大变形网格上时间二阶精度扩散方程的保正格式  

POSITIVITY-PRESERVING SCHEME FOR DIFFUSION EQUATION WITH SECOND ORDER TIME ACCURACY ON DEFORMDE MESHES

作　　者：谢晨元 兰斌 杨德贤 李海燕 Xie Chenyuan;Lan Bin;Yang Dexian;Li Haiyan(North Minzu University,School of Mathematics and Information Sciences,Yinchuan 750021,China;Haiyuan Third Middle School,Zhongwei 755200,China)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021 [2]海原县第三中学,中卫755200

出　　处：《计算数学》2024年第1期38-46,共9页Mathematica Numerica Sinica

基　　金：校级科研启动项目(2019KYQD36);国家自然科学基金(12001015,12162001);宁夏自然科学基金(2020AAC03233)资助。

摘　　要：本文基于已有的连续扩散通量的两点非线性离散格式,构造了2D非稳态扩散方程大变形网格上的两层非线性有限体积格式.该格式利用Crank-Nicolson(C-N)方法的思想在时间方向获得了二阶精度.由于所得代数方程组的系数矩阵的转置是M矩阵,从而能够保持解的正性,并利用Brouwer不动点定理证明了格式解的存在性.数值实验结果表明,在较大时间步长下,该格式具有二阶计算精度.A two-layer nonlinear finite volume scheme for 2D unstationary diffusion equations is constructed on deformed meshes,which based on a two-point nonlinear discrete scheme of continuous diffusion flux.The scheme uses the idea of Crank-Nicolson(C-N)method to achieve second-order accuracy for time evolution.Since the transpose of the resulting algebraic system of coefficient matrix is an M-matrix,it is guaranteed that the scheme preserves positivity.The existence of discrete solution for the present scheme is proved by using Brouwer fixed-point theorem.Numerical results illustrate that the scheme has secondorder accuracy with a larger time step.

关 键 词：扩散方程 大变形网格 二阶精度 保正格式 

分 类 号：O241.82[理学—计算数学]