Amodified SPH approach for fluids with large density differences

We introduce a modified SPH approach that is based on discretising the particle density instead of the mass density. This approach makes it possible to use SPH particles with very different masses to simulate multi-phase flows with large differences inmass density between the phases.We test our formulationwith a simple advection problem, with sound waves encountering a density discontinuity, and with shock tubes containing an interface between air and Diesel oil. For all examined problems where particles have different masses, the new formulation yields better results than standard SPH, even in the case of a single-phase flow.