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.