An upscaling approach to Multipoint Flux Approximations
R. Potsepaev (Schlumberger, UK), A.J. Fitzpatrick and C.L. Farmer
This paper concerns the control-volume discretization of –div(K(x) grad u) = f(x), the equation describing fluid flow through anisotropic porous media. The permeability tensor, K(x), is allowed to have discontinuities. The Multipoint Flux Approximation (MPFA) is used, and transmissibility coefficients are obtained from local numerical flow experiments (transmissibility upscaling) for each cell face. For regular K-orthogonal grids, with a uniform permeability tensor, the scheme reduces to the standard two-point flux approximation. Monotonicity and symmetry properties of the solution matrix are discussed. Numerical examples and results for 3D structured grids with highly distorted geometry are used to evaluate the method.