A novel Roe solver for incompressible two-phase flow problems

Abstract

In this paper, a novel Roe-type Riemann solver is developed for solving incompressible two-phase flow problems. The two-phase flow is modeled by coupling the artificial compressibility based Navier-Stokes equations and an interface advection equation in a conservative level set framework. The proposed Roe solver does not assume a locally constant density field while evaluating the flux Jacobian. As a result, the solver is capable of capturing the exact jump conditions across the contact and shear waves, which in turn helps in enhancing the accuracy of the interface motion. Moreover, mass conservation characteristics are significantly improved by adopting conservative level set framework together with finite volume discretization of the system of equations. A dual time stepping method with explicit pseudo-time marching scheme is used for modeling the unsteady terms. The efficacy of the proposed solver is demonstrated using various standard incompressible two-phase flow problems, involving low amplitude sloshing, broken dam, Rayleigh-Taylor instability and droplet splash.