A conservative, unconditionally stable, second‐order three‐point differencing scheme for the diffusion–convection equation

Abstract

A three‐point differencing scheme for the diffusion–convection equation is presented that offers all the advantages of both the central and the one‐sided ('upwind') differencing scheme without suffering from their drawbacks. Specifically, the scheme is conservative, unconditionally stable, and second‐order‐accurate in space. It is free of oscillations and over‐ or undershoots, simple to code, and requires essentially no more computing time than the one‐sided scheme. Although known for a relatively long time in numerical mathematics, the scheme apparently has not received sufficient attention from modellers of hydrothermal systems or contaminant transport in the geosciences. In order to fill this gap a comparison is made between this scheme and the widely used one‐sided scheme for the transient diffusion–convection equation in different time discretizations. The results are discussed taking into account other approaches towards minimizing numerical diffusion. Copyright © 1987, Wiley Blackwell. All rights reserved