计算数学
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计算数学  2019, Vol. 41 Issue (4): 381-394    DOI:
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非定常对流扩散方程保正格式解的存在性
张燕美1, 兰斌1,2, 盛志强3, 袁光伟3
1. 中国工程物理研究院研究生院, 2101信箱, 北京 100088;
2. 北方民族大学, 银川 750021;
3. 北京应用物理与计算数学研究所计算物理实验室, 8009信箱, 北京 100088
EXISTENCE OF SOLUTIONS OF A POSITIVE FINITE VOLUME SCHEME FOR UNSTEADY ADVECTION-DIFFUSION EQUATIONS
Zhang Yanmei1, Lan Bin1,2, Sheng Zhiqiang3, Yuan Guangwei3
1. The Graduate School of China Academy of Engineering Physics, P. O. Box 2101, Beijing 100088, China;
2. North Minzu University, Yinchuan 750021, China;
3. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China
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摘要 本文发展了非定常对流扩散方程的非线性保正格式.该格式为单元中心型有限体积格式,保持局部通量的守恒性,适用于任意星形多边形网格,本文证明了该离散格式解的存在性,并给出数值结果,表明该格式具有二阶精度.
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关键词对流扩散方程   有限体积格式   保正性   存在性     
Abstract: A nonlinear positive finite volume scheme is developed in this paper for unsteady advection-diffusion equations on star-shaped polygonal meshes. The scheme has only cellcentered unknowns and preserves local conservation. Moreover, the existence of discrete solution for the nonlinear scheme is proved by using Brouwer fixed-point theorem. Numerical results are presented to show that the scheme obtains second-order accuracy.
Key wordsadvection-diffusion equations   finite volume scheme   positivity   existence   
收稿日期: 2018-03-12; 出版日期: 2019-11-16
基金资助:

国家自然科学基金(11571047,11971069),NSAF (U1630249)和科学挑战专题(No.TZ2016002)资助项目.

通讯作者: 袁光伟,Email:yuan_guangwei@iapcm.ac.cn.     E-mail: yuan_guangwei@iapcm.ac.cn
引用本文:   
. 非定常对流扩散方程保正格式解的存在性[J]. 计算数学, 2019, 41(4): 381-394.
. EXISTENCE OF SOLUTIONS OF A POSITIVE FINITE VOLUME SCHEME FOR UNSTEADY ADVECTION-DIFFUSION EQUATIONS[J]. Mathematica Numerica Sinica, 2019, 41(4): 381-394.
 
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