Relaxation Equations to Treat Multi Phase Viscous Flow for SPH Method(Fluids Engineering)

Abstract

In this report, we propose equations, named relaxation equations, to treat multiphase viscous flow for the smoothed particle hydrodynamics (SPH) method, suited to suppress the numerical disorder around the interface of two different fluids. They are possible to be applied for particles across the interface between different fluids to evaluate stress and acceleration of the particles, and make it possible to analyze the flow explicitly without separating the flow in each fluid. Errors of these equations are discussed and numerical simulations are carried out for the water-kerosene two-phase Poieuille flow between two plates to confirm the effects of these equations.