Name
Title | ||
|---|---|---|
Diffusion front capturing schemes for a class of Fokker-Planck equations: Application to the relativistic heat equation |
Abstract | ||
|---|---|---|
In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker-Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant-Friedrichs-Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker-Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numerical approximations of the solution of the relativistic heat equation for a set of examples in one and two dimensions including continuous initial data that develops jump discontinuities in finite time. We perform the numerical experiments through a class of explicit high order accurate conservative and stable numerical schemes and a semi-implicit nonlinear Crank-Nicolson type scheme. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jcp.2009.12.014 | J. Comput. Physics |
Keywords | Field | DocType |
conservative finite difference scheme,limited diffusion,anisotropic diffusion,limited diffusion fokker-planck equation,explicit conservative finite difference,fokker-planck equation,fokker–planck equation,diffusion front,numerical experiment,relativistic heat equation,numerical approximation,courant-friedrichs-lewy parabolic time step,diffusion fronts,stable numerical scheme,fokker planck equation,two dimensions,heat equation,neumann boundary condition,crank nicolson | Anisotropic diffusion,Fokker–Planck equation,Boundary value problem,Nonlinear system,Mathematical analysis,FTCS scheme,Heat equation,Initial value problem,Mathematics,Diffusion equation | Journal |
Volume | Issue | ISSN |
229 | 7 | Journal of Computational Physics |
Citations | PageRank | References |
1 | 0.51 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antonio Marquina | 1 | 431 | 45.30 |