各向异性扩散问题Kershaw格式的守恒保正修复算法

计算物理 ›› 2017, Vol. 34 ›› Issue (3): 283-293.

各向异性扩散问题Kershaw格式的守恒保正修复算法

曹富军^1,2,3, 姚彦忠²

1. 中国科学技术大学数学科学学院, 合肥 230026;
2. 北京应用物理与计算数学研究所, 北京 100088;
3. 内蒙古科技大学理学院, 包头 014010

收稿日期:2016-03-11 修回日期:2016-06-16 出版日期:2017-05-25 发布日期:2017-05-25
通讯作者: 姚彦忠,E-mail:yao_yanzhong@iapcm.ac.cn
作者简介:曹富军(1984-),男,汉族,内蒙古包头,讲师,博士,主要从事偏微分方程计算方法研究,E-mail:caofujun@imust.cn
基金资助:
国家自然科学基金（11571048，11571047和11671049）及内蒙古科技大学校内创新基金（2014QDL004）资助项目

Conservative Positivity-Preserving Algorithm for Kershaw Scheme of Anisotropic Diffusion Problems

CAO Fujun^1,2,3, YAO Yanzhong²

1. School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China;
2. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
3. School of Science, Inner Mongolia University of Science and Technology, Baotou 014010, China

Received:2016-03-11 Revised:2016-06-16 Online:2017-05-25 Published:2017-05-25

摘要/Abstract

摘要： 针对各向异性扩散方程Kershaw格式的数值解在正交网格及扭曲网格上计算出负的现象，给出一种守恒的保正修复算法（CENZ），该算法对简单遇负置零（ENZ）方法进行改进，使修复后的数值解不仅具有非负性，而且保持法向通量的局部守恒性.数值算例表明，该方法不受计算网格类型和扩散系数各向异性比的限制，可用于对任意违背单调性（或保正性）的有限体积格式数值解的修复.

关键词: 保正性修复, 守恒性, 各向异性扩散, 任意多边形网格

Abstract: Kershaw scheme is not positivity-preserving. Negative values emerge in numerical simulation for anisotropic diffusion equations on both orthogonal and distorted meshes. A conservative enforcing negative value to zero(CENZ) algorithm is proposed, which is an improvement of traditional method. It not only repairs numerical solution nonnegative, but also keeps local conservation of energy fluxes. Numerical examples demonstrate that the method is not limited by anisotropic ratio of diffusion coefficients. The algorithm can be used for numerical solution of finite volume schemes which violate monotony or positivity-preserving.

Key words: positivity-preserving, conservation, anisotropic diffusion, distorted mesh

中图分类号:

O241.8

曹富军, 姚彦忠. 各向异性扩散问题Kershaw格式的守恒保正修复算法[J]. 计算物理, 2017, 34(3): 283-293.

CAO Fujun, YAO Yanzhong. Conservative Positivity-Preserving Algorithm for Kershaw Scheme of Anisotropic Diffusion Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(3): 283-293.

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