Nonlinear Finite Volume Scheme Preserving Positivity for 2D Convection-Diffusion Equations on Polygonal Meshes

Bin Lan and Jianqiang Dong

Mathematical Problems in Engineering, 2020, vol. 2020, 1-11

Abstract:

In this paper, a nonlinear finite volume scheme preserving positivity for solving 2D steady convection-diffusion equation on arbitrary convex polygonal meshes is proposed. First, the nonlinear positivity-preserving finite volume scheme is developed. Then, in order to avoid the computed solution beyond the upper bound, the cell-centered unknowns and auxiliary unknowns on the cell-edge are corrected. We prove that the present scheme can avoid the numerical solution beyond the upper bound. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results show that our scheme preserves the above conclusion and has second-order accuracy for solution.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:7343716

DOI: 10.1155/2020/7343716

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