Numerical solution of the convective and diffusive transport problems in a heterogeneous porous medium using finite element method

The finite element approximation of the convective and diffusive transport equation has been considered. Different methods for stabilization of the finite element approximation have been discussed: upwind approximation of the convective term using artificial diffusion (AD) and streamline upwind Petrov–Galerkin (SUPG) method, both used for stabilization of the classic Galerkin method. Another approach to approximation of the transport equation related to the discontinuous Galerkin method (DG) has been investigated. This method also allows to approximate the convective term using upwind schemes. The results of the numerical comparison of the considered schemes for the convective and diffusive transport problems in a porous media have been presented. The flow and transport in a highly contrast heterogeneous porous media that lead to the significant pressure gradients and, therefore, high velocities have been considered as test problems.