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

• Published in: Applied mathematics and mechanics Vol. 34; no. 4; pp. 417 - 436
• Main Author: 袁益让 李长峰 孙同军 刘允欣
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University 01.04.2013; Institute of Mathematics, Shandong University, Jinan 250100, P.R.China%School of Economics, Shandong University, Jinan 250100, P.R.China
• Subjects: Applications of Mathematics; Classical Mechanics; Computer simulation; Dynamical systems; Fluid- and Aerodynamics; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear dynamics; Nonlinearity; Operators; Partial Differential Equations; Percolation; 修改; 收敛性分析; 流体动力学模拟; 渗流系统; 特征差分; 移动; 边界值问题; 非线性; 76M25; numerical simulation of energy source; 65M06; multilayer nonlinear percolation system; moving boundary values; 76S05; O241.82; optimal order convergence analysis; modified characteristic fractional finite difference; 65N30
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-013-1681-8

A fractional step scheme with modified characteristic finite differences run- ning 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 differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.