A 3RD-ORDER NUMERICAL SCHEME WITH UPWIND WEIGHTING FOR SOLVING THE SOLUTE TRANSPORT-EQUATION

Solute transport in the subsurface is generally described quantitative ly with the convection-dispersion transport equation. Accurate numeric al solutions of this equation are important to ensure physically reali stic predictions of contaminant transport in a variety of applications . An accurate third-order in time numerical approximation of the solut e transport equation was derived. The approach leads to corrections fo r both the dispersion coefficient and the convective velocity when use d in numerical solutions of the transport equation. The developed algo rithm is as extension of previous work to solute transport conditions involving transient variably saturated fluid flow and non-linear adsor ption. The third-order algorithm is shown to yield very accurately sol utions near sharp concentration fronts, thereby showing its ability to eliminate numerical dispersion. However, the scheme does suffer from numerical oscillations. The oscillations could be avoided by employing upwind weighting techniques in the numerical scheme. Solutions obtain ed with the proposed method were free of numerical oscillations and ex hibited negligible numerical dispersion. Results for several examples, including those involving highly non-linear sorption and infiltration into initially dry soils, were found to be very accurate when compare d to other solutions. (C) 1997 by John Wiley & Sons, Ltd.