Numerical Solution of coupled Flow and Mass Transport equations in porous medium Using Discontinuous Galerkin Method

The present paper aims to evaluate a class of discontinuous Galerkin methods for modeling of coupled flow and mass transport equations in porous medium. Various combinations of primal discontinuous Galerkin methods were used for discretization of the coupled nonlinear system of flow and mass transport equations in a saturated porous medium and a fully implicit backward Euler scheme was applied for temporal discretization. The primal DGs have been developed successfully for density-dependent flows by applying both Cauchy and Dirichlet boundary conditions to the mass transport equation. To avoid the errors arising from non-compatible selection of DG methods for flow and mass transport equations, only compatible combinations were applied. To linearize the resulting nonlinear systems, Picard iterative technique was applied and a slope limiter was used to eliminate the nonphysical oscillations appeared in solution. For the purpose of consistent velocity approximation, Frolkovic-Knabner method was used. Three benchmark problems were simulated for validation and verification of the numerical code, which the results from the simulations show a good accuracy and low numerical dispersion for the model. Finally, to highlight the significance of consistent velocity approximation, a hydrostatic test problem was prepared.