A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes
A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes
复制标题
一般网格上异质和各向异性扩散方程的线性保持单元中心方案
DOI：
10.1002/fld.2496
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发表时间：
2011-12-30
影响因子：
1.8
通讯作者：
Wu, Jiming
中科院分区：
文献类型：
--
作者：
Gao, Zhiming;Wu, Jiming
本文在一般的、可能不相容的网格上提出了异质和各向异性扩散方程的有限体积方案。该方案具有以单元为中心的未知数和顶点未知数。顶点未知数被视为中间未知数，并表示为周围以单元为中心的未知数的线性加权组合，这将方案简化为完全以单元为中心的方案。我们提出了两种新的显式权重，它们允许任意扩散张量，并且既不依赖于不连续性，也不依赖于网格拓扑。该方案的推导和新权重的推导均满足线性保持准则，该准则要求离散化方案在线性解上应该是精确的。由此产生的新方案被称为线性保持单元中心方案，数值结果表明，在扩散张量被视为各向异性、有时是异质的和/或不连续的情况下，它在一般多边形扭曲网格上保持解和通量的最佳收敛速度。版权所有 (C) 2010 约翰·威利父子有限公司
In this paper a finite volume scheme for the heterogeneous and anisotropic diffusion equations is proposed on general, possibly nonconforming meshes. This scheme has both cell-centered unknowns and vertex unknowns. The vertex unknowns are treated as intermediate ones and are expressed as a linear weighted combination of the surrounding cell-centered unknowns, which reduces the scheme to a completely cell-centered one. We propose two types of new explicit weights which allow arbitrary diffusion tensors, and are neither discontinuity dependent nor mesh topology dependent. Both the derivation of the scheme and that of new weights satisfy the linearity-preserving criterion which requires that a discretization scheme should be exact on linear solutions. The resulting new scheme is called as the linearity-preserving cell-centered scheme and the numerical results show that it maintain optimal convergence rates for the solution and flux on general polygonal distorted meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous. Copyright (C) 2010 John Wiley & Sons, Ltd.