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

• We present a central scheme to be used with incompressible multiphase solvers.
• The scheme derives from Kurganov and Tadmor central scheme.
• The scheme is monotone and can be used along with polyhedral meshes.
• An application to the Algebraic Slip Mixture Model is presented.
• Settling cases are solved showing excellent results in conservation and boundedness.

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.