An improved monotone finite volume scheme for diffusion equation on polygonal meshes

  • Authors:

  • Zhiqiang Sheng;Guangwei Yuan

  • Affiliations:

  • Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China;Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

We construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes. The new scheme uses the cell-edge unknowns instead of cell-vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes. Specially, numerical results show that the new scheme is robust, and more accurate than the existing monotone scheme on some kinds of meshes.