Numerical solution of subsurface moisture transport problems

Abstract

An algorithm is proposed for solving difference problems of subsurface hydromechanics by the alternating triangular method ( ATM ). For second, third, and mixed boundary-valued problems of subsurface moisture transport in the elastic regime, we use an improved ATM generalization scheme, which has been tested by the authors in application to the first boundary-value problem. The proposed algorithm can be applied to various problems of subsurface mass transport.The most efficient methods for solving problems of subsurface hydromechanics in nonhomogeneous anisotropic porous media are numerical, such as the finite-difference method. The application of this method replaces the original differential problem with a system of grid equations, which is solved by both direct and iteration methods.The alternating triangular iteration method (ATM) proposed by Samarskii [4] and developed in [1, 2, 6] has a fast rate of convergence for the solution of elliptical grid equations. It is also applicable to the solution of unsteady seepage problems with mixed boundary conditions on a nonuniform grid.