A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes |
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| Authors: | Qi Zhang Zhiqiang Sheng Guangwei Yuan |
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| Affiliation: | 1. The Graduate School of China Academy of Engineering Physics, Beijing, China;2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China |
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| Abstract: | We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | extremum principle nonlinear finite volume scheme convection– diffusion equation polygonal meshes advection‐dominated diffusion‐dominated |
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