimensional Schroedinger equation

International Nuclear Information System (INIS)

Melezhik, V.S.

1992-01-01

A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables, Ω, from X={R,Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigenvalue) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and 'dipole' scatterer, a hydrogen atom in a homogenous magnetic field) and for a three-dimensional problem of the helium-atom bound states. (author)

Fifth-order amplitude equation for traveling waves in isothermal double diffusive convection

International Nuclear Information System (INIS)

Mendoza, S.; Becerril, R.

2009-01-01

Third-order amplitude equations for isothermal double diffusive convection are known to hold the tricritical condition all along the oscillatory branch, predicting that stable traveling waves exist Only at the onset of the instability. In order to properly describe stable traveling waves, we perform a fifth-order calculation and present explicitly the corresponding amplitude equation.

Convective instability of RCP modes for a magnetized chiral plasma

International Nuclear Information System (INIS)

Torres-Silva, Hector; Sakanaka, P.H.; Reggiani, N.

1998-01-01

Using the Maxwell's equations and the proposed constitutive relations for a chiral plasma medium, the dispersion relations for right circularly polarized waves, (RCP), depending on the characteristics of the distribution, a new mode conversion and instabilities are found due to the chiral effect. From the dispersion relations and considering that the chirowave magnetic field may be important when the condition of velocity isotropy is dropped, we find that growing modes (instabilities) can occur at resonance and for frequencies below the electron gyrofrequency. We study, in this paper, the convective instability of RCP waves in a two-component bi-Lorentzian chiroplasma which can model the solar wind particle distributions. (author)

Drift-free kinetic equations for turbulent dispersion

Science.gov (United States)

Bragg, A.; Swailes, D. C.; Skartlien, R.

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Science.gov (United States)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Approximate solutions for the two-dimensional integral transport equation. Solution of complex two-dimensional transport problems

International Nuclear Information System (INIS)

Sanchez, Richard.

1980-11-01

This work is divided into two parts: the first part deals with the solution of complex two-dimensional transport problems, the second one (note CEA-N-2166) treats the critically mixed methods of resolution. A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the interface current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding, and water, or homogenized structural material. The cells are divided into zones that are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is effected by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: CALLIOPE uses a cylindrical cell model and one or three terms for the flux expansion, and NAUSICAA uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes, one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark problems and by calculations performed in the APOLLO multigroup code [fr

Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation

International Nuclear Information System (INIS)

Hu, Xing-Biao; Yu, Guo-Fu

2007-01-01

In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented

Modeling contaminant transport in porous media in relation to nuclear-waste disposal: a review

International Nuclear Information System (INIS)

Grove, D.B.; Kipp, K.L.

1980-01-01

The modeling of solute transport in saturated porous media is reviewed as it is applied to the movement of radioactive waste in the subsurface. Those processes, both physical and chemical, that affect radionuclide movement are discussed and the references that best illustrate these processes listed. Movement is separated into convection, convection-dispersion, and convection-dispersion and chemical reactions. Solutions of equations describing such movement are divided into one-, two-, and three-dimensional analytical and numerical examples. Discussions of recent work in the area of stochastic modeling are followed by discussions of applications of the models to selected field sites

A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor

Directory of Open Access Journals (Sweden)

B. Godongwana

2010-01-01

Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.

Entropy Generation Analysis of Natural Convection in Square Enclosures with Two Isoflux Heat Sources

Directory of Open Access Journals (Sweden)

S. Z. Nejad

2017-04-01

Full Text Available This study investigates entropy generation resulting from natural convective heat transfer in square enclosures with local heating of the bottom and symmetrical cooling of the sidewalls. This analysis tends to optimize heat transfer of two pieces of semiconductor in a square electronic package. In this simulation, heaters are modeled as isoflux heat sources and sidewalls of the enclosure are isothermal heat sinks. The top wall and the non-heated portions of the bottom wall are adiabatic. Flow and temperature fields are obtained by numerical simulation of conservation equations of mass, momentum and energy in laminar, steady and two dimensional flows. With constant heat energy into the cavity, effect of Rayleigh number, heater length, heater strength ratios and heater position is evaluated on flow and temperature fields and local entropy generation. The results show that a minimum entropy generation rate is obtained under the same condition in which a minimum peak heater temperature is obtained.

Two-dimensional numerical modeling and solution of convection heat transfer in turbulent He II

Science.gov (United States)

Zhang, Burt X.; Karr, Gerald R.

1991-01-01

Numerical schemes are employed to investigate heat transfer in the turbulent flow of He II. FEM is used to solve a set of equations governing the heat transfer and hydrodynamics of He II in the turbulent regime. Numerical results are compared with available experimental data and interpreted in terms of conventional heat transfer parameters such as the Prandtl number, the Peclet number, and the Nusselt number. Within the prescribed Reynolds number domain, the Gorter-Mellink thermal counterflow mechanism becomes less significant, and He II acts like an ordinary fluid. The convection heat transfer characteristics of He II in the highly turbulent regime can be successfully described by using the conventional turbulence and heat transfer theories.

Application of linear and non-linear low-Re k-ε models in two-dimensional predictions of convective heat transfer in passages with sudden contractions

International Nuclear Information System (INIS)

Raisee, M.; Hejazi, S.H.

2007-01-01

This paper presents comparisons between heat transfer predictions and measurements for developing turbulent flow through straight rectangular channels with sudden contractions at the mid-channel section. The present numerical results were obtained using a two-dimensional finite-volume code which solves the governing equations in a vertical plane located at the lateral mid-point of the channel. The pressure field is obtained with the well-known SIMPLE algorithm. The hybrid scheme was employed for the discretization of convection in all transport equations. For modeling of the turbulence, a zonal low-Reynolds number k-ε model and the linear and non-linear low-Reynolds number k-ε models with the 'Yap' and 'NYP' length-scale correction terms have been employed. The main objective of present study is to examine the ability of the above turbulence models in the prediction of convective heat transfer in channels with sudden contraction at a mid-channel section. The results of this study show that a sudden contraction creates a relatively small recirculation bubble immediately downstream of the channel contraction. This separation bubble influences the distribution of local heat transfer coefficient and increases the heat transfer levels by a factor of three. Computational results indicate that all the turbulence models employed produce similar flow fields. The zonal k-ε model produces the wrong Nusselt number distribution by underpredicting heat transfer levels in the recirculation bubble and overpredicting them in the developing region. The linear low-Re k-ε model, on the other hand, returns the correct Nusselt number distribution in the recirculation region, although it somewhat overpredicts heat transfer levels in the developing region downstream of the separation bubble. The replacement of the 'Yap' term with the 'NYP' term in the linear low-Re k-ε model results in a more accurate local Nusselt number distribution. Moreover, the application of the non-linear k

Model of two-temperature convective transfer in porous media

Science.gov (United States)

Gruais, Isabelle; Poliševski, Dan

2017-12-01

In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an ɛ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are ɛ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

Science.gov (United States)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2012-01-01

We construct a Darboux transformation for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix. Our transformation is based on the two-dimensional supersymmetry formalism for the Schrödinger equation. The transformed Fokker-Planck equation and its solutions are obtained in explicit form.

Non-Darcy Free Convection of Power-Law Fluids Over a Two-Dimensional Body Embedded in a Porous Medium

KAUST Repository

El-Amin, Mohamed

2010-11-27

A boundary layer analysis was presented to study the non-Darcy-free convection of a power-law fluid over a non-isothermal two-dimensional body embedded in a porous medium. The Ostwald-de Waele power-law model was used to characterize the non-Newtonian fluid behavior. Similarity solutions were obtained with variations in surface temperature or surface heat flux. In view of the fact that most of the non-Newtonian fluids have large Prandtl numbers, this study was directed toward such fluids. The effects of the porous medium parameters, k1 and k2, body shape parameter, m, and surface thermal variations parameter, p, as well as the power-law index, n, were examined. © 2010 Springer Science+Business Media B.V.

Non-Darcy Free Convection of Power-Law Fluids Over a Two-Dimensional Body Embedded in a Porous Medium

KAUST Repository

El-Amin, Mohamed; Sun, Shuyu; El-Ameen, M. A.; Jaha, Y. A.; Gorla, Rama Subba Reddy

2010-01-01

A boundary layer analysis was presented to study the non-Darcy-free convection of a power-law fluid over a non-isothermal two-dimensional body embedded in a porous medium. The Ostwald-de Waele power-law model was used to characterize the non-Newtonian fluid behavior. Similarity solutions were obtained with variations in surface temperature or surface heat flux. In view of the fact that most of the non-Newtonian fluids have large Prandtl numbers, this study was directed toward such fluids. The effects of the porous medium parameters, k1 and k2, body shape parameter, m, and surface thermal variations parameter, p, as well as the power-law index, n, were examined. © 2010 Springer Science+Business Media B.V.

Analysis of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients in an inhomogeneous medium

Science.gov (United States)

Chai, Han-Peng; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Guan, Yue-Yang

2017-08-01

Korteweg-de Vries (KdV)-type equations are seen to describe the shallow-water waves, lattice structures and ion-acoustic waves in plasmas. Hereby, we consider an extension of the KdV-type equations called the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients in an inhomogeneous medium. Via the Hirota bilinear method and symbolic computation, we derive the bilinear forms, N-soliton solutions and Bäcklund transformation. Effects of the first- and higher-order dispersion terms are investigated. Soliton evolution and interaction are graphically presented and analyzed: Both the propagation velocity and direction of the soliton change when the dispersion terms are time-dependent; The interactions between/among the solitons are elastic, independent of the forms of the coefficients in the equations.

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

Science.gov (United States)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

The determination of time-stationary two-dimensional convection patterns with single-station radars

International Nuclear Information System (INIS)

Freeman, M.P.; Ruohoniemi, J.M.; Greenwald, R.A.

1991-01-01

At the present time, most ground-based radar estimations of ionospheric convection use observations from single-station facilities. This approach requires certain assumptions as to the spatial and/or temporal uniformity of the convection. In this paper the authors present a critical examination of the accuracy of these vector velocity determinations, using realistic modeled flow patterns that are time-stationary but not spatially uniform. They find that under certain circumstances the actual and inferred flow fields show considerable discrepancy, sometimes not even agreeing in the sense of flow direction. Specifically, they show that the natural curvature present in ionospheric convection on varying spatial scales can introduce significant error in the velocity estimate, particularly when the radius of curvature of the flow structure is less than or equal to the radar range to the scattering volume. The presence of flow curvature cannot be detected by radars which determine velocities from measurements in two viewing directions, and it might not be detected by radars using azimuth scanning techniques. Thus they argue that every effort should be made to measure the ionospheric convection by bidirectional or multidirectional observations of a common ionospheric volume and that a synthesis of coherent and incoherent radar observations from different sites is preferable to multidirectional single-station observations using either radar alone. These conclusions are applicable to any Doppler measurement technique and are equally valid for high-latitude wind patterns using Fabry-Perot interferometer techniques

Simulation of natural convection in a rectangular loop using finite elements

International Nuclear Information System (INIS)

Pepper, D.W.; Hamm, L.L.; Kehoe, A.B.

1984-01-01

A two-dimensional finite-element analysis of natural convection in a rectangular loop is presented. A psi-omega formulation of the Boussinesque approximation to the Navier-Stokes equation is solved by the false transient technique. Streamlines and isotherms at Ra = 10 4 are shown for three different modes of heating. The results indicate that corner effects should be considered when modeling flow patterns in thermosyphons

Ring-shaped quasi-soliton solutions to the two-and three-dimensional Sine-Gordon equation

International Nuclear Information System (INIS)

Christiansen, P.L.; Olsen, O.H.

1979-01-01

Ring-shaped solitary wave solutions to the Sine-Gordon equation in two and three spatial dimensions are investigated by numerical computation. Each expanding wave exhibits a return effect. The reflection of the shrinking wave at the singularity at the center of the wave is investigated in a particular case. Collision experiments in numero for expanding and shrinking concentric ring waves show that the solutions possess quasisoliton properties. A Baecklund transformation for the non-symmetric three-dimensional case is given. (Auth.)

Instability of traveling waves of the convective-diffusive Cahn-Hilliard equation

International Nuclear Information System (INIS)

Gao Hongjun; Liu Changchun

2004-01-01

In this paper we study the instability of the traveling waves of the convective-diffusive Cahn-Hilliard equation. We prove that it is nonlinearly unstable under H 2 perturbations, for some traveling wave solution that is asymptotic to a constant as x→∞

Chaotic convection of viscoelastic fluids in porous media

Energy Technology Data Exchange (ETDEWEB)

Sheu, L.-J. [Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan (China)], E-mail: ljsheu@chu.edu.tw; Tam, L.-M. [Department of Electromechanical Engineering, University of Macau, Macau (China)], E-mail: fstlmt@umac.mo; Chen, J.-H. [Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan (China)], E-mail: chen@chu.edu.tw; Chen, H.-K. [Department of Industrial Engineering and Management, Hsiuping Institute of Technology, Taichung, Taiwan (China)], E-mail: kanechen@giga.net.tw; Lin, K.-T. [Department of Mechanical Engineering, Chung Yuan Christian University, Chung Li, Taiwan (China)], E-mail: willie@nanya.edu.tw; Kang Yuan [Department of Mechanical Engineering, Chung Yuan Christian University, Chung Li, Taiwan (China)], E-mail: yk@cycu.edu.tw

2008-07-15

Buoyancy-induced convection in a viscoelastic fluid-saturated porous medium was analyzed using an Oldroydian-type constitutive relation. An autonomous system with four differential equations was deduced by applying the truncated Galerkin expansion to the momentum and heat transfer equations. The four-dimensional system can be reduced to many systems provided in the literature such as the Lorenz system, Vadasz system, Khayat system, and Akhatov system. Depending on the flow parameters, the asymptotic behavior can be stationary, periodic, or chaotic. Generation of a four-scroll, or two-'butterfly', chaotic attractor was observed. Results also show that stress relaxation tends to precipitate the onset of chaos.

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

Directory of Open Access Journals (Sweden)

Fukang Yin

2013-01-01

Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

Absorption and scattering coefficients estimation in two-dimensional participating media using the generalized maximum entropy and Levenberg-Marquardt methods; Estimacion del coeficiente de absorcion y dispersion en medios participantes bidimensionales utilizando el metodo de maxima entropia generalizada y el metodo Levenberg-Marquardt

Energy Technology Data Exchange (ETDEWEB)

Berrocal T, Mariella J. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]|[Universidad Nacional de Ingenieria, Lima (Peru); Roberty, Nilson C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; Silva Neto, Antonio J. [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico. Dept. de Engenharia Mecanica e Energia]|[Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

The solution of inverse problems in participating media where there is emission, absorption and dispersion of the radiation possesses several applications in engineering and medicine. The objective of this work is to estimative the coefficients of absorption and dispersion in two-dimensional heterogeneous participating media, using in independent form the Generalized Maximum Entropy and Levenberg Marquardt methods. Both methods are based on the solution of the direct problem that is modeled by the Boltzmann equation in cartesian geometry. Some cases testes are presented. (author)

Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium

International Nuclear Information System (INIS)

Patra, A.; Saha Ray, S.

2014-01-01

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution

Comparison of preconditioned generalized conjugate gradient methods to two-dimensional neutron and photon transport equation

International Nuclear Information System (INIS)

Chen, G.S.; Yang, D.Y.

1998-01-01

We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used: TFQMR (transpose free quasi-minimal residual algorithm) CGS (conjugate gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These subroutines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. The reasons to choose the generalized conjugate gradient methods are that the methods have better residual (equivalent to error) control procedures in the computation and have better convergent rate. The pointwise incomplete LU factorization ILU, modified pointwise incomplete LU factorization MILU, block incomplete factorization BILU and modified blockwise incomplete LU factorization MBILU are the preconditioning techniques used in the several testing problems. In Bi-CGSTAB, CGS, TFQMR and QMRCGSTAB method, we find that either CGS or Bi-CGSTAB method combined with preconditioner MBILU is the most efficient algorithm in these methods in the several testing problems. The numerical solution of flux by preconditioned CGS and Bi-CGSTAB methods has the same result as those from Cray computer, obtained by either the point successive relaxation method or the line successive relaxation method combined with Gaussian elimination

A closed-form solution for the two-dimensional transport equation by the LTSN nodal method in the range of Compton Effect

International Nuclear Information System (INIS)

Rodriguez, Barbara D.A.; Tullio de Vilhena, Marco; Hoff, Gabriela

2008-01-01

In this paper we report a two-dimensional LTS N nodal solution for homogeneous and heterogeneous rectangular domains, assuming the Klein-Nishina scattering kernel and multigroup model. The main idea relies on the solution of the two one-dimensional S N equations resulting from transverse integration of the S N equations in the rectangular domain by the LTS N nodal method, considering the leakage angular fluxes approximated by exponential, which allow us to determine a closed-form solution for the photons transport equation. The angular flux and the parameters of the medium are used for the calculation of the absorbed energy in rectangular domains with different dimensions and compositions. The incoming photons will be tracked until their whole energy is deposited and/or they leave the domain of interest. In this study, the absorbed energy by Compton Effect will be considered. The remaining effects will not be taken into account. We present numerical simulations and comparisons with results obtained by using Geant4 (version 9.1) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the Klein-Nishina scattering kernel. (authors)

Self-organization analysis for a nonlocal convective Fisher equation

Energy Technology Data Exchange (ETDEWEB)

Cunha, J.A.R. da [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil); Penna, A.L.A. [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil)], E-mail: penna.andre@gmail.com; Vainstein, M.H. [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil); Morgado, R. [International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil); Departamento de Matematica, Universidade de Brasilia, 70910-900 Brasilia DF (Brazil); Oliveira, F.A. [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil)

2009-02-02

Using both an analytical method and a numerical approach we have investigated pattern formation for a nonlocal convective Fisher equation with constant and spatial velocity fields. We analyze the limits of the influence function due to nonlocal interaction and we obtain the phase diagram of critical velocities v{sub c} as function of the width {mu} of the influence function, which characterize the self-organization of a finite system.

Basal melting driven by turbulent thermal convection

Science.gov (United States)

Rabbanipour Esfahani, Babak; Hirata, Silvia C.; Berti, Stefano; Calzavarini, Enrico

2018-05-01

Melting and, conversely, solidification processes in the presence of convection are key to many geophysical problems. An essential question related to these phenomena concerns the estimation of the (time-evolving) melting rate, which is tightly connected to the turbulent convective dynamics in the bulk of the melt fluid and the heat transfer at the liquid-solid interface. In this work, we consider a convective-melting model, constructed as a generalization of the Rayleigh-Bénard system, accounting for the basal melting of a solid. As the change of phase proceeds, a fluid layer grows at the heated bottom of the system and eventually reaches a turbulent convection state. By means of extensive lattice-Boltzmann numerical simulations employing an enthalpy formulation of the governing equations, we explore the model dynamics in two- and three-dimensional configurations. The focus of the analysis is on the scaling of global quantities like the heat flux and the kinetic energy with the Rayleigh number, as well as on the interface morphology and the effects of space dimensionality. Independently of dimensionality, we find that the convective-melting system behavior shares strong resemblances with that of the Rayleigh-Bénard one, and that the heat flux is only weakly enhanced with respect to that case. Such similarities are understood, at least to some extent, considering the resulting slow motion of the melting front (with respect to the turbulent fluid velocity fluctuations) and its generally little roughness (compared to the height of the fluid layer). Varying the Stefan number, accounting for the thermodynamical properties of the material, also seems to have only a mild effect, which implies the possibility of extrapolating results in numerically delicate low-Stefan setups from more convenient high-Stefan ones. Finally, we discuss the implications of our findings for the geophysically relevant problem of modeling Arctic ice melt ponds.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

International Nuclear Information System (INIS)

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-01-01

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.

Numerical simulations of convectively excited gravity waves

International Nuclear Information System (INIS)

Glatzmaier, G.A.

1983-01-01

Magneto-convection and gravity waves are numerically simulated with a nonlinear, three-dimensional, time-dependent model of a stratified, rotating, spherical fluid shell heated from below. A Solar-like reference state is specified while global velocity, magnetic field, and thermodynamic perturbations are computed from the anelastic magnetohydrodynamic equations. Convective overshooting from the upper (superadiabatic) part of the shell excites gravity waves in the lower (subadiabatic) part. Due to differential rotation and Coriolis forces, convective cell patterns propagate eastward with a latitudinally dependent phase velocity. The structure of the excited wave motions in the stable region is more time-dependent than that of the convective motions above. The magnetic field tends to be concentrated over giant-cell downdrafts in the convective zone but is affected very little by the wave motion in the stable region

Mathematical modeling and the two-phase constitutive equations

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

Filtering of sound from the Navier-Stokes equations. [An approximation for describing thermal convection in a compressible fluid

Energy Technology Data Exchange (ETDEWEB)

Paolucci, S.

1982-12-01

An approximation leading to anelastic equations capable of describing thermal convection in a compressible fluid is given. These equations are more general than the Oberbeck-Boussinesq equations and different than the standard anelastic equations in that they can be used for the computation of convection in a fluid with large density gradients present. We show that the equations do not contain acoustic waves, while at the same time they can still describe the propagation of internal waves. Throughout we show that the filtering of acoustic waves, within the limits of the approximation, does not appreciably alter the description of the physics.

Solving Two -Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé Approximants

Directory of Open Access Journals (Sweden)

Mohammad Siddique

2010-08-01

Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.

Two-dimensional transport of tokamak plasmas

International Nuclear Information System (INIS)

Hirshman, S.P.; Jardin, S.C.

1979-01-01

A reduced set of two-fluid transport equations is obtained from the conservation equations describing the time evolution of the differential particle number, entropy, and magnetic fluxes in an axisymmetric toroidal plasma with nested magnetic surfaces. Expanding in the small ratio of perpendicular to parallel mobilities and thermal conductivities yields as solubility constraints one-dimensional equations for the surface-averaged thermodynamic variables and magnetic fluxes. Since Ohm's law E +u x B =R', where R' accounts for any nonideal effects, only determines the particle flow relative to the diffusing magnetic surfaces, it is necessary to solve a single two-dimensional generalized differential equation, (partial/partialt) delpsi. (delp - J x B) =0, to find the absolute velocity of a magnetic surface enclosing a fixed toroidal flux. This equation is linear but nonstandard in that it involves flux surface averages of the unknown velocity. Specification of R' and the cross-field ion and electron heat fluxes provides a closed system of equations. A time-dependent coordinate transformation is used to describe the diffusion of plasma quantities through magnetic surfaces of changing shape

Analysis and classification of nonlinear dispersive evolution equations in the potential representation

International Nuclear Information System (INIS)

Eichmann, U.A.; Draayer, J.P.; Ludu, A.

2002-01-01

A potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves reduction of a third-order partial differential equation to a first-order ordinary differential equation. The potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation. In particular, the paper deals with the so-called K(n, m) equations. Starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation. As a result, e.g., all equations with linear dispersion join the same equivalence class with the Korteweg-deVries equation being its representative, and all soliton solutions of higher order nonlinear equations are thus equivalent to the KdV soliton. Certain equations with both linear and quadratic dispersions can also be treated within this equivalence class. (author)

An interfacial shear term evaluation study for adiabatic dispersed air–water two-phase flow with the two-fluid model using CFD

Energy Technology Data Exchange (ETDEWEB)

Sharma, S.L., E-mail: sharma55@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN (United States); Hibiki, T.; Ishii, M. [School of Nuclear Engineering, Purdue University, West Lafayette, IN (United States); Schlegel, J.P. [Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO (United States); Buchanan, J.R.; Hogan, K.J. [Bettis Laboratory, Naval Nuclear Laboratory, West Mifflin, PA (United States); Guilbert, P.W. [ANSYS UK Ltd, Oxfordshire (United Kingdom)

2017-02-15

Highlights: • Closure form of the interfacial shear term in three-dimensional form is investigated. • Assessment against adiabatic upward bubbly air–water flow data using CFD. • Effect of addition of the interfacial shear term on the phase distribution. - Abstract: In commercially available Computational Fluid Dynamics (CFD) codes such as ANSYS CFX and Fluent, the interfacial shear term is missing in the field momentum equations. The derivation of the two-fluid model (Ishii and Hibiki, 2011) indicates the presence of this term as a momentum source in the right hand side of the field momentum equation. The inclusion of this term is considered important for proper modeling of the interfacial momentum coupling between phases. For separated flows, such as annular flow, the importance of the shear term is understood in the one-dimensional (1-D) form as the major mechanism by which the wall shear is transferred to the gas phase (Ishii and Mishima, 1984). For gas dispersed two-phase flow CFD simulations, it is important to assess the significance of this term in the prediction of phase distributions. In the first part of this work, the closure of this term in three-dimensional (3-D) form in a CFD code is investigated. For dispersed gas–liquid flow, such as bubbly or churn-turbulent flow, bubbles are dispersed in the shear layer of the continuous phase. The continuous phase shear stress is mainly due to the presence of the wall and the modeling of turbulence through the Boussinesq hypothesis. In a 3-D simulation, the continuous phase shear stress can be calculated from the continuous fluid velocity gradient, so that the interfacial shear term can be closed using the local values of the volume fraction and the total stress of liquid phase. This form also assures that the term acts as an action-reaction force for multiple phases. In the second part of this work, the effect of this term on the volume fraction distribution is investigated. For testing the model two

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

Science.gov (United States)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

On the pollutant removal, dispersion, and entrainment over two-dimensional idealized street canyons

Science.gov (United States)

Liu, Chun-Ho; Wong, Colman C. C.

2014-01-01

Pollutant dispersion over urban areas is not that well understood, in particular at the street canyon scale. This study is therefore conceived to examine how urban morphology modifies the pollutant removal, dispersion, and entrainment over urban areas. An idealized computational domain consisting of 12 two-dimensional (2D) identical street canyons of unity aspect ratio is employed. The large-eddy simulation (LES) is used to calculate the turbulent flows and pollutant transport in the urban boundary layer (UBL). An area source of uniform pollutant concentration is applied on the ground of the first street canyon. A close examination on the roof-level turbulence reveals patches of low-speed air masses in the streamwise flows and narrow high-speed downdrafts in the shear layer. Different from the flows over a smooth surface, the turbulence intensities are peaked near the top of the building roughness. The pollutant is rather uniformly distributed inside a street canyon but disperses quickly in the UBL over the buildings. Partitioning the vertical pollutant flux into its mean and turbulent components demystifies that the pollutant removal is mainly governed by turbulence. Whereas, mean wind carries pollutant into and out of a street canyon simultaneously. In addition to wind speed promotion, turbulent mixing is thus required to dilute the ground-level pollutants, which are then removed from the street canyon to the UBL. Atmospheric flows slow down rapidly after the leeward buildings, leading to updrafts carrying pollutants away from the street canyons (the basic pollutant removal mechanism).

Two-dimensional topological field theories coupled to four-dimensional BF theory

International Nuclear Information System (INIS)

Montesinos, Merced; Perez, Alejandro

2008-01-01

Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level

Stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable duffing oscillator and bifurcation of moment equation

International Nuclear Information System (INIS)

Zhang Guangjun; Xu Jianxue; Wang Jue; Yue Zhifeng; Zou Hailin

2009-01-01

In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.

A Marker Method for the Solution of the Damped Burgers' Equation

International Nuclear Information System (INIS)

Jerome L.V. Lewandowski

2005-01-01

A new method for the solution of the damped Burgers equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations

Phonon-assisted damping of plasmons in three- and two-dimensional metals

Science.gov (United States)

Caruso, Fabio; Novko, Dino; Draxl, Claudia

2018-05-01

We investigate the effects of crystal lattice vibrations on the dispersion of plasmons. The loss function of the homogeneous electron gas (HEG) in two and three dimensions is evaluated numerically in the presence of electronic coupling to an optical phonon mode. Our calculations are based on many-body perturbation theory for the dielectric function as formulated by the Hedin-Baym equations in the Fan-Migdal approximation. The coupling to phonons broadens the spectral signatures of plasmons in the electron-energy loss spectrum (EELS) and it induces the decay of plasmons on timescales shorter than 1 ps. Our results further reveal the formation of a kink in the plasmon dispersion of the two-dimensional HEG, which marks the onset of plasmon-phonon scattering. Overall, these features constitute a fingerprint of plasmon-phonon coupling in EELS of simple metals. It is shown that these effects may be accounted for by resorting to a simplified treatment of the electron-phonon interaction which is amenable to first-principles calculations.

Developing A New Predictive Dispersion Equation Based on Tidal Average (TA) Condition in Alluvial Estuaries

Science.gov (United States)

Anak Gisen, Jacqueline Isabella; Nijzink, Remko C.; Savenije, Hubert H. G.

2014-05-01

Dispersion mathematical representation of tidal mixing between sea water and fresh water in The definition of dispersion somehow remains unclear as it is not directly measurable. The role of dispersion is only meaningful if it is related to the appropriate temporal and spatial scale of mixing, which are identified as the tidal period, tidal excursion (longitudinal), width of estuary (lateral) and mixing depth (vertical). Moreover, the mixing pattern determines the salt intrusion length in an estuary. If a physically based description of the dispersion is defined, this would allow the analytical solution of the salt intrusion problem. The objective of this study is to develop a predictive equation for estimating the dispersion coefficient at tidal average (TA) condition, which can be applied in the salt intrusion model to predict the salinity profile for any estuary during different events. Utilizing available data of 72 measurements in 27 estuaries (including 6 recently studied estuaries in Malaysia), regressions analysis has been performed with various combinations of dimensionless parameters . The predictive dispersion equations have been developed for two different locations, at the mouth D0TA and at the inflection point D1TA (where the convergence length changes). Regressions have been carried out with two separated datasets: 1) more reliable data for calibration; and 2) less reliable data for validation. The combination of dimensionless ratios that give the best performance is selected as the final outcome which indicates that the dispersion coefficient is depending on the tidal excursion, tidal range, tidal velocity amplitude, friction and the Richardson Number. A limitation of the newly developed equation is that the friction is generally unknown. In order to compensate this problem, further analysis has been performed adopting the hydraulic model of Cai et. al. (2012) to estimate the friction and depth. Keywords: dispersion, alluvial estuaries, mixing, salt

Analysis of photonic band gap in dispersive properties of tunable three-dimensional photonic crystals doped by magnetized plasma

International Nuclear Information System (INIS)

Zhang HaiFeng; Liu Shaobin; Yang Huan; Kong Xiangkun

2013-01-01

In this paper, the magnetooptical effects in dispersive properties for two types of three-dimensional magnetized plasma photonic crystals (MPPCs) containing homogeneous dielectric and magnetized plasma with diamond lattices are theoretically investigated for electromagnetic (EM) wave based on plane wave expansion (PWE) method, as incidence EM wave vector is parallel to the external magnetic field. The equations for two types of MPPCs with diamond lattices (dielectric spheres immersed in magnetized plasma background or vice versa) are theoretically deduced. The influences of dielectric constant, plasma collision frequency, filling factor, the external magnetic field, and plasma frequency on the dispersive properties for both types of structures are studied in detail, respectively, and some corresponding physical explanations are also given. From the numerical results, it has been shown that the photonic band gaps (PBGs) for both types of MPPCs can be manipulated by plasma frequency, filling factor, the external magnetic field, and the relative dielectric constant of dielectric, respectively. Especially, the external magnetic field can enlarge the PBG for type-2 structure (plasma spheres immersed in dielectric background). However, the plasma collision frequency has no effect on the dispersive properties of two types of three-dimensional MPPCs. The locations of flatbands regions for both types of structures cannot be tuned by any parameters except for plasma frequency and the external magnetic field. The analytical results may be informative and of technical use to design the MPPCs devices.

Macroscopic balance equations for two-phase flow models

International Nuclear Information System (INIS)

Hughes, E.D.

1979-01-01

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

General solution of the Dirac equation for quasi-two-dimensional electrons

Energy Technology Data Exchange (ETDEWEB)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

2016-06-15

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

Directory of Open Access Journals (Sweden)

M. P. Markakis

2010-01-01

Full Text Available Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1 equations. Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

On nonlinear equations associated with Lie algebras of diffeomorphism groups of two-dimensional manifolds

International Nuclear Information System (INIS)

Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.

1990-01-01

Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs

Absorption and scattering coefficients estimation in two-dimensional participating media using the generalized maximum entropy and Levenberg-Marquardt methods

International Nuclear Information System (INIS)

Berrocal T, Mariella J.; Roberty, Nilson C.; Silva Neto, Antonio J.; Universidade Federal, Rio de Janeiro, RJ

2002-01-01

The solution of inverse problems in participating media where there is emission, absorption and dispersion of the radiation possesses several applications in engineering and medicine. The objective of this work is to estimative the coefficients of absorption and dispersion in two-dimensional heterogeneous participating media, using in independent form the Generalized Maximum Entropy and Levenberg Marquardt methods. Both methods are based on the solution of the direct problem that is modeled by the Boltzmann equation in cartesian geometry. Some cases testes are presented. (author)

On the confinement of a Dirac particle to a two-dimensional ring

International Nuclear Information System (INIS)

Bakke, K.; Furtado, C.

2012-01-01

In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring for systems described by the Dirac equation by introducing a new coupling into the Dirac equation. We show that the introduction of this new coupling into the Dirac equation yields a generalization of the two-dimensional quantum ring model proposed by Tan and Inkson [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635] for relativistic spin-half quantum particles. -- Highlights: ► Two-dimensional ring model for condensed matter systems described by the Dirac equation. ► Exact solutions of the Dirac equation. ► Persistent currents for Dirac-like systems confined to a two-dimensional quantum ring.

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

Directory of Open Access Journals (Sweden)

Roman Cherniha

2018-04-01

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

A quasi-one-dimensional theory of sound propagation in lined ducts with mean flow

Science.gov (United States)

Dokumaci, Erkan

2018-04-01

Sound propagation in ducts with locally-reacting liners has received the attention of many authors proposing two- and three-dimensional solutions of the convected wave equation and of the Pridmore-Brown equation. One-dimensional lined duct models appear to have received less attention. The present paper proposes a quasi-one-dimensional theory for lined uniform ducts with parallel sheared mean flow. The basic assumption of the theory is that the effects of refraction and wall compliance on the fundamental mode remain within ranges in which the acoustic fluctuations are essentially uniform over a duct section. This restricts the model to subsonic low Mach numbers and Helmholtz numbers of less than about unity. The axial propagation constants and the wave transfer matrix of the duct are given by simple explicit expressions and can be applied with no-slip, full-slip or partial slip boundary conditions. The limitations of the theory are discussed and its predictions are compared with the fundamental mode solutions of the convected wave equation, the Pridmore-Brown equation and measurements where available.

On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

Directory of Open Access Journals (Sweden)

Kilic Bulent

2016-01-01

Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.

Characteristics and stability analyses of transient one-dimensional two-phase flow equations and their finite difference approximations

International Nuclear Information System (INIS)

Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W.; Hughes, E.D.

1975-01-01

Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)

Analytical solutions of one-dimensional advection–diffusion

Indian Academy of Sciences (India)

Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal finite initially solute free domain,for two dispersion problems.In the first one,temporally dependent solute dispersion along uniform flow in homogeneous domain is studied.In the second problem the ...

Lie algebra contractions on two-dimensional hyperboloid

International Nuclear Information System (INIS)

Pogosyan, G. S.; Yakhno, A.

2010-01-01

The Inoenue-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1 . The text was submitted by the authors in English.

Two-dimensional convection and interchange motions in fluids and magnetized plasmas

DEFF Research Database (Denmark)

Garcia, O.E.; Bian, N.H.; Naulin, V.

2006-01-01

fluids, emphasizing its relation to interchange motions of non- uniformly magnetized plasmas. This is followed by a review of the theories for the onset of convection and quasi-linear saturation in driven-dissipative systems. Non-linear numerical simulations which result in stationary convective states...... behaviour of the fluctuation level which is associated with relaxation oscillations in the kinetic energy of the azimuthally mean flows. This leads to a state of large-scale intermittency manifested by exponential tails in the single-point probability distribution function of the dependent variables...

A asymptotic numerical method for the steady-state convection diffusion equation

International Nuclear Information System (INIS)

Wu Qiguang

1988-01-01

In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.

2010-12-08

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.; Goriely, A.; Saccomandi, G.

2010-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Analytical determination of 3-D global modes in Rayleigh-Benard-Poiseuille-type mixed convection flow; Determination analytique des modes globaux tridimensionnels en ecoulement de convection mixte du type Rayleigh-Benard-Poiseuille

Energy Technology Data Exchange (ETDEWEB)

Martinand, D

2003-01-15

This analytical study deals with the spatio-temporal evolution of linear thermo-convective instabilities in a horizontal fluid layer heated from below (the Rayleigh--Benard system) and subject to a horizontal pressure gradient (Poiseuille flow). The novelty consists of a spatially inhomogeneous temperature, in the form of a two-dimensional bump imposed on the lower plate, while the upper plate is kept at a constant temperature. The inhomogeneous boundary temperature and the mean flow of the Rayleigh--Benard--Poiseuille system break the symmetries of the classical Rayleigh--Benard system. The instabilities of interest are therefore spatially localised packets of convection rolls. If a mode of this type is synchronized, it is called a global mode. Assuming that the characteristic scale of the spatial variation of the lower plate temperature is large compared to the wavelength of the rolls, global modes are sought in the form of Eigenmodes in the confined vertical direction, modulated by a two-dimensional WKBJ expansion in the slowly-varying horizontal directions. Such an expansion breaks down at points where the group velocity of the instability vanishes, i.e. at WKBJ turning points. In the neighbourhood of one such point, located at the top of the temperature bump, the boundedness of the solution imposes a selection criterion for the global modes which provides the growth rate (or equivalently the critical threshold), the frequency and the wave vector of the most amplified global mode. This study thus generalizes to two-dimensional cases the methods used and the results obtained for one-dimensional inhomogeneities. The analysis is first applied to a simplified governing equation obtained by an envelope formalism and the analytical results are compared with numerical solutions of the amplitude equation. The formalism is finally applied to the Rayleigh--Benard--Poiseuille system described by the Navier--Stokes equations with the Boussinesq approximation. (author)

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.

Advanced numerical methods for three dimensional two-phase flow calculations

International Nuclear Information System (INIS)

Toumi, I.; Caruge, D.

1997-01-01

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

Dirac equation in 5- and 6-dimensional curved space-time manifolds

International Nuclear Information System (INIS)

Vladimirov, Yu.S.; Popov, A.D.

1984-01-01

The program of plotting unified multidimensional theory of gravitation, electromagnetism and electrically charged matter with transition from 5-dimensional variants to 6-dimensional theory possessing signature (+----+) is developed. For recording the Dirac equation in 5- and 6-dimensional curved space-time manifolds the tetrad formalism and γ-matrix formulation of the General Relativity Theory are used. It is shown that the 6-dimensional theory case unifies the two private cases of 5-dimensional theory and corresponds to two possibilities of the theory developed by Kadyshevski

Feasibility of maintaining natural convection mode core cooling in research reactor power upgrades

International Nuclear Information System (INIS)

Ha, J.J.; Belhadj, M.; Aldemir, T.; Christensen, R.N.

1987-01-01

Two operational concerns for natural convection coooled research reactors using plate type fuels are: 1) pool top 16 N activity (PTNA), and 2) nucleate boiling in core channels. The feasibility assessment of a power upgrade while maintaining natural convection mode core cooling requires addressing these operational concerns. Previous studies have shown that: a) The conventional technique for reducing PTNA by plume dispersion may not be effective in a large power upgrade of research reactors with small pools. b) Currently used correlations to predict onset of nucleate boiling (ONB) in thin, rectangular core channels are not valid for low-velocity, upward flows such as encountered in natural convection cooling. The PTNA depends on the velocity distribution in the reactor pool. COMMIX-1A code is used to determine the three-dimensional velocity fields in The Ohio State University Research Reactor (OSURR) pool as a function of varying design conditions, following a power upgrade to 500 kW with LEU fuel. It is shown that a sufficiently deep stagnant water layer can be created below the pool top by properly choosing the disperser flow rate. The ONB heat flux is experimentally determined for channel gaps and upward flow velocities in the range 2mm-4mm and 3-16 cm/sec., respectively. Two alternatives to plume dispersion for reducing PTNA and a new correlation to determine the ONB heat flux in thin, rectangular channels under low-velocity, upward flow conditions are proposed. (Author)

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations

Science.gov (United States)

Hou, Thomas Y.; Liu, Pengfei; Wang, Fei

2018-05-01

We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.

Solution Procedure for Transport Modeling in Effluent Recharge Based on Operator-Splitting Techniques

Directory of Open Access Journals (Sweden)

Shutang Zhu

2008-01-01

Full Text Available The coupling of groundwater movement and reactive transport during groundwater recharge with wastewater leads to a complicated mathematical model, involving terms to describe convection-dispersion, adsorption/desorption and/or biodegradation, and so forth. It has been found very difficult to solve such a coupled model either analytically or numerically. The present study adopts operator-splitting techniques to decompose the coupled model into two submodels with different intrinsic characteristics. By applying an upwind finite difference scheme to the finite volume integral of the convection flux term, an implicit solution procedure is derived to solve the convection-dominant equation. The dispersion term is discretized in a standard central-difference scheme while the dispersion-dominant equation is solved using either the preconditioned Jacobi conjugate gradient (PJCG method or Thomas method based on local-one-dimensional scheme. The solution method proposed in this study is applied to the demonstration project of groundwater recharge with secondary effluent at Gaobeidian sewage treatment plant (STP successfully.

Darboux transformation and explicit solutions for some (2+1)-dimensional equations

International Nuclear Information System (INIS)

Wang Yan; Shen Lijuan; Du Dianlou

2007-01-01

Three systems of (2+1)-dimensional soliton equations and their decompositions into the (1+1)-dimensional soliton equations are proposed. These equations include KPI, CKP, MKPI. With the help of Darboux transformation of (1+1)-dimensional equations, we get the explicit solutions of the (2+1)-dimensional equations

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

Science.gov (United States)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

Global vertical mass transport by clouds - A two-dimensional model study

International Nuclear Information System (INIS)

Olofsson, Mats

1988-05-01

A two-dimensional global dispersion model, where vertical transport in the troposphere carried out by convective as well as by frontal cloud systems is explicitly treated, is developed from an existing diffusion model. A parameterization scheme for the cloud transport, based on global cloud statistics, is presented. The model has been tested by using Kr-85, Rn-222 and SO 2 as tracers. Comparisons have been made with observed distributions of these tracers, but also with model results without the cloud transport, using eddy diffusion as the primary means of vertical transport. The model results indicate that for trace species with a turnover time of days to weeks, the introduction of cloud-transport gives much more realistic simulations of their vertical distribution. Layers of increased mixing ratio with height, which can be found in real atmosphere, are reproduced in our cloud-transport model profiles, but can never be simulated with a pure eddy diffusion model. The horizontal transport in the model, by advection and eddy diffusion, gives a realistic distribution between the hemispheres of the more long-lived tracers (Kr-85). A combination of vertical transport by convective and frontal cloud systems is shown to improve the model simulations, compared to limiting it to convective transport only. The importance of including cumulus clouds in the convective transport scheme, in addition to the efficient transport by cumulonimbus clouds, is discussed. The model results are shown to be more sensitive to the vertical detrainment distribution profile than to the absolute magnitude of the vertical mass transport. The scavenging processes for SO 2 are parameterized without the introduction of detailed chemistry. An enhanced removal, due to the increased contact with droplets in the in-cloud lifting process, is introduced in the model. (author)

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established

General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

International Nuclear Information System (INIS)

Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

2005-01-01

A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

Combined analytical-numerical procedure to solve multigroup spherical harmonics equations in two-dimensional r-z geometry

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1986-01-01

In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)

Strongly coupled dispersed two-phase flows; Ecoulements diphasiques disperses fortement couples

Energy Technology Data Exchange (ETDEWEB)

Zun, I.; Lance, M.; Ekiel-Jezewska, M.L.; Petrosyan, A.; Lecoq, N.; Anthore, R.; Bostel, F.; Feuillebois, F.; Nott, P.; Zenit, R.; Hunt, M.L.; Brennen, C.E.; Campbell, C.S.; Tong, P.; Lei, X.; Ackerson, B.J.; Asmolov, E.S.; Abade, G.; da Cunha, F.R.; Lhuillier, D.; Cartellier, A.; Ruzicka, M.C.; Drahos, J.; Thomas, N.H.; Talini, L.; Leblond, J.; Leshansky, A.M.; Lavrenteva, O.M.; Nir, A.; Teshukov, V.; Risso, F.; Ellinsen, K.; Crispel, S.; Dahlkild, A.; Vynnycky, M.; Davila, J.; Matas, J.P.; Guazelli, L.; Morris, J.; Ooms, G.; Poelma, C.; van Wijngaarden, L.; de Vries, A.; Elghobashi, S.; Huilier, D.; Peirano, E.; Minier, J.P.; Gavrilyuk, S.; Saurel, R.; Kashinsky, O.; Randin, V.; Colin, C.; Larue de Tournemine, A.; Roig, V.; Suzanne, C.; Bounhoure, C.; Brunet, Y.; Tanaka, A.T.; Noma, K.; Tsuji, Y.; Pascal-Ribot, S.; Le Gall, F.; Aliseda, A.; Hainaux, F.; Lasheras, J.; Didwania, A.; Costa, A.; Vallerin, W.; Mudde, R.F.; Van Den Akker, H.E.A.; Jaumouillie, P.; Larrarte, F.; Burgisser, A.; Bergantz, G.; Necker, F.; Hartel, C.; Kleiser, L.; Meiburg, E.; Michallet, H.; Mory, M.; Hutter, M.; Markov, A.A.; Dumoulin, F.X.; Suard, S.; Borghi, R.; Hong, M.; Hopfinger, E.; Laforgia, A.; Lawrence, C.J.; Hewitt, G.F.; Osiptsov, A.N.; Tsirkunov, Yu. M.; Volkov, A.N.

2003-07-01

-phase flow, current distribution and mass transfer along a vertical gas evolving electrode; a two-way coupled model for dilute multiphase flows. Topic 3: turbulence modulation by particles, droplets or bubbles in dense systems: influence of particles on the transition to turbulence in pipe flow; comparison between a point particle model and a finite-diameter-model for the particle turbulence interaction in a suspension; the effect on turbulence by bubbles rising through it under buoyancy; the physical mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles; influence of hydrodynamic interactions between particles on the turbulent flow in a suspension; review of relationships between Lagrangian and Eulerian scales; a two-point PDF for modelling turbulent dispersed two-phase flows and derivation of a two field model; mathematical and numerical modeling of two-phase compressible flows with micro-inertia. Topic 4: collective effects in dispersed two-phase flows clustering and phase distribution: hydrodynamic structure of downward bubbly flow; influence of gravity on the dynamics of a turbulent bubbly pipe flow; experimental study of two-phase flows; particle clusters formed in dispersed gas-solid flows: simulations and experiments; experimental study of the turbulence in bubbly flows at high void fraction; first step in the study of the correlation between air/water flow fluctuations and random buffering forces; clustering and settling velocity of micro-droplets in a grid turbulence. Topic 5: large scale instabilities and gravity driven dispersed flows: new 'non-isothermal' linear instability modes in fluidized beds and bubbly flows; large scale instability in a confined buoyant shear layer; convective instability in uniform dispersed layers; structures in gravity driven bubbly flows; effects of concentration profiles on velocity profiles in sewer; pyroclastic density currents viewed as mammoth scale two-phase flows; mixing and

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

Science.gov (United States)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Two-dimensional time dependent Riemann solvers for neutron transport

International Nuclear Information System (INIS)

Brunner, Thomas A.; Holloway, James Paul

2005-01-01

A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem

Study of nonequilibrium dispersed two phase flow

International Nuclear Information System (INIS)

Reyes, J.N. Jr.

1986-01-01

Understanding the behavior of liquid droplets in a superheated steam environment is essential to the accurate prediction of nuclear fuel rod surface temperatures during the blowdown and reflood phase of a loss-of-coolant-accident (LOCA). In response to this need, this treatise presents several original and significant contributions to the field of thermofluid physics. The research contained herein presents a statistical derivation of the two-phase mass, momentum, and energy-conservation equations using a droplet continuity equation analogous to that used in the Kinetic Theory of Gases. Unlike the Eulerian volume and time-averaged conservation equations generally used to describe dispersed two-phase flow behavior, this statistical averaging approach results in an additional mass momentum or energy term in each of the respective conservation equations. Further, this study demonstrates that current definitions of the volumetric vapor generation rate used in the mass conservation equation are inappropriate results under certain circumstances. The mass conservation equation derived herein is used to obtain a new definition for the volumetric vapor-generation rate. Last, a simple two phase phenomenological model, based on the statistically averaged conservation equations, is presented and solved analytically. It is shown that the actual quality and vapor temperature, under these circumstances, depend on a single dimensionless group

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

Science.gov (United States)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

Directory of Open Access Journals (Sweden)

Boričić Zoran

2009-01-01

Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.

Multigrid solution of the convection-diffusion equation with high-Reynolds number

Energy Technology Data Exchange (ETDEWEB)

Zhang, Jun [George Washington Univ., Washington, DC (United States)

1996-12-31

A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.

Dimensional reduction of a general advection–diffusion equation in 2D channels

Science.gov (United States)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Conservation laws for two (2 + 1)-dimensional differential-difference systems

International Nuclear Information System (INIS)

Yu Guofu; Tam, H.-W.

2006-01-01

Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced

The relative contributions of thermo-solutal Marangoni convections on flow patterns in a liquid bridge

Science.gov (United States)

Minakuchi, H.; Takagi, Y.; Okano, Y.; Gima, S.; Dost, S.

2014-01-01

A numerical simulation study was carried out to investigate the relative contributions of thermal and solutal Marangoni convections on transport structures in a liquid bridge under zero gravity. The liquid bridge in the model represents a three dimensional half-zone configuration of the Floating Zone (FZ) growth system. Three dimensional field equations of the liquid zone, i.e. continuity, momentum, energy, and diffusion equations, were solved by the PISO algorithm. Computations were performed using the open source software OpenFOAM. The numerical simulation results show that the flow field becomes three-dimensional and time-depended when the solutal Marangoni number is larger than the critical value. It was also shown that not only flow patterns but also the azimuthal wave number (m) changes due to the competing contributions of thermal and solutal Marangoni convective flows.

Mode-to-mode energy transfers in convective patterns

Indian Academy of Sciences (India)

Abstract. We investigate the energy transfer between various Fourier modes in a low- dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical ...

Heat transport in two-dimensional materials by directly solving the phonon Boltzmann equation under Callaway's dual relaxation model

Science.gov (United States)

Guo, Yangyu; Wang, Moran

2017-10-01

The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

Directory of Open Access Journals (Sweden)

Pratibha Joshi

2014-12-01

Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

Numerical modeling method on the movement of water flow and suspended solids in two-dimensional sedimentation tanks in the wastewater treatment plant.

Science.gov (United States)

Zeng, Guang-Ming; Jiang, Yi-Min; Qin, Xiao-Sheng; Huang, Guo-He; Li, Jian-Bing

2003-01-01

Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity-stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two-dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.

One-Dimensional Convective Thermal Evolution Calculation Using a Modified Mixing Length Theory: Application to Saturnian Icy Satellites

Science.gov (United States)

Kamata, Shunichi

2018-01-01

Solid-state thermal convection plays a major role in the thermal evolution of solid planetary bodies. Solving the equation system for thermal evolution considering convection requires 2-D or 3-D modeling, resulting in large calculation costs. A 1-D calculation scheme based on mixing length theory (MLT) requires a much lower calculation cost and is suitable for parameter studies. A major concern for the MLT scheme is its accuracy due to a lack of detailed comparisons with higher dimensional schemes. In this study, I quantify its accuracy via comparisons of thermal profiles obtained by 1-D MLT and 3-D numerical schemes. To improve the accuracy, I propose a new definition of the mixing length (l), which is a parameter controlling the efficiency of heat transportation due to convection, for a bottom-heated convective layer. Adopting this new definition of l, I investigate the thermal evolution of Saturnian icy satellites, Dione and Enceladus, under a wide variety of parameter conditions. Calculation results indicate that each satellite requires several tens of GW of heat to possess a thick global subsurface ocean suggested from geophysical analyses. Dynamical tides may be able to account for such an amount of heat, though the reference viscosity of Dione's ice and the ammonia content of Dione's ocean need to be very high. Otherwise, a thick global ocean in Dione cannot be maintained, implying that its shell is not in a minimum stress state.

A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

KAUST Repository

Allen, Rebecca; Reis, Tim; Sun, Shuyu

2013-01-01

-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE

Solar Internal Rotation and Dynamo Waves: A Two Dimensional ...

Indian Academy of Sciences (India)

tribpo

Solar Internal Rotation and Dynamo Waves: A Two Dimensional. Asymptotic Solution in the Convection Zone ... We calculate here a spatial 2 D structure of the mean magnetic field, adopting real profiles of the solar internal ... of the asymptotic solution in low (middle) and high (right panel) latitudes. field is shifted towards the ...

A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study

International Nuclear Information System (INIS)

Angelo, P.M.; Riela, G.

1981-01-01

We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)

About Navier-Stokes Equation in the Theory of Convective Heat Transfer

Science.gov (United States)

Davidzon, M. Y.

2017-10-01

A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).

Vorticity imbalance and stability in relation to convection

Science.gov (United States)

Read, W. L.; Scoggins, J. R.

1977-01-01

A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately.

Similarity Solution for Combined Free-Forced Convection Past a Vertical Porous Plate in a Porous Medium with a Convective Surface Boundary Condition

Directory of Open Access Journals (Sweden)

Garg P.

2016-12-01

Full Text Available This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

The effect of heat generation on mixed convection flow in nano fluids over a horizontal circular cylinder

Science.gov (United States)

Juliyanto, Bagus; Widodo, Basuki; Imron, Chairul

2018-04-01

The purpose of this research is to study the effect of heat generation on mixed convection flow on Nano fluids over a horizontal circular cylinder of a heated in two dimension form. A stream of fluids are steady and incompressible, a stream flowing vertically upwards for circular cylinder and the boundary layer at the stagnation point. Three different types of nanoparticles considered are Cu, Al2O3, and TiO2. Mixed convection flow in Nano fluids on the surface of a circular cylinder will cause the boundary layer. The governing boundary layer equations are transformed into a non-dimensional form, and then the non-dimensional forms are transformed into a similar boundary equations by using stream function. Furthermore, an implicit finite-difference scheme known as the Keller-box method is applied to solve numerically the resulting similar boundary layer equations. The result of the research by varying the non-dimensional parameters are mixed convection, Prandtl number, nanoparticle volume fraction, heat generation, and radius of a cylinder are as follows. First, the velocity profile increase and temperature profile decrease when mixed convection parameter increase. Second, the velocity and temperature profiles decrease when Prandtl number parameter increase. Third, the velocity profile with the variation of nanoparticle volume fraction (χ) is increased when the value of χ is 0,1 ≤ χ ≤ 0,15 and the velocity profile decreases when the value of χ is 0,19 ≤ χ ≤ 0,5 while the temperature profile is increasing when the value of χ is 0,1 ≤ χ ≤ 0,5. Fourth, the velocity and temperature profiles increase when heat generation and the radius of the cylinder increase. The last, Cu, Al 2 O 3, and TiO 2 nanoparticles produce the same velocity and temperature profiles, but the three types of nanoparticles are different at the velocity and temperature values.

Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

OpenAIRE

Kihara, Hironobu

2008-01-01

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

Modelling of subcooled boiling and DNB-type boiling crisis in forced convection

International Nuclear Information System (INIS)

Bricard, Patrick

1995-01-01

This research thesis aims at being a contribution to the modelling of two phenomena occurring during a forced convection: the axial evolution of the vacuum rate, and the boiling crisis. Thus, the first part of this thesis addresses the prediction of the vacuum rate, and reports the development of a modelling of under-saturated convection in forced convection. The author reports the development and assessment of two-fluid one-dimensional model, the development of a finer analysis based on an averaging of local equations of right cross-sections in different areas. The second part of this thesis addresses the prediction of initiation of a boiling crisis. The author presents generalities and motivations for this study, reports a bibliographical study and a detailed analysis of mechanistic models present in this literature. A mechanism of boiling crisis is retained, and then further developed in a numerical modelling which is used to assess some underlying hypotheses [fr

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Group Analysis of Free Convection Flow of a Magnetic Nanofluid with Chemical Reaction

Directory of Open Access Journals (Sweden)

Md. Jashim Uddin

2015-01-01

Full Text Available A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species conservation are derived. Our (group analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional to x-1/4 whilst the reaction rate is proportional to x-1/2, where x is the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.

Symmetries, integrals, and three-dimensional reductions of Plebanski's second heavenly equation

International Nuclear Information System (INIS)

Neyzi, F.; Sheftel, M. B.; Yazici, D.

2007-01-01

We study symmetries and conservation laws for Plebanski's second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems

Zakharov-Shabat-Mikhailov scheme of construction of two-dimensional completely integrable field theories

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Columbia Univ., New York; Chudnovsky, G.V.; Columbia Univ., New York

1980-01-01

General algebraic and analytic formalism for derivation and solution of general two dimensional field theory equations of Zakharov-Shabat-Mikhailov type is presented. The examples presented show that this class of equations covers most of the known two-dimensional completely integrable equations. Possible generalizations for four dimensional systems require detailed analysis of Baecklund transformation of these equations. Baecklund transformation is presented in the form of Riemann problem and one special case of dual symmetry is worked out. (orig.)

Exact Solutions to (2+1)-Dimensional Kaup-Kupershmidt Equation

International Nuclear Information System (INIS)

Lu Hailing; Liu Xiqiang

2009-01-01

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G'/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. (general)

dimensional nonlinear evolution equations

Indian Academy of Sciences (India)

in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.

Effect of Chemical Reaction on Unsteady MHD Free Convective Two

African Journals Online (AJOL)

Joseph et al.

radiation effects on mixed convection heat and mass transfer over a vertical plate in ... numerically by finite difference method and analytically by perturbation. ... Brinkman equation was used to model the flow in the porous region. The.

Dispersed plug flow model for upflow anaerobic sludge bed reactors with focus on granular sludge dynamics

NARCIS (Netherlands)

Kalyuzhnyi, S.V.; Fedorovich, V.V.; Lens, P.N.L.

2006-01-01

A new approach to model upflow anaerobic sludge bed (UASB)-reactors, referred to as a one-dimensional dispersed plug flow model, was developed. This model focusses on the granular sludge dynamics along the reactor height, based on the balance between dispersion, sedimentation and convection using

Solution-Based Processing and Applications of Two-Dimensional Heterostructures

Science.gov (United States)

Hersam, Mark

Two-dimensional materials have emerged as promising candidates for next-generation electronics and optoelectronics, but advances in scalable nanomanufacturing are required to exploit this potential in real-world technology. This talk will explore methods for improving the uniformity of solution-processed two-dimensional materials with an eye toward realizing dispersions and inks that can be deposited into large-area thin-films. In particular, density gradient ultracentrifugation allows the solution-based isolation of graphene, boron nitride, montmorillonite, and transition metal dichalcogenides (e.g., MoS2, WS2, ReS2, MoSe2, WSe2) with homogeneous thickness down to the atomically thin limit. Similarly, two-dimensional black phosphorus is isolated in organic solvents or deoxygenated aqueous surfactant solutions with the resulting phosphorene nanosheets showing field-effect transistor mobilities and on/off ratios that are comparable to micromechanically exfoliated flakes. By adding cellulosic polymer stabilizers to these dispersions, the rheological properties can be tuned by orders of magnitude, thereby enabling two-dimensional material inks that are compatible with a range of additive manufacturing methods including inkjet, gravure, screen, and 3D printing. The resulting solution-processed two-dimensional heterostructures show promise in several device applications including photodiodes, anti-ambipolar transistors, gate-tunable memristors, and heterojunction photovoltaics.

Comparison of scale analysis and numerical simulation for saturated zone convective mixing processes

International Nuclear Information System (INIS)

Oldenburg, C.M.

1998-01-01

Scale analysis can be used to predict a variety of quantities arising from natural systems where processes are described by partial differential equations. For example, scale analysis can be applied to estimate the effectiveness of convective missing on the dilution of contaminants in groundwater. Scale analysis involves substituting simple quotients for partial derivatives and identifying and equating the dominant terms in an order-of-magnitude sense. For free convection due to sidewall heating of saturated porous media, scale analysis shows that vertical convective velocity in the thermal boundary layer region is proportional to the Rayleigh number, horizontal convective velocity is proportional to the square root of the Rayleigh number, and thermal boundary layer thickness is proportional to the inverse square root of the Rayleigh number. These scale analysis estimates are corroborated by numerical simulations of an idealized system. A scale analysis estimate of mixing time for a tracer mixing by hydrodynamic dispersion in a convection cell also agrees well with numerical simulation for two different Rayleigh numbers. Scale analysis for the heating-from-below scenario produces estimates of maximum velocity one-half as large as the sidewall case. At small values of the Rayleigh number, this estimate is confirmed by numerical simulation. For larger Rayleigh numbers, simulation results suggest maximum velocities are similar to the sidewall heating scenario. In general, agreement between scale analysis estimates and numerical simulation results serves to validate the method of scale analysis. Application is to radioactive repositories

Generalized Runge-Kutta method for two- and three-dimensional space-time diffusion equations with a variable time step

International Nuclear Information System (INIS)

Aboanber, A.E.; Hamada, Y.M.

2008-01-01

An extensive knowledge of the spatial power distribution is required for the design and analysis of different types of current-generation reactors, and that requires the development of more sophisticated theoretical methods. Therefore, the need to develop new methods for multidimensional transient reactor analysis still exists. The objective of this paper is to develop a computationally efficient numerical method for solving the multigroup, multidimensional, static and transient neutron diffusion kinetics equations. A generalized Runge-Kutta method has been developed for the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic time step control. In addition, the A(α)-stability properties of the method are investigated. The analyses of two- and three-dimensional benchmark problems as well as static and transient problems, demonstrate that very accurate solutions can be obtained with assembly-sized spatial meshes. Preliminary numerical evaluations using two- and three-dimensional finite difference codes showed that the presented generalized Runge-Kutta method is highly accurate and efficient when compared with other optimized iterative numerical and conventional finite difference methods

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

Science.gov (United States)

Bilyeu, David

code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular

New high accuracy super stable alternating direction implicit methods for two and three dimensional hyperbolic damped wave equations

Directory of Open Access Journals (Sweden)

R.K. Mohanty

2014-01-01

Full Text Available In this paper, we report new three level implicit super stable methods of order two in time and four in space for the solution of hyperbolic damped wave equations in one, two and three space dimensions subject to given appropriate initial and Dirichlet boundary conditions. We use uniform grid points both in time and space directions. Our methods behave like fourth order accurate, when grid size in time-direction is directly proportional to the square of grid size in space-direction. The proposed methods are super stable. The resulting system of algebraic equations is solved by the Gauss elimination method. We discuss new alternating direction implicit (ADI methods for two and three dimensional problems. Numerical results and the graphical representation of numerical solution are presented to illustrate the accuracy of the proposed methods.

The (2+1)-dimensional axial universes—solutions to the Einstein equations, dimensional reduction points and Klein–Fock–Gordon waves

International Nuclear Information System (INIS)

Fiziev, P P; Shirkov, D V

2012-01-01

The paper presents a generalization and further development of our recent publications, where solutions of the Klein–Fock–Gordon equation defined on a few particular D = (2 + 1)-dimensional static spacetime manifolds were considered. The latter involve toy models of two-dimensional spaces with axial symmetry, including dimensional reduction to the one-dimensional space as a singular limiting case. Here, the non-static models of space geometry with axial symmetry are under consideration. To make these models closer to physical reality, we define a set of ‘admissible’ shape functions ρ(t, z) as the (2 + 1)-dimensional Einstein equation solutions in the vacuum spacetime, in the presence of the Λ-term and for the spacetime filled with the standard ‘dust’. It is curious that in the last case the Einstein equations reduce to the well-known Monge–Ampère equation, thus enabling one to obtain the general solution of the Cauchy problem, as well as a set of other specific solutions involving one arbitrary function. A few explicit solutions of the Klein–Fock–Gordon equation in this set are given. An interesting qualitative feature of these solutions relates to the dimensional reduction points, their classification and time behavior. In particular, these new entities could provide us with novel insight into the nature of P- and T-violations and of the Big Bang. A short comparison with other attempts to utilize the dimensional reduction of the spacetime is given. (paper)

New numerical solutions of three-dimensional compressible hydrodynamic convection. [in stars

Science.gov (United States)

Hossain, Murshed; Mullan, D. J.

1990-01-01

Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

Science.gov (United States)

Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

2017-12-01

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

Solutions and Conservation Laws of a (2+1-Dimensional Boussinesq Equation

Directory of Open Access Journals (Sweden)

Letlhogonolo Daddy Moleleki

2013-01-01

Full Text Available We study a nonlinear evolution partial differential equation, namely, the (2+1-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1-dimensional Boussinesq equation. Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1-dimensional Boussinesq equation.

Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

International Nuclear Information System (INIS)

Ka-Lin, Su; Yuan-Xi, Xie

2010-01-01

By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)

Average pollutant concentration in soil profile simulated with Convective-Dispersive Equation. Model and Manual

Science.gov (United States)

Different parts of soil solution move with different velocities, and therefore chemicals are leached gradually from soil with infiltrating water. Solute dispersivity is the soil parameter characterizing this phenomenon. To characterize the dispersivity of soil profile at field scale, it is desirable...

Exact Solutions for Two Equation Hierarchies

International Nuclear Information System (INIS)

Song-Lin, Zhao; Da-Jun, Zhang; Jie, Ji

2010-01-01

Bilinear forms and double-Wronskian solutions are given for two hierarchies, the (2+1)-dimensional breaking Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, Jordan block solutions, rational solutions, complexitons and mixed solutions. (general)

On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension

International Nuclear Information System (INIS)

Pelinovsky, D. E.; Stefanov, A.

2008-01-01

Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, Hφ=(-Δ+V)φ=-(φ n+1 +φ n-1 -2φ n )+V n φ n . We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e itH P a.c. (H) parallel l σ 2 →l -σ 2 -3/2 for any fixed σ>(5/2) and any t>0, where P a.c. (H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e itH P a.c. (H) parallel l 1 →l ∞ -1/3 , which are sharp for the discrete Schroedinger operators even for V=0

MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation

Energy Technology Data Exchange (ETDEWEB)

Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko

1997-10-01

A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)

Finite element solution of two dimensional time dependent heat equation

International Nuclear Information System (INIS)

Maaz

1999-01-01

A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)

Low-dimensional model of resistive interchange convection in magnetized plasma

International Nuclear Information System (INIS)

Bazdenkov, S.; Sato, Tetsuya

1997-09-01

Self-organization and generation of large shear flow component in turbulent resistive interchange convection in magnetized plasma is considered. The effect of plasma density-electrostatic potential coupling via the inertialess electron dynamics along the magnetic field is shown to play significant role in the onset of shear component. The results of large-scale numerical simulation and low-dimensional (reduced) model are presented and compared. (author)

Global solubility of the three-dimensional Navier-Stokes equations with uniformly large initial vorticity

International Nuclear Information System (INIS)

Makhalov, A S; Nikolaenko, V P

2003-01-01

This paper is a survey of results concerning the three-dimensional Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. The existence of regular solutions of the three-dimensional Navier-Stokes equations on an unbounded time interval is proved for large initial data both in R 3 and in bounded cylindrical domains. Moreover, the existence of smooth solutions on large finite time intervals is established for the three-dimensional Euler equations. These results are obtained without additional assumptions on the behaviour of solutions for t>0. Any smooth solution is not close to any two-dimensional manifold. Our approach is based on the computation of singular limits of rapidly oscillating operators, non-linear averaging, and a consideration of the mutual absorption of non-linear oscillations of the vorticity field. The use of resonance conditions, methods from the theory of small divisors, and non-linear averaging of almost periodic functions leads to the limit resonant Navier-Stokes equations. Global solubility of these equations is proved without any conditions on the three-dimensional initial data. The global regularity of weak solutions of three-dimensional Navier-Stokes equations with uniformly large vorticity at t=0 is proved by using the regularity of weak solutions and the strong convergence

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

Science.gov (United States)

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

Numerical simulation of natural convection in annuli with internal fins

International Nuclear Information System (INIS)

Ha, Man Yeong; Kim, Joo Goo

2004-01-01

The solution for the natural convection in internally finned horizontal annuli is obtained by using a numerical simulation of time-dependent and two-dimensional governing equations. The fins existing in annuli influence the flow pattern, temperature distribution and heat transfer rate. The variations of the fin configuration suppress or accelerate the free convective effects compared to those of the smooth tubes. The effects of fin configuration, number of fins and ratio of annulus gap width to the inner cylinder radius on the fluid flow and heat transfer in annuli are demonstrated by the distribution of the velocity vector, isotherms and streamlines. The governing equations are solved efficiently by using a parallel implementation. The technique is adopted for reduction of the computation cost. The parallelization is performed with the domain decomposition technique and message passing between sub-domains on the basis of the MPI library. The results from parallel computation reveal in consistency with those of the sequential program. Moreover, the speed-up ratio shows linearity with the number of processor

Natural convection in a porous medium: External flows

International Nuclear Information System (INIS)

Cheng, P.

1985-01-01

Early theoretical work on heat transfer in porous media focussed its attention on the onset of natural convection and cellular convection in rectangular enclosures with heating from below. Recently, increased attention has been directed to the study of natural convection in a porous medium external to heated surfaces and bodies. Boundary layer approximations were introduced, and similarly solutions have been obtained for steady natural convection boundary layers adjacent to a heated flat plate, a horizontal cylinder and a sphere as well as other two-dimensional and axisymmetric bodies of arbitrary shape. Higher order boundary layer theories have been carried out to assess the accuracy of the boundary layer approximation. The effects of entrainments at the edge of the boundary layer, the inclination angle of the heated inclined plate, and the upstream geometry on the heat transfer characteristics have been investigated based on the method of matched asymptotic expansions. The conditions for the onset of vortex instability in porous layers heated from below were determined based on linear stability analyses. The effects of no-slip boundary conditions, non-Darcy and thermal dispersion, which were neglected in all of the previous theoretical investigations, have recently been re-examined. Experimental investigations on natural convection about a vertical and inclined heated plate, a horizontal cylinder, as well as plume rise from a horizontal line source of heat have been conducted. All of this work is reviewed in this paper

Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1977-01-01

A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schroedinger problem and the KPI equation

International Nuclear Information System (INIS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.K.; Polivanov, M.C.

1993-01-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. The authors demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schroedinger equation as an example, it is shown that all types of solutions of the linear problem, as well as spectral data known in the literature, are given as specific values of this unique function - the resolvent function. A new form of the inverse problem is formulated. 7 refs

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

Science.gov (United States)

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

Science.gov (United States)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

Science.gov (United States)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Multisoliton formula for completely integrable two-dimensional systems

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1979-01-01

For general two-dimensional completely integrable systems, the exact formulae for multisoliton type solutions are given. The formulae are obtained algebrically from solutions of two linear partial differential equations

Analytical approach to (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev-Petviashvili equation

Energy Technology Data Exchange (ETDEWEB)

Sariaydin, Selin; Yildirim, Ahmet [Ege Univ., Dept. of Mathematics, Bornova-Izmir (Turkey)

2010-05-15

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation u{sub tt} - u{sub xx} - u{sub yy} - (u{sup 2}){sub xx} - u{sub xxxx} = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation u{sub xt} - 6u{sub x}{sup 2} + 6uu{sub xx} - u{sub xxxx} - u{sub yy} - u{sub zz} = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically. (orig.)

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

International Nuclear Information System (INIS)

Sá, Lucas

2017-01-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism. (paper)

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

Energy Technology Data Exchange (ETDEWEB)

Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)

2013-08-15

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

International Nuclear Information System (INIS)

Hoang-Do, Ngoc-Tram; Pham, Dang-Lan; Le, Van-Hoang

2013-01-01

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity

Numerical Simulations of Scattering of Light from Two-Dimensional Rough Surfaces Using the Reduced Rayleigh Equation

Directory of Open Access Journals (Sweden)

Tor eNordam

2013-09-01

Full Text Available A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. Implementation and performance issues of the method, and various consistency checks of it, are presented and discussed. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization. As an illustration, we calculate the full angular distribution of the mean differential reflection coefficient for the scattering of p- or s-polarized light incident on two-dimensional dielectric or metallic randomly rough surfaces defined by (isotropic or anisotropic Gaussian and cylindrical power spectra. Simulation results obtained by the proposed method agree well with experimentally measured scattering data taken from similar well-characterized, rough metal samples, or to results obtained by other numerical methods.

On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

KAUST Repository

Settle, Sean O.; Douglas, Craig C.; Kim, Imbunm; Sheen, Dongwoo

2013-01-01

- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make

The one-dimensional Gross-Pitaevskii equation and its some excitation states

Energy Technology Data Exchange (ETDEWEB)

Prayitno, T. B., E-mail: trunk-002@yahoo.com [Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jl. Pemuda Rawamangun no. 10, Jakarta, 13220 (Indonesia)

2015-04-16

We have derived some excitation states of the one-dimensional Gross-Pitaevskii equation coupled by the gravitational potential. The methods that we have used here are taken by pursuing the recent work of Kivshar et. al. by considering the equation as a macroscopic quantum oscillator. To obtain the states, we have made the appropriate transformation to reduce the three-dimensional Gross-Pitaevskii equation into the one-dimensional Gross-Pitaevskii equation and applying the time-independent perturbation theory in the general solution of the one-dimensional Gross-Pitaevskii equation as a linear superposition of the normalized eigenfunctions of the Schrödinger equation for the harmonic oscillator potential. Moreover, we also impose the condition by assuming that some terms in the equation should be so small in order to preserve the use of the perturbation method.

Beam stabilization in the two-dimensional nonlinear Schrodinger equation with an attractive potential by beam splitting and radiation

DEFF Research Database (Denmark)

leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich

2004-01-01

The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...... losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials....

Surface acoustic waves in two dimensional phononic crystal with anisotropic inclusions

Directory of Open Access Journals (Sweden)

Ketata H.

2012-06-01

Full Text Available An analysis is given to the band structure of the two dimensional solid phononic crystal considered as a semi infinite medium. The lattice includes an array of elastic anisotropic materials with different shapes embedded in a uniform matrix. For illustration two kinds of phononic materials are assumed. A particular attention is devoted to the computational procedure which is mainly based on the plane wave expansion (PWE method. It has been adapted to Matlab environment. Numerical calculations of the dispersion curves have been achieved by introducing particular functions which transform motion equations into an Eigen value problem. Significant improvements are obtained by increasing reasonably the number of Fourier components even when a large elastic mismatch is assumed. Such approach can be generalized to different types of symmetry and permit new physical properties as piezoelectricity to be added. The actual semi infinite phononic structure with a free surface has been shown to support surface acoustic waves (SAW. The obtained dispersion curves reveal band gaps in the SAW branches. It has been found that the influence, of the filling factor and anisotropy on their band gaps, is different from that of bulk waves.

Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

DEFF Research Database (Denmark)

Eldeberky, Y.; Madsen, Per A.

1999-01-01

and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

Two-dimensional sparse wavenumber recovery for guided wavefields

Science.gov (United States)

Sabeti, Soroosh; Harley, Joel B.

2018-04-01

The multi-modal and dispersive behavior of guided waves is often characterized by their dispersion curves, which describe their frequency-wavenumber behavior. In prior work, compressive sensing based techniques, such as sparse wavenumber analysis (SWA), have been capable of recovering dispersion curves from limited data samples. A major limitation of SWA, however, is the assumption that the structure is isotropic. As a result, SWA fails when applied to composites and other anisotropic structures. There have been efforts to address this issue in the literature, but they either are not easily generalizable or do not sufficiently express the data. In this paper, we enhance the existing approaches by employing a two-dimensional wavenumber model to account for direction-dependent velocities in anisotropic media. We integrate this model with tools from compressive sensing to reconstruct a wavefield from incomplete data. Specifically, we create a modified two-dimensional orthogonal matching pursuit algorithm that takes an undersampled wavefield image, with specified unknown elements, and determines its sparse wavenumber characteristics. We then recover the entire wavefield from the sparse representations obtained with our small number of data samples.

A closed-form solution for the two-dimensional transport equation by the LTS{sub N} nodal method in the energy range of Compton effect

Energy Technology Data Exchange (ETDEWEB)

Rodriguez, B.D.A., E-mail: barbararodriguez@furg.b [Universidade Federal do Rio Grande, Instituto de Matematica, Estatistica e Fisica, Rio Grande, RS (Brazil); Vilhena, M.T., E-mail: vilhena@mat.ufrgs.b [Universidade Federal do Rio Grande do Sul, Departamento de Matematica Pura e Aplicada, Porto Alegre, RS (Brazil); Hoff, G., E-mail: hoff@pucrs.b [Pontificia Universidade Catolica do Rio Grande do Sul, Faculdade de Fisica, Porto Alegre, RS (Brazil); Bodmann, B.E.J., E-mail: bardo.bodmann@ufrgs.b [Universidade Federal do Rio Grande do Sul, Departamento de Matematica Pura e Aplicada, Porto Alegre, RS (Brazil)

2011-01-15

In the present work we report on a closed-form solution for the two-dimensional Compton transport equation by the LTS{sub N} nodal method in the energy range of Compton effect. The solution is determined using the LTS{sub N} nodal approach for homogeneous and heterogeneous rectangular domains, assuming the Klein-Nishina scattering kernel and a multi-group model. The solution is obtained by two one-dimensional S{sub N} equation systems resulting from integrating out one of the orthogonal variables of the S{sub N} equations in the rectangular domain. The leakage angular fluxes are approximated by exponential forms, which allows to determine a closed-form solution for the photons transport equation. The angular flux and the parameters of the medium are used for the calculation of the absorbed energy in rectangular domains with different dimensions and compositions. In this study, only the absorbed energy by Compton effect is considered. We present numerical simulations and comparisons with results obtained by using the simulation platform GEANT4 (version 9.1) with its low energy libraries.

THE EFFECT OF SOLAR RADIATION ON AUTOMOBILE ENVIRONMENT THROUGH NATURAL CONVECTION AND MIXED CONVECTION

Directory of Open Access Journals (Sweden)

MD. FAISAL KADER

2012-10-01

Full Text Available In the present paper, the effect of solar radiation on automobiles has been studied by both experimentally and numerically. The numerical solution is done by an operation friendly and fast CFD code – SC/Tetra with a full scale model of a SM3 car and turbulence is modeled by the standard k-ε equation. Numerical analysis of the three-dimensional model predicts a detailed description of fluid flow and temperature distribution in the passenger compartment during both the natural convection due to the incoming solar radiation and mixed convection due to the flow from defrost nozzle and radiation. It can be seen that solar radiation is an important parameter to raise the compartment temperature above the ambient temperature during summer. During natural convection, the rate of heat transfer is fast at the initial period. In the mixed convection analyses, it is found that the temperature drops down to a comfortable range almost linearly at the initial stage. Experimental investigations are performed to determine the temperature contour on the windshield and the local temperature at a particular point for further validation of the numerical results.

Solving the two-dimensional Schrödinger equation using basis ...

Indian Academy of Sciences (India)

Ihab H Naeim

2017-10-19

Oct 19, 2017 ... We shall study the case of a two-dimensional quantum system .... Solving (6) for ck,l is tantamount to pro- ... case, the final computational problem becomes quite ..... matrix approach fails in the case of two particles con-.

FREQUENCY SHIFTS OF RESONANT MODES OF THE SUN DUE TO NEAR-SURFACE CONVECTIVE SCATTERING

International Nuclear Information System (INIS)

Bhattacharya, J.; Hanasoge, S.; Antia, H. M.

2015-01-01

Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the “surface term.” The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary three-dimensional (3D) flows, can be reduced to an effective “quiet-Sun” wave equation with altered sound speed, Brünt–Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection

Modifications in the Teach-C computer code for convection analysis-two-dimensional transient diffusion

International Nuclear Information System (INIS)

Sampaio, P.A.B. de.

1987-08-01

Some modifications in Teach-C computer program to analyse the heat conduction with convective heat transport are presented. The utilization of the program to solve a convective - diffusion problem is studied and the results are compared with an analysis of the same problem, in steady - state conditions, by finite element method [pt

Time-dependent patterns in quasivertical cylindrical binary convection

Science.gov (United States)

Alonso, Arantxa; Mercader, Isabel; Batiste, Oriol

2018-02-01

This paper reports on numerical investigations of the effect of a slight inclination α on pattern formation in a shallow vertical cylindrical cell heated from below for binary mixtures with a positive value of the Soret coefficient. By using direct numerical simulation of the three-dimensional Boussinesq equations with Soret effect in cylindrical geometry, we show that a slight inclination of the cell in the range α ≈0.036 rad =2∘ strongly influences pattern selection. The large-scale shear flow (LSSF) induced by the small tilt of gravity overcomes the squarelike arrangements observed in noninclined cylinders in the Soret regime, stratifies the fluid along the direction of inclination, and produces an enhanced separation of the two components of the mixture. The competition between shear effects and horizontal and vertical buoyancy alters significantly the dynamics observed in noninclined convection. Additional unexpected time-dependent patterns coexist with the basic LSSF. We focus on an unsual periodic state recently discovered in an experiment, the so-called superhighway convection state (SHC), in which ascending and descending regions of fluid move in opposite directions. We provide numerical confirmation that Boussinesq Navier-Stokes equations with standard boundary conditions contain the essential ingredients that allow for the existence of such a state. Also, we obtain a persistent heteroclinic structure where regular oscillations between a SHC pattern and a state of nearly stationary longitudinal rolls take place. We characterize numerically these time-dependent patterns and investigate the dynamics around the threshold of convection.

Relativistic two-and three-particle scattering equations using instant and light-front dynamics

International Nuclear Information System (INIS)

Adhikari, S.K.; Tomio, L.; Frederico, T.

1992-01-01

Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander; Petrova, Guergana

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions

Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

KAUST Repository

Zhang, Zhendong; Schuster, Gerard T.; Liu, Yike; Hanafy, Sherif M.; Li, Jing

2016-01-01

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized

Two-dimensional effects in nonlinear Kronig-Penney models

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim

1997-01-01

An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...

Two-Dimensional Motions of Rockets

Science.gov (United States)

Kang, Yoonhwan; Bae, Saebyok

2007-01-01

We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…

The Weight Loss Effect of Heated Inner Cylinder by Free Convection in Horizontal Cylindrical Enclosure

Science.gov (United States)

Sboev, I. O.; Kondrashov, A. N.; Rybkin, K. A.; Burkova, L. N.; Goncharov, M. M.

2018-03-01

The work presents results of numerical simulations of natural convection in cavity formed by the surfaces of two horizontal coaxial cylinders. The temperature of the outer cylinder is constant. The area between the cylinders is filled with an ideal incompressible fluid. The inner cylinder is set as the heater. The solution of the equations of thermal convection in a two-dimensional approximation performed by the software package ANSYS Fluent with finite volume method. The study compares the results of numerical simulation with several well-known theoretical and experimental results. The nature of interaction of the inner cylinder with a convection current created in the gap was observed. It was shown that the flux appeared around a heated cylinder affects the weight of the heat source and causes an additional lift force from the surrounding fluid. The various Rayleigh numbers (from 1.0 ṡ 103 to 1.5 ṡ 106) and fluid with different Prandtl number (from 0.5 to 1.0 ṡ 105) are considered.

Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

International Nuclear Information System (INIS)

Zhou, Xiafeng; Guo, Jiong; Li, Fu

2015-01-01

Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn

2015-12-15

Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

Impact of magnetic field in three-dimensional flow of Sisko nanofluid with convective condition

Energy Technology Data Exchange (ETDEWEB)

Hayat, T. [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Ahmad, B. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)

2016-09-01

This communication addresses the magnetohydrodynamic (MHD) three dimensional flow of Sisko nanofluid bounded by a surface stretched bidirectionally. Nanofluid model includes the Brownian motion and thermophoresis. Heat transfer through convective condition is discussed. Developed condition with the zero nanoparticles mass flux at the surface is implemented. The governing problems subject to boundary layer approximations are computed for the convergent series solutions. Effects of interesting flow parameters on the temperature and nanoparticles concentration distributions are studied and discussed. Skin friction coefficients and the local Nusselt number are computed and analyzed. - Highlights: • Three-dimensional flow of Sisko nanofluid is modeled. • Uniform applied magnetic field is adopted. • Brownian motion and thermophoresis effects are accounted. • Heat transfer convective condition is utilized. • Recently constructed condition with zero nanoparticles mass flux is implemented.

Topological aspect of disclinations in two-dimensional crystals

International Nuclear Information System (INIS)

Wei-Kai, Qi; Tao, Zhu; Yong, Chen; Ji-Rong, Ren

2009-01-01

By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given. (the physics of elementary particles and fields)

Exact solutions of the vacuum Einstein's equations allowing for two noncommuting Killing vectors

International Nuclear Information System (INIS)

Aliev, V.N.; Leznov, A.N.

1990-01-01

Einstein's equations are written in the form of covariant gauge theory in two-dimensional space with binomial solvable gauge group, with respect to two noncommutative of Killing vectors. The theory is exact integrable in one-dimensional case and series of partial exact solutions are constructed in two-dimensional. 5 refs

Direct numerical simulation of the passive scalar field in a two-dimensional turbulent channel flow

International Nuclear Information System (INIS)

Kasagi, N.; Tomita, Y.; Kuroda, A.

1991-01-01

This paper reports on a direct numerical simulation (DNS) of the fully developed thermal field in a two-dimensional turbulent channel flow of air that was carried out. The iso-flux condition is imposed on the walls so that the local mean temperature linearly increases in the streamwise direction. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained include rms velocity and temperature fluctuations, Reynolds stresses, turbulent heat fluxes and other higher order correlations. They are compared mainly with the DNS data obtained by Kim and Moin (1987) and Kim (1987) in a higher Reynolds number flow with isothermal walls. Agreement between these two results is generally good. Each term in the budget equations of temperature variance, its dissipation rate and turbulent heat fluxes is also calculated in order to establish a data base of convective heat transfer for thermal turbulence modeling

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

Science.gov (United States)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

Numerical simulation of convection and heat transfer in Czochralski crystal growth by multiple-relaxation-time LBM

Science.gov (United States)

Liu, Ding; Huang, Weichao; Zhang, Ni

2017-07-01

A two-dimensional axisymmetric swirling model based on the lattice Boltzmann method (LBM) in a pseudo Cartesian coordinate system is posited to simulate Czochralski (Cz) crystal growth in this paper. Specifically, the multiple-relaxation-time LBM (MRT-LBM) combined with the finite difference method (FDM) is used to analyze the melt convection and heat transfer in the process of Cz crystal growth. An incompressible axisymmetric swirling MRT-LB D2Q9 model is applied to solve for the axial and radial velocities by inserting thermal buoyancy and rotational inertial force into the two-dimensional lattice Boltzmann equation. In addition, the melt temperature and the azimuthal velocity are solved by MRT-LB D2Q5 models, and the crystal temperature is solved by FDM. The comparison results of stream functions values of different methods demonstrate that our hybrid model can be used to simulate the fluid-thermal coupling in the axisymmetric swirling model correctly and effectively. Furthermore, numerical simulations of melt convection and heat transfer are conducted under the conditions of high Grashof (Gr) numbers, within the range of 105 ˜ 107, and different high Reynolds (Re) numbers. The experimental results show our hybrid model can obtain the exact solution of complex crystal-growth models and analyze the fluid-thermal coupling effectively under the combined action of natural convection and forced convection.

1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

International Nuclear Information System (INIS)

Biswas, Anjan

2009-01-01

In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.

Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains

Directory of Open Access Journals (Sweden)

Arnaldo Simal do Nascimento

1997-12-01

Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...

Indian Academy of Sciences (India)

Aly R Seadawy

2017-09-13

Sep 13, 2017 ... We considered the two-dimensional DASWs in colli- sionless, unmagnetized cold plasma consisting of dust fluid, ions and electrons. The dynamics of DASWs is governed by the normalized fluid equations of nonlin- ear continuity (1), nonlinear motion of system (2) and. (3) and linear Poisson equation (4) as.

Revised predictive equations for salt intrusion modelling in estuaries

NARCIS (Netherlands)

Gisen, J.I.A.; Savenije, H.H.G.; Nijzink, R.C.

2015-01-01

For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion

Iterative solution of the semiconductor device equations

Energy Technology Data Exchange (ETDEWEB)

Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)

1996-12-31

Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.

Light propagation in two-dimensional photonic crystals based on uniaxial polar materials: results on polaritonic spectrum

Science.gov (United States)

Gómez-Urrea, H. A.; Duque, C. A.; Pérez-Quintana, I. V.; Mora-Ramos, M. E.

2017-03-01

The dispersion relations of two-dimensional photonic crystals made of uniaxial polaritonic cylinders arranged in triangular lattice are calculated. The particular case of the transverse magnetic polarization is taken into account. Three different uniaxial materials showing transverse phonon-polariton excitations are considered: aluminum nitride, gallium nitride, and indium nitride. The study is carried out by means of the finite-difference time-domain technique for the solution of Maxwell equations, together with the method of the auxiliary differential equation. It is shown that changing the filling fraction can result in the modification of both the photonic and polaritonic bandgaps in the optical dispersion relations. Wider gaps appear for smaller filling fraction values, whereas a larger number of photonic bandgaps will occur within the frequency range considered when a larger filling fraction is used. The effect of including the distinct wurtzite III-V nitride semiconductors as core materials in the cylinders embedded in the air on the photonic properties is discussed as well, highlighting the effect of the dielectric anisotropy on the properties of the polaritonic part of the photonic spectrum.

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian; Sparber, Christof; Markowich, Peter A.

2014-01-01

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass

Interaction phenomenon to dimensionally reduced p-gBKP equation

Science.gov (United States)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

Positioning in a flat two-dimensional space-time: The delay master equation

International Nuclear Information System (INIS)

Coll, Bartolome; Ferrando, Joan Josep; Morales-Lladosa, Juan Antonio

2010-01-01

The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [B. Coll, J. J. Ferrando, and J. A. Morales, Phys. Rev. D 73, 084017 (2006); ibid.74, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here, generic relativistic positioning systems in the Minkowski plane are studied. The information that can be obtained from the data received by a user of the positioning system is analyzed in detail. In particular, it is shown that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so-called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. These results are illustrated with the obtention of the dynamics of the emitters and of the user from specific sets of data received by the user.

Classical solutions of two dimensional Stokes problems on non smooth domains. 2: Collocation method for the Radon equation

International Nuclear Information System (INIS)

Lubuma, M.S.

1991-05-01

The non uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities. (author). 34 refs

On Devising Boussinesq-type Equations with Bounded Eigenspectra: Two Horizontal Dimensions

DEFF Research Database (Denmark)

Eskilsson, Claes; Engsig-Karup, Allan Peter

2015-01-01

Boussinesq-type equations are used to describe the propagation and transformation of free-surface waves in the nearshore region. The nonlinear and dispersive performance of the equations are determined by tunable parameters. Recently the authors presented conditions on the free parameters under...... study and provide numerical experimentswhich confirms the theoretical results also is valid in two horizontal dimensions....

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

KAUST Repository

Wu, Zedong

2018-04-05

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

Two-dimensional fourier transform spectrometer

Science.gov (United States)

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

Hydromagnetic transport phenomena from a stretching or shrinking nonlinear nanomaterial sheet with Navier slip and convective heating: A model for bio-nano-materials processing

Energy Technology Data Exchange (ETDEWEB)

Uddin, M.J., E-mail: jashim_74@yahoo.com [Department of Mathematics, American International University-Bangladesh, Banani Dhaka 1213 (Bangladesh); Bég, O. Anwar [Gort Engovation Research (Propulsion/Biomechanics), Gabriel' s Wing House, 15 Southmere Ave., Bradford, BD7 3NU England (United Kingdom); Amin, N. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor (Malaysia)

2014-11-15

Steady two-dimensional magnetohydrodynamic laminar free convective boundary layer slip flow of an electrically conducting Newtonian nanofluid from a translating stretching/shrinking sheet in a quiescent fluid is studied. A convective heating boundary condition is incorporated. The transport equations along with the boundary conditions are first converted into dimensionless form and following the implementation of a linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth fifth order method from Maple. Validation of the Maple solutions is achieved with previous non-magnetic published results. The effects of the emerging thermophysical parameters; namely, stretching/shrinking, velocity slip, magnetic field, convective heat transfer and buoyancy ratio parameters, on the dimensionless velocity, temperature and concentration (nanoparticle fraction) are depicted graphically and interpreted at length. It is found that velocity increases whilst temperature and concentration reduce with the velocity slip. Magnetic field causes to reduce velocity and enhances temperature and concentration. Velocity, temperature as well as concentration rises with convective heating parameter. The study is relevant to the synthesis of bio-magnetic nanofluids of potential interest in wound treatments, skin repair and smart coatings for biological devices. - Highlights: • This paper analyses MHD slip flow of nofluid with convective boundary conditions. • Group method is used to transform governing equations into similarity equations. • The Runge–Kutta–Fehlberg method is used for numerical computations. • The study is relevant to synthesis of bio-magnetic nanofluids.

Five-dimensional truncation of the plane incompressible navier-stokes equations

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C [Camerino Univ. (Italy). Istituto di Matematica; Franceschini, V [Modena Univ. (Italy). Istituto Matematico

1979-01-01

A five-modes truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a torus is considered. A computer analysis shows that for a certain range of the Reynolds number the system exhibits a stochastic behaviour, approached through an involved sequence of bifurcations.

Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity

Energy Technology Data Exchange (ETDEWEB)

Bettaibi, Soufiene, E-mail: Bettaibisoufiene@gmail.com [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia); Kuznik, Frédéric [INSA-Lyon, CETHIL, F-69621 Villeurbanne (France); Université de Lyon, CNRS, UMR5008, F-69622 Villeurbanne (France); Sediki, Ezeddine [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia)

2014-06-27

Highlights: • Mixed convection heat transfer in 2D lid-driven cavity is studied numerically. • Hybrid scheme with multiple relaxation time lattice Boltzmann method is used to obtain the velocity field. • Finite difference method is used to compute the temperature. • Effect of both Richardson and Reynolds numbers for mixed convection is studied. - Abstract: Mixed convection heat transfer in two-dimensional lid-driven rectangular cavity filled with air (Pr=0.71) is studied numerically. A hybrid scheme with multiple relaxation time lattice Boltzmann method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the finite difference method (FDM). The main objective of this work is to investigate the model effectiveness for mixed convection flow simulation. Results are presented in terms of streamlines, isotherms and Nusselt numbers. Excellent agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of our proposed approach.

Intrinsic two-dimensional states on the pristine surface of tellurium

Science.gov (United States)

Li, Pengke; Appelbaum, Ian

2018-05-01

Atomic chains configured in a helical geometry have fascinating properties, including phases hosting localized bound states in their electronic structure. We show how the zero-dimensional state—bound to the edge of a single one-dimensional helical chain of tellurium atoms—evolves into two-dimensional bands on the c -axis surface of the three-dimensional trigonal bulk. We give an effective Hamiltonian description of its dispersion in k space by exploiting confinement to a virtual bilayer, and elaborate on the diminished role of spin-orbit coupling. These intrinsic gap-penetrating surface bands were neglected in the interpretation of seminal experiments, where two-dimensional transport was otherwise attributed to extrinsic accumulation layers.

Turbulent Plume Dispersion over Two-dimensional Idealized Urban Street Canyons

Science.gov (United States)

Wong, C. C. C.; Liu, C. H.

2012-04-01

Human activities are the primary pollutant sources which degrade the living quality in the current era of dense and compact cities. A simple and reasonably accurate pollutant dispersion model is helpful to reduce pollutant concentrations in city or neighborhood scales by refining architectural design or urban planning. The conventional method to estimate the pollutant concentration from point/line sources is the Gaussian plume model using empirical dispersion coefficients. Its accuracy is pretty well for applying to rural areas. However, the dispersion coefficients only account for the atmospheric stability and streamwise distance that often overlook the roughness of urban surfaces. Large-scale buildings erected in urban areas significantly modify the surface roughness that in turn affects the pollutant transport in the urban canopy layer (UCL). We hypothesize that the aerodynamic resistance is another factor governing the dispersion coefficient in the UCL. This study is thus conceived to study the effects of urban roughness on pollutant dispersion coefficients and the plume behaviors. Large-eddy simulations (LESs) are carried out to examine the plume dispersion from a ground-level pollutant source over idealized 2D street canyons in neutral stratification. Computations with a wide range of aspect ratios (ARs), including skimming flow to isolated flow regimes, are conducted. The vertical profiles of pollutant distribution for different values of friction factor are compared that all reach a self-similar Gaussian shape. Preliminary results show that the pollutant dispersion is closely related to the friction factor. For relatively small roughness, the factors of dispersion coefficient vary linearly with the friction factor until the roughness is over a certain level. When the friction factor is large, its effect on the dispersion coefficient is less significant. Since the linear region covers at least one-third of the full range of friction factor in our empirical

Two-level schemes for the advection equation

Science.gov (United States)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

MASCOT user's guide--Version 2.0: Analytical solutions for multidimensional transport of a four-member radionuclide decay chain in ground water

International Nuclear Information System (INIS)

Gureghian, A.B.

1988-07-01

The MASCOT code computes the two- and three-dimensional space-time dependent convective-dispersive transport of a four-member radionuclide decay chain in unbounded homogeneous porous media, for constant and radionuclide-dependent release, and assuming steady- state isothermal ground-water flow and parallel streamlines. The model can handle a single or multiple finite line source or a Gaussian distributed source in the two-dimensional case, and a single or multiple patch source or bivariate-normal distributed source in the three-dimensional case. The differential equations are solved by Laplace and Fourier transforms and a Gauss-Legendre integration scheme. 33 figs., 3 tabs

Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

Science.gov (United States)

Servan-Camas, Borja; Tsai, Frank T.-C.

2010-02-01

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).

Developing of two-dimensional model of the corium cooling and behavior with non-condensible gas injection

Energy Technology Data Exchange (ETDEWEB)

Chung, Chang Hyun; Cho, Jae Seon; Kim, Ju Youl; Kim, Do Hyoung [Seoul National University, Seoul (Korea, Republic of)

1997-07-01

The purpose of this study is to understand the effect of the non-condensible gas injection into the molten corium on the heat transfer and dynamic behavior within the melt when molten core-concrete interaction occurs during the hypothetical severe accident. Corium behavior with gas injection effect is two phase fluid pattern in which droplet has dispersed gas phase in continuous liquid phase of corium. To analyze this behavior, two dimensional governing equation using the governing equation, the computer program is accomplished using the finite difference method and SIMPLER algorithm. And benchmarking calculation is performed for the KfK experiment, which consider the gas injection effect. After this pre-calculation, an analyses is performed with typical corium under severe accidents. It is concluded that the heat transfer within corium increases as the metal components of the corium and gas injection velocity increase. 88 refs., 23 tabs., 35 figs. (author)

Galactic Cosmic-ray Transport in the Global Heliosphere: A Four-Dimensional Stochastic Model

Science.gov (United States)

Florinski, V.

2009-04-01

We study galactic cosmic-ray transport in the outer heliosphere and heliosheath using a newly developed transport model based on stochastic integration of the phase-space trajectories of Parker's equation. The model employs backward integration of the diffusion-convection transport equation using Ito calculus and is four-dimensional in space+momentum. We apply the model to the problem of galactic proton transport in the heliosphere during a negative solar minimum. Model results are compared with the Voyager measurements of galactic proton radial gradients and spectra in the heliosheath. We show that the heliosheath is not as efficient in diverting cosmic rays during solar minima as predicted by earlier two-dimensional models.

Self-focusing instability of two-dimensional solitons and vortices

DEFF Research Database (Denmark)

Kuznetsov, E.A.; Juul Rasmussen, J.

1995-01-01

The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl...

Numerical investigation of double diffusive buoyancy forces induced natural convection in a cavity partially heated and cooled from sidewalls

Directory of Open Access Journals (Sweden)

Rasoul Nikbakhti

2016-03-01

Full Text Available This paper deals with a numerical investigation of double-diffusive natural convective heat and mass transfer in a cavity filled with Newtonian fluid. The active parts of two vertical walls of the cavity are maintained at fixed but different temperatures and concentrations, while the other two walls, as well as inactive areas of the sidewalls, are considered to be adiabatic and impermeable to mass transfer. The length of the thermally active part equals half of the height. The non-dimensional forms of governing transport equations that describe double-diffusive natural convection for two-dimensional incompressible flow are functions of temperature or energy, concentration, vorticity, and stream-function. The coupled differential equations are discretized via FDM (Finite Difference Method. The Successive-Over-Relaxation (SOR method is used in the solution of the stream function equation. The analysis has been done for an enclosure with different aspect ratios ranging from 0.5 to 11 for three different combinations of partially active sections. The results are presented graphically in terms of streamlines, isotherms and isoconcentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers for various parameters including thermal Grashof number, Lewis number, buoyancy ratio and aspect ratio. It is revealed that the placement order of partially thermally active walls and the buoyancy ratio influence significantly the flow pattern and the corresponding heat and mass transfer performance in the cavity.

Thermal convection around a heat source embedded in a box containing a saturated porous medium

Energy Technology Data Exchange (ETDEWEB)

Himasekhar, K.; Bau, H.H. (Univ. of Pennsylvania, Philadelphia (USA))

1988-08-01

A study of the thermal convection around a uniform flux cylinder embedded in a box containing a saturated porous medium is carried out experimentally and theoretically. The experimental work includes heat transfer and temperature field measurements. It is observed that for low Rayleigh numbers, the flow is two dimensional and time independent. Once a critical Rayleigh number is exceeded, the flow undergoes a Hopf bifurcation and becomes three dimensional and time dependent. The theoretical study involves the numerical solution of the two-dimensional Darcy-Oberbeck-Boussinesq equations. The complicated geometry is conveniently handled by mapping the physical domain onto a rectangle via the use of boundary-fitted coordinates. The numerical code can easily be extended to handle diverse geometric configurations. For low Rayleigh numbers, the theoretical results agree favorably with the experimental observations. However, the appearance of three-dimensional flow phenomena limits the range of utility of the numerical code.

On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer

Directory of Open Access Journals (Sweden)

R. Idris

2013-01-01

Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.