Effective finite‐difference methods for the solutions of filtration problems in multilayer domains

Abstract

In papers [1,2] there were consider different assumptions for averaging methods along the vertical coordinate.These methods were applied for the mathematical simulation of the mass transfer process in multilayered underground systems. A specific feature of these problems is that it is necessity to solve the 3‐D initial‐boundary‐value problems for parabolic type partial differential equations of second order with piece‐wise parameters in multilayer domain.Therefore here an effective finite‐difference method for solving a problem of the above type is developed.This method may be considered as a generalization of the method of finite volumes [3] for the layered systems. In the case of constant piece‐wise coefficients we obtain the exact discrete approximation of steady‐state 1‐D boundary‐value problem.This procedure allows to reduce the 3‐D problem to a system of 2‐D problems and the 2‐D problem to a system of 1‐D problems.

First Published Online: 14 Oct 2010