Abstract
In this paper we introduce a new control volume method for the discretization of a partial differential equation. The interpolation in this method utilizes ‘bilinear’, spline, or weighted distance functions. We call this new method the control volume function approximation (CVFA) method. It can accurately approximate both the pressure and velocity in the simulation of multiphase flow in porous media, effectively reduce grid orientation effects, and be easily applied to arbitrarily shaped control volumes. It is suitable for hybrid grid porous media simulations. In this paper we focus on its development, numerical study, and comparison with a standard control volume finite element method. A two-phase incompressible flow problem is used to show the efficiency and accuracy of the CVFA.
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