A positive scheme for diffusion problems on deformed meshes
A positive scheme for diffusion problems on deformed meshes
复制标题
DOI：
10.1002/zamm.201400234
复制
发表时间：
2016-06
期刊：
影响因子：
--
通讯作者：
X. Blanc;E. Labourasse
中科院分区：
文献类型：
--
作者：
X. Blanc;E. Labourasse
本文提出了一种变形网格上求解扩散方程的正有限体积方法。这种方法主要是从启发，并使用辅助未知数在节点的网格。通量被计算为两点非线性通量，产生一个矩阵，该矩阵是M矩阵的转置，这确保了该格式是正的。特别注意的是辅助未知数的计算。我们提出了一个新的策略，其目的是提供一个易于实现的方案，在并行区域分解设置。对该方案进行了分析：证明了非线性系统解的存在性，并研究了不动点策略的收敛性。
We present in this article a positive finite volume method for diffusion equation on deformed meshes. This method is mainly inspired from , and uses auxiliary unknowns at the nodes of the mesh. The flux is computed so as to be a two‐point nonlinear flux, giving rise to a matrix which is the transpose of an M‐matrix, which ensures that the scheme is positive. A particular attention is given to the computation of the auxiliary unknowns. We propose a new strategy, which aims at providing a scheme easy to implement in a parallel domain decomposition setting. An analysis of the scheme is provided: existence of a solution for the nonlinear system is proved, and the convergence of a fixed‐point strategy is studied.