The backward group preserving scheme for 1D backward in time advection‐dispersion equation

Abstract

AbstractIn this article, we propose a backward group preserving scheme (BGPS) on the advection‐dispersion equation (ADE) for tackling of the contamination problems. The BGPS has been successfully applied on the backward heat conduction problems as well as the backward in time Burgers equation, but it has never been applied to solve the ADE. The BGPS is able to recover the spatial distribution of groundwater contaminant concentration in this work. Several numerical examples are worked out, and we show, based on those numerical examples, that the BGPS is applicable to the ADE and the method can also handle the ADE with piecewise constant dispersion coefficients. When a steep gradient is appeared in the solution, several steps of the BGPS can be used to retrieve the desired initial data and its result is better than the marching‐jury backward beam equation (MJBBE) method as far as our examples are concerned. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010