An ISPH scheme for Newtonian/non-Newtonian multi-phase flows including semi-analytical solutions for two-phase inelastic Poiseuille flows

An incompressible smoothed particle hydrodynamics (ISPH) method is developed for the modelling ofmulti-phase Newtonian and inelastic non-Newtonian ows at low density ratios. This new method isthe multi-phase extension of Xenakis et al. (2015), J. Non-Newtonian Fluid Mech., 218, 1-15, whichhas been shown to be stable and accurate, with a virtually noise-free pressure eld for single-phasenon-Newtonian ows. For the validation of the method a semi-analytical solution of a two-phaseNewtonian/non-Newtonian (inelastic) Poiseuille ow is derived. The developed method is also comparedwith the benchmark multi-phase case of the Rayleigh Taylor instability and a submarine landslide,thereby demonstrating capability in both Newtonian/Newtonian and Newtonian/non-Newtoniantwo-phase applications. Comparisons with analytical solutions, experimental and previously publishedresults are conducted and show that the proposed methodology can accurately predict the free-surfaceand interface proles of complex incompressible multi-phase ows at low density ratios relevant, forexample, to geophysical environmental applications.