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Abstract
In this paper, the time-dependent system of governing differential equation for contaminant transport in porous media is considered. Numerical solution of this equation indicates spurious spatial oscillations for different time steps and mesh sizes. The upwind finite element scheme (UFEM) is used to overcome the oscillations associated with the solution of two-dimensional transient contaminant transport equation under advection-dominated and purely advective conditions. The results of a conventional finite element model and the UFEM are compared with an analytical solution. In order to evaluate the robustness of UFEM, a cross comparison is made between this method and third-order total-variation-diminishing scheme which is broadly recognised as an oscillation-free method for solving advection-dominated problems. It is shown that the upwind finite element solution is free of oscillations and it minimises numerical dispersion. Furthermore, in upwind finite element method there is flexibility over the solution by using proper damping coefficients based on the nature of the problem.