MFE_TRANSP: One-dimensional moving-finite-element program for modeling solute transport in porous media

Abstract

Solute transport problems with sharp transitions or high advection are difficult to solve with traditional finite-difference (FD) and finite-element (FE) techniques. If advection dominates, the solution obtained by these traditional methods typically suffer numerical smearing or oscillations. In these situations acceptable numerical solutions of the classical advection-dispersion equation by FE and FD techniques can be obtained only by using a fine discretization on space and time that allows the stability requirements expressed by the Courant and Peclet numbers to be satisfied. This leads to large computer time. A way for overcoming this problem is to use a moving grid method. The dynamically self-adaptive moving-finite-element (MFE) grid method, used in this program, obtains accurate and efficient solutions of the advection-dispersion equation for a wide range of Courant and Peclet numbers. The program accurately simulates, with no oscillations, steep fronts using space and time step sizes well beyond conventional constraints of the Peclet and Courant numbers. The listing of the computer code written in FORTRAN 77 is included along with the user manual. To demonstrate the accuracy and efficiency of the MFE method, some examples are presented where the MFE, FD and analytical solutions are compared.