Validating numerical solution of transient Darcy flow using the stabilized mixed finite element method

The natural flows through porous media often exhibit transient behavior. Some of the examples include water movement in aquifers, oil flow in reservoirs and blood passing through arteries walls. For accurate modeling of such flows, the Darcy model is used with an additional time-dependent pressure term. In this paper, validation of the three-dimensional numerical solution of transient Darcy flow using the stabilized mixed finite element method is presented. The proposed numerical solution employs the implicit backward difference method for the discretization of time, whereas, for space discretization, the Galerkin technique is used. The model is validated against analytical models including the Theis equation for pressure drawdown near a pumping well. The proposed solution is tested for different values of the viscosity of the fluid, and the permeability and specific storage of the medium. The error analysis shows that the stabilized mixed Galerkin methods give stable solutions with no oscillations and spurious results. It is also found that the viscosity of the fluid and the permeability of the medium have prominent effects on the transient behavior of Darcy flow.