A boundary element method for analysis of contaminant transport in porous media I: Homogeneous porous media

A boundary element method is developed for the analysis of contaminant migration in porous media. The technique involves, firstly, taking the Laplace transform with respect to time then followed by a co-ordinate transform and a mathematical transform of the well-known advection-dispersion equation. The series of transforms reduce the equation into the modified Helmholz equation and this greatly facilitates the formulation of the boundary integral equation and a system of approximating algebraic boundary element equations. The algebraic equations are solved simultaneously in the transform space before being inverted numerically to obtain the concentration of the contaminant in real time and space. The application of this technique is demonstrated by some illustrative examples.