Analysis of semi-staggered finite-difference method with application to Bingham flows

In this paper, a finite-difference scheme for incompressible flow problems is treated. The scheme uses non-staggered grid for velocity approximation. A special stabilization is introduced to ensure the well-posedness and optimal approximation properties of the scheme. The stability estimate is proved in the form of a mesh-independent bound for the norm of discrete operator inverse. The finite-difference method is particularly suitable for problems in which velocity vector is involved in additional quantities that enter the system of flow equations as, for example, in the Bingham problem. We describe this application in the paper in some detail. Results of numerical experiments are included that confirm the applicability and optimality of the method.