Control-volume Mixed Finite Element Methods
نویسنده
چکیده
A key ingredient in simulation of ow in porous media is accurate determination of the velocities that drive the ow. 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 nite 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 elementsized \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. This researchwas supported in part by the National Aeronautics and Space Administrationunder NASA Contract No. NAS1-19480 while the rst author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001
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