THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

doi:10.1016/S0252-9602(11)60282-8

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 857-881.doi: 10.1016/S0252-9602(11)60282-8

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

袁益让

Institute of Mathematics, Shandong University, Jinan 250100, China

收稿日期:2009-07-13 修回日期:2009-11-16 出版日期:2011-05-20 发布日期:2011-05-20
基金资助:
This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Programs (20050200069), the National Natural Science Foundation of China (10771124; 10372052), the Doctorate Foundation of the Ministry of Education of China (20030422047), Shandong Provance Natural Science Foundation (2R2009AQ12), and the Independent Innovation Foundation of Shandong University (2010TS031).

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

YUAN Yi-Rang

Institute of Mathematics, Shandong University, Jinan 250100, China

Received:2009-07-13 Revised:2009-11-16 Online:2011-05-20 Published:2011-05-20
Supported by:
This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Programs (20050200069), the National Natural Science Foundation of China (10771124; 10372052), the Doctorate Foundation of the Ministry of Education of China (20030422047), Shandong Provance Natural Science Foundation (2R2009AQ12), and the Independent Innovation Foundation of Shandong University (2010TS031).

摘要/Abstract

摘要：

Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. The upwind finite difference
schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a
complete set. Some techniques, such as change of variables, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. The estimates in l ²norm are derived to determine the error in the approximate solution. This method was already applied to the numerical simulation of migration-accumulation of oil resources.

关键词: multilayer coupled system, moving boundary values, upwind finite difference method, convergence, numerical simulation of energy

Abstract:

Key words: multilayer coupled system, moving boundary values, upwind finite difference method, convergence, numerical simulation of energy sources

中图分类号:

65M06

袁益让. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM[J]. 数学物理学报(英文版), 2011, 31(3): 857-881.

YUAN Yi-Rang. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM[J]. Acta mathematica scientia,Series B, 2011, 31(3): 857-881.

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THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

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