多流管网格上九点格式的节点插值方法

doi:10.19596/j.cnki.1001-246x.8212

计算物理 ›› 2021, Vol. 38 ›› Issue (2): 153-164.DOI: 10.19596/j.cnki.1001-246x.8212

多流管网格上九点格式的节点插值方法

徐金景^1,2, 袁光伟²

1. 中国工程物理研究院研究生院, 北京 100088;
2. 北京应用物理与计算数学研究所, 北京 100088

收稿日期:2020-03-19 修回日期:2020-07-16 发布日期:2021-09-29
通讯作者: Yuan Guangwei, E-mail:yuan_guangwei@iapcm.ac.cn
作者简介:Xu Jinjing(1994-), PhD candidate, research interests:numerical methods for partial differential equations, E-mail:xujinjing18@gscaep.ac.cn
基金资助:
Supported by the National Science Foundation of China (11971069) and Science Challenge Project (TZ2016002)

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

XU Jinjing^1,2, YUAN Guangwei²

1. Graduate School of China Academy of Engineering Physics, Beijing 100088, China;
2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2020-03-19 Revised:2020-07-16 Published:2021-09-29
Supported by:
Supported by the National Science Foundation of China (11971069) and Science Challenge Project (TZ2016002)

摘要/Abstract

摘要： 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。

关键词: 九点格式, 扩散方程, 节点插值, 多流管网格

Abstract: 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.

Key words: nine-point scheme, diffusion equation, vertex interpolation, multi-flow-tube meshes

中图分类号:

O241.82

徐金景, 袁光伟. 多流管网格上九点格式的节点插值方法[J]. 计算物理, 2021, 38(2): 153-164.

XU Jinjing, YUAN Guangwei. Vertex Interpolation Methods for Nine-point Scheme on Multi-flow-tube Meshes[J]. Chinese Journal of Computational Physics, 2021, 38(2): 153-164.

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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

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