Simulating advective-dispersive transport by finite elements: Criteria for accuracy of an explicit Runge-Kutta method

Galerkin finite element models (GFEMs) are reported to predict advective-dispersive transport more accurately than the traditional finite difference models. The inference is based on either first- or second-order approximation of the time derivative. Accuracy of the GFEM for higher-order temporal discretization is not, however, known. The objective of this paper is to develop a fifth-order explicit Runge-Kutta GFEM (RKG-FEM) and develop criteria to obtain oscillation-free accurate results. The ability of the RKGFEM to provide oscillation-free accurate results is found to be a function of the time length of simulation. In general, the model predictions are oscillation free and accurate when Peclet number, Pe&le40 and Courant number, CrLSEQ1.