A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media

An hybridizable discontinuous Galerkin method of arbitrary high order is formulated to solve the miscible displacement problem in porous media. The spatial discretization is combined with a sequential algorithm that decouples the flow and the transport equations. Hybridization produces a linear system for the globally coupled degrees of freedom, that is smaller in size compared to the system resulting from the interior penalty discontinuous Galerkin methods. We study the impact of increasing the polynomial order on the accuracy of the solution. Numerical experiments show that the method converges optimally and that it is robust for highly heterogeneous porous media in two and three dimensions.