REMOVING NUMERICALLY INDUCED DISPERSION FROM FINITE-DIFFERENCE MODELSFOR SOLUTE AND WATER TRANSPORT IN UNSATURATED SOILS

Numerically induced dispersion is an important, but often ignored, sou rce 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 stud y, a general transport equation for unsaturated water and solute trans port is obtained by casting the one-dimensional Richards and convectio n-dispersion equations into general form. Correction terms for removin g 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 c onstant 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 equation s 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 a nd skewness and, in some cases, numerical oscillations in depth. The s uggested procedure for deriving and validating correction terms for nu merical dispersion can easily be extended to other FD schemes.