Articles

Characteristic fractional step finite difference method for nonlinear section coupled system

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

Received date: 2013-09-30

  Revised date: 2014-02-14

  Online 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)

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.

Cite this article

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, 2014 , 35(10) : 1311 -1330 . DOI: 10.1007/s10483-014-1869-9

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