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This paper presents a detailed analysis of a numerical solution of three-dimensional transient Darcy flow. The numerical solution of the governing parabolic partial differential equations is obtained by using stabilized mixed Galerkin method and backward Euler method for the discretization of space and time, respectively. The resulting well-posed system of algebraic equations is subsequently solved using conjugate gradient method. The proposed model is validated against Mongan’s analytical model for underground water flow using a set of hexahedral and tetrahedral meshes. The model is used to analyze the transient behavior by simulating the Darcy flow through homogeneous and heterogeneous as well as isotropic and anisotropic media. For large meshes, a parallel algorithm of the transient Darcy flow is also developed for shared memory architecture using OpenMP library. For structured meshes, a speedup of over 22 is obtained on dual AMD Opteron processors. The proposed numerical method for transient Darcy flow offers stability, ease of implementation in higher dimensions and parallel solution for large and complex geometry using standard finite element spaces. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]