A Comparative Study of Two Different Density Estimation Techniques for Multi-Phase Flow Simulations Using SPH

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian method, highly suitable for numerical simulation of free-surface and interfacial flows. In the SPH literature, several numerical algorithms have been proposed for solving multi-phase fluid flow problems. One of the fundamental distinction between different methods hinges on the density estimation procedure. The present study assesses two such methods viz. the summation and continuity density approach. For these two methods, we perform a comparative analysis of accuracy, convergence, stability and energy conservation. The multi-phase flow simulations involve density ratio r = (ρdense/ρlight), ranging from 1 to 1000. The benchmark problems chosen for the analysis are dam break, bubble rise in a water column, Rayleigh–Taylor instability and non-Boussinesq lock exchange. The numerical solution for these problems is validated with experimental and other numerical benchmark results available in the literature. From detailed multi-phase flow simulations, it was observed that, for low density ratios, the continuity density algorithm provides better accuracy and energy conservation, whereas for high density ratios (r>10), summation density algorithm is preferable.