| 非定常对流扩散方程保正格式解的存在性 |
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| 引用本文： | 张燕美,兰斌,盛志强,袁光伟.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. |
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| 作者姓名： | 张燕美 兰斌 盛志强 袁光伟 |
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| 作者单位： | 中国工程物理研究院研究生院,北京,100088;中国工程物理研究院研究生院,北京100088;北方民族大学,银川750021;北京应用物理与计算数学研究所计算物理实验室,北京,100088 |
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| 基金项目： | 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. |
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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 |
| 收稿时间： | 2018-03-12 |
EXISTENCE OF SOLUTIONS OF A POSITIVE FINITE VOLUME SCHEME FOR UNSTEADY ADVECTION-DIFFUSION EQUATIONS |
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| Zhang Yanmei,Lan Bin,Sheng Zhiqiang,Yuan Guangwei.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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| Authors: | Zhang Yanmei Lan Bin Sheng Zhiqiang Yuan Guangwei |
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| Institution: | 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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| 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. |
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| Keywords: | advection-diffusion equations finite volume scheme positivity existence |
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