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.

[1]  K. O'Neill.  Highly efficient, oscillation free solution of the transport equation over long times and large spaces , 1981 .

[2]  William H. Press,et al.  Numerical recipes , 1990 .

[3]  J. Bear.  Hydraulics of Groundwater , 1979 .

[4]  T. F. Russell,et al.  An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation , 1990 .

[5]  S. P. Neuman,et al.  A Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids , 1981 .

[6]  Keith Miller,et al.  Moving Finite Elements. I , 1981 .

[7]  O. C. Zienkiewicz,et al.  An ‘upwind’ finite element scheme for two‐dimensional convective transport equation , 1977 .

[8]  M. Venutelli,et al.  Moving finite element model for one‐dimensional infiltration in unsaturated soil , 1992 .

[9]  Keith Miller,et al.  The moving finite element method: Applications to general partial differential equations with multiple large gradients☆ , 1981 .

[10]  J. Verwer,et al.  A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines , 1990 .

[11]  O. C. Zienkiewicz,et al.  Finite element methods for second order differential equations with significant first derivatives , 1976 .

[12]  W. G. Gray,et al.  An analysis of the numerical solution of the transport equation , 1976 .

[13]  A. Westerberg,et al.  An implementation of a moving finite element method , 1986 .

[14]  E. Dick.  Accurate Petrov‐Galerkin methods for transient convective diffusion problems , 1983 .