Numerical investigation of Newtonian and non-Newtonian multiphase flows using ISPH method

We have presented a multiphase incompressible smoothed particle hydrodynamics method with an improved interface treatment procedure. To demonstrate the effectiveness of the interface treatment which can handle multiphase flow problems with high density and viscosity ratios, we have modeled several challenging two phase flow problems; namely, single vortex flow, square droplet deformation, droplet deformation in shear flow, and finally the Newtonian bubble rising in viscous and viscoelastic liquids. The proposed interface treatment includes the usage of (i) different smoothing functions (in this work, cubic spline kernel function for discretizing equations associated with the calculation of the surface tension force while the quintic spline for the discretization of governing equations and the relevant boundary conditions), and (ii) a new discretization scheme for calculating the pressure gradient. It is shown that with the application of the improved interface treatment, it becomes possible to model multiphase flow problems with the density and viscosity ratios up to 1000 and 100 respectively while using standard projection method. The utilization of cubic spline for the continuum surface force model significantly improves the quality of the calculated interface, thereby eliminating the interphase particle penetrations, and in turn leading to the calculation of more accurate velocity and pressure fields.