Numerical convergence of the MPFA O-method and U-method for general quadrilateral grids

Abstract

Control-volume discretization methods are applicable for problems that require good numerical approximations of fluxes. Here, a class of flux-continuous discretization methods, denoted multipoint flux approximation methods (MPFA), is discussed, and two different approaches are derived. The resulting discrete equations use pressures as the only unknowns, and the fluxes will be given explicitly as weighted sums of the discrete pressures. The two methods are denoted the O-method and the U-method, respectively, and differ in the way that continuity requirements are embedded in the discrete equations. Numerical tests are provided for smooth problems and problems with discontinuous coefficients for both the O-method and the U-method. Convergence rates of the methods are indicated through numerical experiments on smooth and rough grids. Copyright © 2006 John Wiley & Sons, Ltd.