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

Abstract

AbstractThis 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 © 2006 John Wiley & Sons, Ltd.