One‐Dimensional Moving Finite‐Element Model of Solute Transport

Solute transport problems with sharp transitions or high advection are difficult to solve with traditional finite‐difference (FD) and finite‐element (FE) techniques. When advection dominates, the solutions obtained by these traditional methods typically suffer numerical smearing or oscillations. In these cases, 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 times. 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 work, obtains accurate and efficient solutions of the advection‐dispersion equation in a very wide range of Courant and Peclet numbers. The MFE method accurately simulates, with no oscillations, very steep fronts using space and time step sizes well beyond conventional constraints of the Peclet and Courant numbers. To demonstrate the accuracy and efficiency of the MFE method, some test cases are presented where the MFE, FD, and analytical solutions are compared.