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.
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.
作者
张燕美
兰斌
盛志强
袁光伟
Zhang Yanmei;Lan Bin;Sheng Zhiqiang;Yuan Guangwei(The Graduate School of China Academy of Engineering Physics,Beijing 100088,China;North Minzu University,Yinchuan 750021,China;Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)
出处
《计算数学》
CSCD
北大核心
2019年第4期381-394,共14页
Mathematica Numerica Sinica
基金
国家自然科学基金(11571047,11971069)
NSAF(U1630249)
科学挑战专题(No.TZ2016002)资助项目
关键词
对流扩散方程
有限体积格式
保正性
存在性
advection-diffusion equations
finite volume scheme
positivity,existence
