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Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system

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【作者】 袁益让； 李长峰； 孙同军； 刘允欣；

【Author】 Yi-rang YUAN 1 , Chang-feng LI 2 , Tong-jun SUN 1 , Yun-xin LIU 1 (1. Institute of Mathematics, Shandong University, Jinan 250100, P. R. China; 2. School of Economics, Shandong University, Jinan 250100, P. R. China)

【机构】 Institute of Mathematics, Shandong University； School of Economics, Shandong University；

【摘要】 <Abstract>A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of difference operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l2 norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

【Abstract】 A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of difference operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l2 norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

【关键词】 multilayer nonlinear percolation system； moving boundary values； modified characteristic fractional finite difference； optimal order convergence analysis； numerical simulation of energy source；
【Key words】 multilayer nonlinear percolation system； moving boundary values； modified characteristic fractional finite difference； optimal order convergence analysis； numerical simulation of energy source；
【基金】 Project supported by the Major State Basic Research Program of China (No. 19990328);the National Tackling Key Problems Program (No. 20050200069);the National Natural Science Foundation of China (Nos. 10771124, 10372052, 11101244, and 11271231);the Doctorate Foundation of the Ministry of Education of China (No. 20030422047);the Shandong Province Natural Science Foundation (No. ZR2009AQ012);the Independent Innovation Foundation of Shandong University(No. 2010TS031);the Scientific Research Award Fund for Excellent Middle-Aged and Young Scientists of Shandong Province (No. BS2009NJ003)
  • 【文献出处】 Applied Mathematics and Mechanics(English Edition) ,应用数学和力学(英文版) , 编辑部邮箱 ,2013年04期
  • 【分类号】O357.3;O175.8
  • 【下载频次】36
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