BLOCK-CENTERED FINITE DIFFERENCE METHODS FOR NON-FICKIAN FLOW IN POROUS MEDIA

作     者：Xiaoli Li Hongxing Rui 

作者机构：School of Mathematics Shandong University Jinan Shandong 250100 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2018年第36卷第4期

页      面：492-516页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0701[理学-数学] 

基　　金：This work is supported by the National Natural Science Foundation of China Grant no. 11671233  91330106 

主　　题：Block-centered finite difference Parabolic integro-differential equation Nonuniform Error estimates Numerical analysis 

摘      要：In this article, two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment. Stability analysis and second-order error estimates in spatial meshsize for both pressure and velocity in discrete L^2 norms are established on non-uniform rectangular grid. Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.