一种求解三维非稳态对流扩散反应方程的高精度有限差分格式  

A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations

作　　者：魏剑英 葛永斌 WEI Jianying;GE Yongbin(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,P.R.China)

机构地区：[1]宁夏大学数学统计学院,银川750021

出　　处：《应用数学和力学》2022年第2期187-197,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12161067,11961054,11902170);宁夏自然科学基金(2020AAC03059);宁夏自治区青年拔尖人才培养工程项目。

摘　　要：针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶.利用Fourier稳定性分析法证明了该格式是无条件稳定的.最后给出数值算例验证了理论结果.Based on the 4th-order compact difference scheme for spatial discretization,the Taylor series expansion and the error remainder correction method for temporal discretization,a high-order compact finite difference scheme for solving the 3D unsteady convection diffusion reaction equations was proposed.The unconditional stability was proved with the Fourier analysis method.The proposed scheme has 2nd-order accuracy in time and 4th-order accuracy in space.At last,numerical examples validate the theoretical results.

关 键 词：对流扩散反应方程 变对流项和反应项系数 高精度紧致格式 无条件稳定 有限差分法 

分 类 号：O241.82[理学—计算数学]