Name
Abstract | ||
|---|---|---|
We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity. In the context of anisotropic thermal conduction, this can lead to the violation of the entropy constraints of the second law of thermodynamics, causing heat to flow from regions of lower temperature to higher temperature. In regions of large temperature variations, this can cause the temperature to become negative. Test cases to illustrate this for centered asymmetric and symmetric differencing are presented. Algorithms based on slope limiters, analogous to those used in second order schemes for hyperbolic equations, are proposed to fix these problems. While centered algorithms may be good for many cases, the main advantage of limited methods is that they are guaranteed to avoid negative temperature (which can cause numerical instabilities) in the presence of large temperature gradients. In particular, limited methods will be useful to simulate hot, dilute astrophysical plasmas where conduction is anisotropic and the temperature gradients are enormous, e.g., collisionless shocks and disk-corona interface. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.jcp.2007.07.026 | J. Comput. Physics |
Keywords | Field | DocType |
limited method,lower temperature,anisotropic diffusion,large temperature variation,anisotropic thermal conduction,preserving monotonicity,large temperature gradient,higher temperature,recent symmetric algorithm,finite differencing,temperature gradient,negative temperature,hyperbolic equation,second order,second law of thermodynamics,thermal conductivity | Anisotropic diffusion,Statistical physics,Monotonic function,Mathematical analysis,Negative temperature,Heat transfer,Second law of thermodynamics,Astrophysical plasma,Thermal conduction,Physics,Hyperbolic partial differential equation | Journal |
Volume | Issue | ISSN |
227 | 1 | Journal of Computational Physics |
Citations | PageRank | References |
25 | 1.66 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Prateek Sharma | 1 | 201 | 14.12 |
| Gregory W. Hammett | 2 | 31 | 2.35 |