Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 12, Pages 4899-4909Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.03.009
Keywords
Implicit methods; Finite differencing; Monotonicity; Anisotropic diffusion
Funding
- NASA, Chandra X-ray Center [PF8-90054]
- NASA [NAS8-03060]
- Princeton Plasma Physics Laboratory, DOE [DE-AC02-09CH11466]
- National Science Foundation
- Purdue University
- Direct For Mathematical & Physical Scien [905801] Funding Source: National Science Foundation
- Division Of Astronomical Sciences [905801] Funding Source: National Science Foundation
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Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative temperatures for the anisotropic thermal diffusion equation. In a previous paper we proposed a monotonicity-preserving explicit method which uses limiters (analogous to those used in the solution of hyperbolic equations) to interpolate the temperature gradients at cell faces. However, being explicit, this method was limited by a restrictive Courant-Friedrichs-Lewy (CFL) stability timestep. Here we propose a fast, conservative, directionally-split, semi-implicit method which is second order accurate in space, is stable for large timesteps, and is easy to implement in parallel. Although not strictly monotonicity-preserving. our method gives only small amplitude temperature oscillations at large temperature gradients, and the oscillations are damped in time. With numerical experiments we show that our semi-implicit method can achieve large speed-ups compared to the explicit method, without seriously violating the monotonicity constraint. This method can also be applied to isotropic diffusion, both on regular and distorted meshes. (C)2011 Elsevier Inc. All rights reserved.
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