An incompressible multi-phase SPH method

An incompressible multi-phase SPH method is proposed. In this method, a fractional time-step method is introduced to enforce both the zero-density-variation condition and the velocity-divergence-free condition at each full time-step. To obtain sharp density and viscosity discontinuities in an incompressible multi-phase flow a new multi-phase projection formulation, in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed. Numerical examples for Taylor-Green flow, capillary waves, drop deformation in shear flows and for Rayleigh-Taylor instability are presented and compared to theoretical solutions or references from literature. The results suggest good accuracy and convergence properties of the proposed method.