Standard WCSPH for Free-Surface Multi-Phase Flows with a Large Density Ratio

Abstract

The standard weakly compressible Smoothed Particle Hydrodynamics (WCSPH) is successfully applied to multi-phase problems involving fluids with similar densities, but when density ratio increases at some order of magnitude, serious instability phenomena occur at the interface. Several remedies have been proposed based on numerical correctives that deviate from standard formulation, increasing the algorithm complexity and, sometimes, the computational cost. In this study, the standard SPH has been adapted to treat free-surface multi-phase flows with a large density ratio through a modified form of the governing equations which is based on the specific volume (i.e. the inverse of particle volume) instead of density: the former is continuous across the fluid interface while the latter is not and generates numerical instability. Interface sharpness is assured without cohesion forces; kernel truncation at the interface is avoided. The model, relatively simple to implement, is tested by simulating two-phase dam breaking for two configurations: kinematic and dynamic features are compared with reference data showing good agreement despite the reduced computational effort.