Conservative Positivity-Preserving Algorithm for Kershaw Scheme of Anisotropic Diffusion Problems

Abstract

Abstract: Kershaw scheme is not positivity-preserving. Negative values emerge in numerical simulation for anisotropic diffusion equations on both orthogonal and distorted meshes. A conservative enforcing negative value to zero(CENZ) algorithm is proposed, which is an improvement of traditional method. It not only repairs numerical solution nonnegative, but also keeps local conservation of energy fluxes. Numerical examples demonstrate that the method is not limited by anisotropic ratio of diffusion coefficients. The algorithm can be used for numerical solution of finite volume schemes which violate monotony or positivity-preserving.

Key words: positivity-preserving, conservation, anisotropic diffusion, distorted mesh

CLC Number:

O241.8

CAO Fujun, YAO Yanzhong. Conservative Positivity-Preserving Algorithm for Kershaw Scheme of Anisotropic Diffusion Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(3): 283-293.

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