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

Abstract

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 (RKGFEM) 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⩽40 and Courant number, Cr⩽1.