Dealing with density discontinuities in planetary SPH simulations

Density discontinuities cannot be precisely modelled in standard formulations of smoothed particles hydrodynamics (SPH) because the density field is defined smoothly as a kernel-weighted sum neighbouring particle masses. This problem when performing simulations giant impacts between proto-planets, for example, planets typically do have both at their surfaces and any internal boundaries different materials. The inappropriate densities these regions create artificial forces that effectively suppress mixing material and, consequence, this introduces key unknown systematic error into studies rely on SPH simulations. In work we present novel, computationally cheap method deals simultaneously with types discontinuity We perform hydrodynamical tests several example impact simulations, compare results SPH. simulated Moon-forming using $10^7$ particles, improved treatment affects least 30% some point during simulation.