Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system |
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Authors: | Yi-rang YUAN Chang-feng LI Tong-jun SUN Yun-xin LIU |
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Institution: | 1. Institute of Mathematics, Shandong University, Jinan 250100, P.R.China 2. School of Economics, Shandong University, Jinan 250100, P.R.China |
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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 l 2 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. |
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Keywords: | multilayer nonlinear percolation system moving boundary values modified characteristic fractional finite difference optimal order convergence analysis numerical simulation of energy source |
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