二维非稳态对流扩散方程的高阶紧致差分格式  

High-Order Compact Schemes for 2D Unsteady Convection Diffusion Equations

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

机构地区：[1]宁夏大学数学统计学院,银川750021

出　　处：《西南大学学报（自然科学版）》2022年第1期88-98,共11页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11772165,11961054,11902170);宁夏自然科学基金项目(2020AAC03059);宁夏自治区青年拔尖人才培养工程项目.

摘　　要：针对二维非稳态变系数对流扩散方程,对时间的离散分别采用二阶和三阶向后差分公式,对空间的离散分别采用四阶紧致差分和六阶紧致差分方法,提出了两种高精度紧致差分格式,两种格式的截断误差分别为O(τ^(2)+h^(4)_(x)+h^(4)_(y))和O(τ^(3)+h^(6)_(x)+h^(6)_(y)),并且均是无条件稳定的,最后给出了数值算例验证了理论结果.In this paper,two high-order compact difference schemes for solving two-dimensional unsteady convection diffusion equations with variable coefficients are proposed,using the second-order and the third-order backward difference formulas for temporal discretization and the fourth-order and the sixth-order compact difference methods for spatial discretization.Both schemes are unconditionally stable and their truncation errors are O(τ^(2)+h^(4)_(x)+h^(4)_(y))and O(τ^(3)+h^(6)_(x)+h^(6)_(y)),respectively.The accuracy and stability of the two schemes are verified by some numerical experiments.

关 键 词：对流扩散方程 变系数 高阶紧致差分格式 全隐格式 无条件稳定 

分 类 号：O241.82[理学—计算数学]