A finite volume scheme preserving extremum principle for convection-diffusion equations on polygonal meshes
A finite volume scheme preserving extremum principle for convection-diffusion equations on polygonal meshes
复制标题
多边形网格上对流扩散方程的保留极值原理的有限体积格式
DOI：
10.1002/fld.4366
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发表时间：
2017
影响因子：
1.8
通讯作者：
Yuan Guangwei
中科院分区：
文献类型：
--
作者：
Zhang Qi;Sheng Zhiqiang;Yuan Guangwei
提出了一种求解对流扩散方程的多边形网格上的非线性有限体积格式，并证明了该格式的离散解满足离散极值原理。扩散通量的近似是基于在离散法向通量的构造中选择模板的自适应方法，而对流通量的近似是基于具有适当斜率限制器的二阶迎风方法。我们的方案是局部保守的，只有以细胞为中心的未知数。数值结果表明，该格式能保持离散极值原理，并具有接近二阶精度。版权所有© 2017约翰威利父子有限公司
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.