A Taylor-Galerkin approach for modelling a spherically symmetric advective-dispersive transport problem

This paper presents a numerical approach for examining a spherically symmetric advective-dispersive contaminant transport problem. The Taylor-Galerkin method that is based on an Euler time-integration scheme is used to solve the governing transport equation. A Fourier analysis shows that the Taylor-Galerkin method with a forward Euler time integration can generate an oscillation-free and non-diffusive solution for the pure advection equation when the Courant number satisfies the constraint Cr = 1. Such numerical advantages, however, do not extend to the advection-dispersion equation. Based on these observations, an operator-splitting Euler-integration-based Taylor-Galerkin scheme is developed to model the advection-dominated transport process for a problem that exhibits spherical symmetry. The spherically symmetric transport problem is solved using this approach and a conversion to a one-dimensional linear space with an associated co-ordinate transformation. Copyright (c) 2006 John Wiley & Sons, Ltd.