Accurate discretization of gradients on non-uniform curvilinear staggered grids
The Navier-Stokes equations for incompressible flow are simplified to a considerable extent by keeping only the inertia and pressure terms. These equations can be further reduced to a form which plays a dominant role in the theory of porous media and is referred to as interface problem. The discretization of the reduced form of the Navier-Stokes equations and the interface problem have already been dealt in the literature. The present paper provides a theoretical derivation of the best scheme of discretization available in an earlier work of \textit{R. S. Bernard} and \textit{H. Kapitza} [J. Comput. Phys. 99, 288-298 (1992; Zbl 0743.76053)]. The scheme is proved to be exact for pressure gradient constant on arbitrary grids. Direction for the generalization to three dimensions is also indicated.
scientific article; zbMATH DE number 758609