crn^CD iiu. CONTROL-VOLUME MIXED FINITE ELEMENT METHODS

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 proce-dure 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 veloc-ity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions