The Laplace Transform Galerkin technique for efficient time-continuous solution of solute transport in double-porosity media

Abstract

A new and efficient technique is presented for numerical solution of solute transport problems in multi-dimensional double-porosity media. The method is based on the Laplace Transform Galerkin (LTG) technique (Sudicky, 1989) and employs a convolution integral in the governing advection-dispersion equation to express the diffusive exchange of solute between the mobile and immobile regions. Because the Laplace transformation is applied to the advection-dispersion equation describing transport in the mobile region, the convolution integral, in addition to the temporal derivative, is effectively removed. After the transformed equation is solved using the Galerkin finite element method, nodal concentrations in the time-domain are obtained using a robust and efficient algorithm for inversion of the Laplace-domain nodal concentrations. The method permits the solution to be evaluated at any future point in time without any need for time steps and permits the use of grids having a relatively coarse spatial discretization while avoiding significant numerical dispersion. Further computational efficiency is achieved for large-grid problems by employing an ORTHOMIN-accelerated iterative solver (Vinsome, 1976) to solve the system of Laplace-domain finite element equations. Influence functions describing the mobile-immobile region solute transfer are presented for the case of slab and sphere geometries for the immobile-fluid zone and for the case of first-order exchange theory, along with expressions which unify the three approaches. The utility of the model is demonstrated by applying it to the problem of solute transport in a sandy-type aquifer having a random, spatially-correlated hydraulic conductivity field and comprised of slightly porous grains that admit intragranular diffusion but do not conduct fluid.