A vertex-centered and positivity-preserving finite volume scheme for two-dimensional three-temperature radiation diffusion equations on general polygonal meshes
A vertex-centered and positivity-preserving finite volume scheme for two-dimensional three-temperature radiation diffusion equations on general polygonal meshes
复制标题
一般多边形网格上二维三温辐射扩散方程的顶点中心保正有限体积格式
DOI：
10.4208/nmtma.oa-2018-0121
复制
发表时间：
2020-06
影响因子：
1.3
通讯作者：
Jiming Wu
中科院分区：
文献类型：
--
作者：
Shuai Su;Jiming Wu
二维三温辐射扩散方程被广泛用于近似描述多物质系统中辐射能量的演化，解释电子、离子和光子之间的能量交换。本文对二维三维辐射扩散方程在一般多边形网格上构造了一个新的保正有限体积格式。顶点未知数被视为主要的有限体积方程的构造。将边中点和单元中心作为辅助未知量，用主未知量进行插值，使最终格式成为纯顶点中心格式。相比之下，现有的大多数保正有限体积格式都是基于协法线的凸分解的，并且是以胞心为中心的。在这里，共法分解一般不是凸的，导致通量近似的固定模板，避免了复杂网格上的某种搜索算法。此外，新格式有效地消除了现有的大部分单元中心格式或混合格式在求解强非线性辐射扩散方程时所遇到的数值热障碍问题。数值实验表明，在各种变形网格上，该方法的解都具有二阶精度和正性。对于无解析解的问题，在变形网格上的数值解的轮廓与光滑四边形网格上的数值解的轮廓雅阁。
Two-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons, ions and photons. In this paper, we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal meshes. The vertex unknowns are treated as primary ones for which the finite volume equations are constructed. The edge-midpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns, which makes the final scheme a pure vertex-centered one. By comparison, most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the co-normal. Here, the co-normal decomposition is not convex in general, leading to a fixed stencil of the flux approximation and avoiding a certain search algorithm on complex grids. Moreover, the new scheme effectively alleviates the numerical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion equations. Numerical experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted grids. For the problem without analytic solution, the contours of the numerical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.