The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media  

作　　者：YUAN Yirang 

机构地区：[1]Institute of Mathematics, Shandong University, Jinan 250100, China

出　　处：《Science China Mathematics》2006年第2期185-211,共27页中国科学：数学（英文版）

基　　金：supported by the Major State Basic Research Program of China(Grant No.19990328);the National Tackling Key Problems Program,the National Natural Science Foundation of China(Grant Nos.10372052&10271066);the Doctorate Foundation of the State Education Commission(Grant No.20030422047).

摘　　要：For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method,multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.

关 键 词：multilayer coupled system NONLINEAR equations UPWIND finite difference fractional STEPS convergence numerical simulation. 

分 类 号：N[自然科学总论]