STABILIZED HYBRID MIXED DGFEM FOR THE STOKES-DARCY PROBLEM

Abstract

In this work we apply the stabilized hybrid mixed finite element method developed and analyzed by Igreja and Loula (2018) to solve the incompressible miscible displacements in heterogeneous media formed by the coupling of the free-fluid with the porous medium. The hydrodynamic problem is governed by the Stokes and Darcy systems coupled by Beavers-Joseph- Saffman interface conditions. To solve the Stokes-Darcy coupled system we use the stabilized hybrid mixed method, characterized by the introduction of the Lagrange multipliers associated with the velocity field in both domains. The global system is assembled involving only the degrees of freedom associated with the multipliers and the variables of interest can be solved at the element level. Considering the velocity fields given by the hybrid method we adopted the SUPG method (Brooks and Hughes, 1982) combined with an implicit finite difference scheme to solve the transport equation associated with miscible displacements. Numerical studies are presented to illustrate the flexibility and robustness of the hybrid formulation. To verify the efficiency of the hybrid method, computer simulations are also presented for the recovery hydrological flow problems in heterogeneous porous media, such as continuous injection.