多流管网格上九点格式的节点插值方法

Vertex Interpolation Methods for Nine-point Scheme on Multi-flow-tube Meshes

多流管方法是二维多介质辐射流体力学数值模拟中一类常用的求解方法,它采用Lagrange-Euler混合型四边形网格,称为多流管网格。通常其网格品质高于一般的四边形网格。在这类网格上,可以利用网格特性对九点扩散格式中的节点插值方法进行改进。本文利用调和平均点和梯度离散构造的方法提出几种节点插值方法。并给出数值实验,说明现有应用程序中的节点插值方法损失精度,而新的节点插值方法能够使得九点格式在多流管网格上具有二阶精度。

The multi-flow tube(MFT)method is mainly designed for two-dimensional(2-D)radiation hydrodynamic problems with multi-material,whose computational mesh is Lagrangian-Eulerian hybrid.Quality of the MFT quadrilateral mesh is usually higher than that of a general quadrilateral mesh.We consider a so-called nine-point diffusion scheme on this kind of meshes,in which the method of calculating vertex unknowns is improved by taking advantage of mesh features.Several methods for eliminating vertex unknowns are proposed by using harmonic averaging points or a gradient reconstruction method.Numerical experiments show that our methods obtain almost second order accuracy on MFT meshes.