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We present a novel approach to the simulation of miscible displacement byemploying adaptive enriched Galerkin finite element methods (EG) coupled withentropy residual stabilization for transport. In particular, numericalsimulations of viscous fingering instabilities in heterogeneous porous mediaand Hele-Shaw cells are illustrated. EG is formulated by enriching theconforming continuous Galerkin finite element method (CG) with piecewiseconstant functions. The method provides locally and globally conservativefluxes, which is crucial for coupled flow and transport problems. Moreover, EGhas fewer degrees of freedom in comparison with discontinuous Galerkin (DG) andan efficient flow solver has been derived which allows for higher orderschemes. Dynamic adaptive mesh refinement is applied in order to savecomputational cost for large-scale three dimensional applications. In addition,entropy residual based stabilization for high order EG transport systemsprevents any spurious oscillations. Numerical tests are presented to show thecapabilities of EG applied to flow and transport.

Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization