A monotone finite volume scheme for diffusion equations on general non-conforming meshes
A monotone finite volume scheme for diffusion equations on general non-conforming meshes
复制标题
一般非相容网格上扩散方程的单调有限体积格式
DOI：
10.1016/j.amc.2017.05.041
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发表时间：
2017
影响因子：
4
通讯作者：
Yuan Guangwei
中科院分区：
文献类型：
--
作者：
Zhang Qi;Sheng Zhiqiang;Yuan Guangwei
在一般的非协调网格上，提出了一种求解扩散方程的非线性单调有限体积格式，该格式严格地处理了间断张量系数。由于法向通量的表达式依赖于定义在包含悬挂节点的单元顶点处的辅助未知量，因此我们提出了一种利用共享顶点的单元中心处的主未知量来消除顶点未知量的新方法。特别是定义在悬挂节点上的未知量被通量连续条件消除。所得到的方案是单调的，并保持了强各向异性和非均匀全张量系数问题的解析解的正性。数值结果表明，采用不同的顶点消元方法得到的单调格式的收敛阶相差很大，新方法可以保证其接近二阶精度，比现有的一些方法精度更高.
A nonlinear monotone finite volume scheme on general non-conforming meshes for diffusion equations is introduced, which deals with discontinuous tensor coefficients rigorously. Since the expression of normal flux depends on auxiliary unknowns defined at cell-vertex including hanging nodes, we propose a new method to eliminate vertex-unknown by using primary unknowns at the centers of the cells sharing the vertex. Especially the unknowns defined on hanging nodes are eliminated by flux continuous conditions. The resulting scheme is monotone and preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficient problems. Numerical results show that the convergent order of the monotone scheme by different methods of eliminating vertex unknowns will vary remarkably, and our new method can assure that it has almost second order accuracy and more accurate than some existing methods.