Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear magnetohydrodynamics simulation using high-order finite elements
Journal of Computational Physics
Modelling of heat transport in magnetised plasmas using non-aligned coordinates
Journal of Computational Physics
IEEE Transactions on Image Processing
Monotone finite volume schemes for diffusion equations on polygonal meshes
Journal of Computational Physics
Journal of Computational Physics
The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
Journal of Computational Physics
A fast semi-implicit method for anisotropic diffusion
Journal of Computational Physics
An efficient method for solving highly anisotropic elliptic equations
Journal of Computational Physics
SIAM Journal on Scientific Computing
An improved monotone finite volume scheme for diffusion equation on polygonal meshes
Journal of Computational Physics
Multi-layer illustrative dense flow visualization
Computer Graphics Forum
Journal of Computational Physics
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Hi-index | 31.49 |
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.