A Numerical Model for Multiphase Flow Based On The GMPPS Formulation, Part II: Dynamics

A numerical method for simulating variable density multiphase fluid flows is presented in this paper. It is a hybrid Eulerian-Lagrangian method solving the incompressible Navier-Stokes equations on a fixed Eulerian grid for velocity and pressure. Fluid phase is tracked in a Lagrangian manner by using marker-particles (Bierbrauer and Zhu, 2007a) to update the grid density and viscosity. A high order Godunov advection scheme, together with an approximate projection scheme to ensure incompressibility, is used to deal with rapid changes in fluid properties. We call this scheme the Godunov-Marker-Particle Projection Scheme (GMPPS), which implements pressure corrections to avoid spurious numerical boundary layers for multiphase flows. We have validated the GMPPS by comparing our numerical results with those calculated from an exact solution, with constant density, as well as some available physical experimental results for a variable density case. It is demonstrated that the scheme has second-order accuracy in time and space for a range of Reynolds numbers. The fact that test results of a two-phase droplet impacting on solid and liquid surfaces compare well with experimental results suggests that the GMPPS has great potential to be used to solve multiphase flow problems.