A constant-density approach for incompressible multi-phase SPH

A constant-density approach, which corrects intermediate density errors by adjusting the half-time-step velocity with exact projection, is proposed for the multi-phase SPH method developed in our previous work [X.Y. Hu, N.A. Adams, An incompressible multi-phase SPH method, J. Comput. Phys. 227 (2007) 264–278]. As no prescribed reference pressure is required, the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection SPH method. Numerical examples for Taylor–Green flow, capillary waves and for Rayleigh–Taylor instability are presented and compared to theoretical solutions or references from the literature.