Characteristic fractional step finite difference method for nonlinear section coupled system

doi:10.1007/s10483-014-1869-9

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (10): 1311-1330.doi: https://doi.org/10.1007/s10483-014-1869-9

Characteristic fractional step finite difference method for nonlinear section coupled system

袁益让¹, 李长峰², 孙同军¹, 刘允欣¹

1. Institute of Mathematics, Shandong University, Jinan 250100, P. R. China;
2. School of Economics, Shandong University, Jinan 250100, P. R. China

收稿日期:2013-09-30 修回日期:2014-02-14 出版日期:2014-10-01 发布日期:2014-10-01
通讯作者: Yi-rang YUAN, yryuan@sdu.edu.cn E-mail:yryuan@sdu.edu.cn
基金资助:
Project supported by the Major State Basic Research Program of China (No. 19990328), the Na- tional Tackling Key Program (No. 20050200069), the National Natural Science Foundation of China (Nos. 10372052, 10771124, 11101244, and 11271231), and the Doctorate Foundation of the State Ed- ucation Commission (No. 20030422047)

Characteristic fractional step finite difference method for nonlinear section coupled system

Yi-rang YUAN¹, Chang-feng LI², Tong-jun SUN¹, Yun-xin LIU¹

1. Institute of Mathematics, Shandong University, Jinan 250100, P. R. China;
2. School of Economics, Shandong University, Jinan 250100, P. R. China

Received:2013-09-30 Revised:2014-02-14 Online:2014-10-01 Published:2014-10-01
Supported by:
Project supported by the Major State Basic Research Program of China (No. 19990328), the Na- tional Tackling Key Program (No. 20050200069), the National Natural Science Foundation of China (Nos. 10372052, 10771124, 11101244, and 11271231), and the Doctorate Foundation of the State Ed- ucation Commission (No. 20030422047)

摘要/Abstract

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 l² 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: numerical simulation, characteristic fractional step, convergence, complete nonlinear equation, three-dimensional section coupled system

Abstract: 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 l² 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.

Key words: characteristic fractional step, numerical simulation, convergence, three-dimensional section coupled system, complete nonlinear equation

中图分类号:

O241.82

袁益让;李长峰;孙同军;刘允欣. Characteristic fractional step finite difference method for nonlinear section coupled system[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1311-1330.

Yi-rang YUAN;Chang-feng LI;Tong-jun SUN;Yun-xin LIU. Characteristic fractional step finite difference method for nonlinear section coupled system[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1311-1330.

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Characteristic fractional step finite difference method for nonlinear section coupled system

Characteristic fractional step finite difference method for nonlinear section coupled system

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