REMOVING NUMERICALLY INDUCED DISPERSION FROM FINITE DIFFERENCE MODELS FOR SOLUTE AND WATER TRANSPORT IN UNSATURATED SOILS

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Abstract
Numerically induced dispersion is an important, but often ignored, source of calculation errors in transport simulations. General correction terms for removing numerical dispersion from the applied calculation schemes would be valuable in improving the accuracy of the simulation results before they are compared with measured soil data. In this study, a general transport equation for unsaturated water and solute transport is obtained by casting the one-dimensional Richards and convection-dispersion equations into general form. Correction terms for removing numerical dispersion from four commonly used finite difference (FD) calculation schemes used on the general transport equation are derived using Taylor series. The correction terms are given both in case of constant and variable depth increments. The derived terms are validated by method of moments analysis and tests against analytical solutions. The use of the correction terms in cases where the transport equations are extended with sink-/source terms is discussed. It is shown that a variable calculation grid should be chosen with care because the use of variable depth increments creates additional numerical dispersion and skewness and, in some cases, numerical oscillations in depth. The suggested procedure for deriving and validating correction terms for numerical dispersion can easily be extended to other FD schemes. © Williams & Wilkins 1994. All Rights Reserved.

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