diffusion of particles

Numerical simulation of multiphase problems with complex interface as well as high density ratios is one of the numerical challenges associated with particle scattering and divergence. Fewer problems have been performed with density-based smooth particle hydrodynamics (WCSPH) to solve complex joint surface currents, and most simulations have been performed using Incompressible Smooth Particle Hydrodynamics (ISPH). Solution of high density flows by the smooth particle hydrodynamics is associated with particle dispersion and divergence. Various methods have been used to eliminate the scattering of particles, such as a repulsive force at the interface or the corrected density re-value, but there is a problem of particle disintegration at the interface at higher times. In the present simulation, to simulate multiphase flows with complex surfaces and high density ratios, a new density-based smooth particle hydrodynamics approach has been utilized. To prevent the scattering of particles, especially at the interface at the end times, a simple method with the removal of incompatible particles is used. In the present study, the particle displacement optimization scheme for regularization at the interface of the phase is created by precisely implementing a two-stage change algorithm, so as to maintain the regular particle distribution continuously and conservatively. To examine the accuracy of the present simulation method, it is firstly compared with two-phase Poiseuille flow with three fluids having different values of viscosity, Reynolds-Taylor instability and single bubble rising in a fully filled container., Then it is compared with analytical and numerical solutions. The accuracy and consistency of the current simulation is higher or equal to other simulations.