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

Abstract

SUMMARYThis 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 advectiondominated 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.

Comparison Between Diffusive and Advective Approach in Quality Analysis of a Real Distribution Network

“…Many authors have dealt with the problem of advection-dispersion transport. Dong at al. (2008) (Dong & Selvadurai, 2008) have developed a model capable of modelling the advection dominated transport process.…”

“…Dong at al. (2008) (Dong & Selvadurai, 2008) have developed a model capable of modelling the advection dominated transport process. Pérez Guerrero et al (2013) (Pérez Guerrero, et al, 2013) have extended the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subject to transient (time-dependent) boundary conditions.…”