块结构自适应网格上任意区域和任意界面的数值积分

计算物理 ›› 2017, Vol. 34 ›› Issue (1): 10-18.

块结构自适应网格上任意区域和任意界面的数值积分

徐建军¹, 史卫东^1,2, 李兴伟^1,2, 舒适²

1. 中国科学院重庆绿色智能技术研究院, 重庆 400714;
2. 湘潭大学数学学院, 湖南湘潭 411105

收稿日期:2015-11-26 修回日期:2016-05-06 出版日期:2017-01-25 发布日期:2017-01-25
作者简介:徐建军(1966-),汉族,男,副研究员,博士,从事计算流体力学研究,E-mail:xujianjun@cigit.ac.cn
基金资助:
国家自然科学基金（91430213，11571293）资助项目

Numerical Integrations Over Arbitrary Domains and Arbitrary Surfaces on Block-Structured Adaptive Meshes

XU Jianjun¹, SHI Weidong^1,2, LI Xingwei^1,2, SHU Shi²

1. Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China;
2. School of Mathematical Sciences, Xiangtan University, Xiangtan, Hunan 411105, China

Received:2015-11-26 Revised:2016-05-06 Online:2017-01-25 Published:2017-01-25

摘要/Abstract

摘要： 研究块结构自适应网格上计算任意界面上和任意区域内的数值积分方法，其中任意界面和任意区域通过一个水平集函数表示.首先介绍在一致网格上任意界面上和任意区域内的数值积分方法.然后，将该方法推广到块结构的自适应网格上.数值算例表明，自适应网格方法有二阶精度.同一致网格方法相比，自适应网格方法显著地减少了计算机存储量的需求.

关键词: 数值积分, 自适应网格, 笛卡尔网格, 水平集函数

Abstract: We study numerical integration over arbitrary interface and arbitrary domain on block-structured adaptive mesh.Arbitrary interface and arbitrary domain are described by a level set function.We first describe numerical methods on uniform Cartesian grid.Then we extend the methods to block-structured adaptive mesh.Numerical calculations demonstrate that adaptive mesh methods are second-order accurate.Compared with uniform mesh methods, the adaptive mesh methods reduce needs on computer storage significantly.

Key words: numerical integration, adaptive mesh, Cartesian grid, level-set function

中图分类号:

O241

徐建军, 史卫东, 李兴伟, 舒适. 块结构自适应网格上任意区域和任意界面的数值积分[J]. 计算物理, 2017, 34(1): 10-18.

XU Jianjun, SHI Weidong, LI Xingwei, SHU Shi. Numerical Integrations Over Arbitrary Domains and Arbitrary Surfaces on Block-Structured Adaptive Meshes[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(1): 10-18.

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