多层非线性渗流耦合系统的特征分数步差分方法

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The Modified Characteristic Finite Difference Fractional Steps Method for Nonlinear Coupled System of Multilayer Fluid Dynamics in Porous Media

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Abstract:

For nonlinear coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L₂ norm are derived to determine the error of the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. Thus the author has thoroughly and completely solved the well-known problem.

Key words: Nonlinear coupled system, Multilayer fluid dynamics in porous media, Characteristic finite difference, Fractional steps, Convergence

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65N12

Yuan Yirang. The Modified Characteristic Finite Difference Fractional Steps Method for Nonlinear Coupled System of Multilayer Fluid Dynamics in Porous Media[J].Acta mathematica scientia,Series A, 2009, 29(4): 858-872.

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