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A monotone finite volume scheme for advection–diffusion equations on distorted meshes |
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| Authors: | Shuai Wang Guangwei Yuan Yonghai Li Zhiqiang Sheng |
| Institution: | 1. Institute of Mathematics, Jilin University, , Changchun 130012, China;2. National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, , P.O.Box8009, Beijing 100088, China;3. School of Mathematics, Jilin University, , Changchun 130012, China |
| Abstract: | A new monotone finite volume method with second‐order accuracy is presented for the steady‐state advection–diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes that guarantee the positivity of the numerical solution. The approximation of the diffusive flux is based on nonlinear two‐point approximation, and the approximation of the advective flux is based on the second‐order upwind method with proper slope limiter. The second‐order convergence rate for concentration and the monotonicity of the nonlinear finite volume method are verified with numerical experiments. Copyright © 2011 John Wiley & Sons, Ltd. |
| Keywords: | advection‐dominated diffusion‐dominated finite volume method discrete maximum principle nonlinear two‐point flux monotone method |