A central scheme for advecting scalars by velocity fields obtained from Finite Volume multiphase incompressible solvers

Abstract

This paper presents an extension of the central scheme of Kurganov and Tadmor (2000) to work with solvers based on conservative face fluxes, which are usual in the solution of incompressible flows by the Finite Volume Method. The proposed scheme retains the desirable properties of simplicity, low numerical viscosity and multidimensionality, and it works on general non-staggered polyhedral meshes. It is applied within a mixture multiphase solver to discretize the mass conservation equation of one of the phases. A series of cases are solved which show that the proposed extension is significantly more robust and monotonicity-preserving than the straightforward application of the Kurganov–Tadmor scheme.