MIXING CELL METHOD FOR SOLVING THE SOLUTE TRANSPORT-EQUATION WITH SPATIALLY-VARIABLE COEFFICIENTS

The advection-dispersion equation with spatially variable coefficients does not have an exact analytical solution and is therefore solved nu merically. However, solutions obtained with several of the traditional finite difference or finite element techniques typically exhibit spur ious oscillation or numerical dispersion when advection is dominant. T he mixing cell and semi-analytical solution methods proposed in this s tudy avoid such oscillation or numerical dispersion when advection dom inates. Both the mixing cell and semi-analytical solution methods calc ulate the spatial step size by equating numerical dispersion to physic al dispersion. Because of the spatial variability of the coefficients the spatial step size varies in space. When the time step size Delta t --> 0, the mixing cell method reduces to the semi-analytical solution method. The results of application to two cases show that the mixing cell and semi-analytical solution methods are better than a finite dif ference method used in the study. (C) 1998 John Wiley & Sons, Ltd.