Modified variable mass incompressible SPH method for simulating internal fluid flows

Abstract

In the conventional divergence free incompressible smoothed particle hydrodynamics method, the density and mass of the particles assumed to be constant over the simulation time. So, the particles are assumed to have constant volumes. At each time step, particles are moved according to the imposed acceleration and so the initial distribution of particles is changed. This paper presents a modified scheme for the incompressible SPH method. The contributions of this work are updating the volume of the particles at each time step and introducing an extra term to the pressure Poisson equation. In the proposed scheme, the mass of the particles are updated in each time step to keep the density of the particles constant and the divergence of convective term of the momentum equation is added to the source term of the pressure Poisson equation. The validity of the proposed scheme is verified, and to show the ability of the presented method, two internal fluid flow examples are solved.