Abstract
A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large-scale irregularities of the geology (faults, fractures, and layers) suggest the use of irregular grids in simulation. This paper presents a control-volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular block-centered grids. The control-volume formulation of Darcy''s law can be viewed as a discretization into element-sized ``tanks'''' with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block-by-block conservation in the usual mixed discretization of the mass-conservation equation. Numerical results in two dimensions show second-order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.
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