Characteristic fractional step finite difference method for nonlinear section coupled system  

作　　者：袁益让 李长峰 孙同军 刘允欣 

机构地区：[1]Institute of Mathematics, Shandong University [2]School of Economics, Shandong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第10期1311-1330,共20页应用数学和力学（英文版）

基　　金：supported by the Major State Basic Research Program of China(No.19990328);the National Tackling Key Program(No.20050200069);the National Natural Science Foundation of China(Nos.10372052,10771124,11101244,and 11271231);the Doctorate Foundation of the State Education Commission(No.20030422047)

摘　　要：For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

关 键 词：three-dimensional section coupled system complete nonlinear equation characteristic fractional step CONVERGENCE numerical simulation 

分 类 号：O241.3[理学—计算数学]