Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow

Two-dimensional stabilized mixed Galerkin method using self-adjoint residual of the momentum equation (Darcy's law) has been previously implemented. In the present work, we are extending the two-dimensional stabilized model by incorporating the third dimension into the mathematical formulation. This extended stabilized mixed model would be able to accurately simulate more realistic flow of incompressible fluid through porous media. In the experimentation, the media is assumed homogeneous and the flow is considered laminar. The study shows that the numerically computed Darcy pressure and the velocity using hexahedral elements are comparable to the analytical solutions. In addition, the approximations converge to the exact solutions as the size of the elements decreases.