Abstract
In this paper, the compatibility of various combinations of numerical schemes for the solution of flow and transport equations in porous media is studied and the possible loss of accuracy and global mass conservation are investigated. Here, the flow equations are solved using three popular finite element methods including the Standard Galerkin (SG), Discontinuous Galerkin (DG) and Mixed Finite Element (MFE) methods among which only the DG method possesses the local conservation property. Besides, the transport of a scalar variable which is governed by a convection-diffusion equation is studied in conjunction with the flow equations. The transport equation is solved using both the Streamline Upwind Petrov-Galerkin (SUPG) and the DG methods. Two test cases are numerically solved using various combinations of methods in order to explore the compatibility of flow and transport solution algorithms. In each test case, the error in total mass conservation and the deviation from the exact solution are compared for various solver combinations.
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