A Generalized Density Dissipation for Weakly-compressible SPH

The weakly compressible Smoothed Particle Hydrodynamics (SPH) is known to suffer from the pressure oscillation, which would undermine the simulation stability and accuracy. To address this issue, we propose a generalized density dissipation scheme suitable for both single-phase and multiphase flow simulations. Our approach consists of two components. Firstly, we replace the basic density dissipation with the density increment dissipation to enable numerical dissipation crossing the interfaces of different fluids in multiphase flow. Secondly, based on the dissipation volume conservation, we utilize dissipation volume correction factor (VCF) to stabilize the simulations for multiphase flows with large density ratio. We demonstrate the accuracy, stability, and robustness of our method through four three-dimensional benchmarks, i.e., the sloshing under external excitations, the single and double bubbles rising, Rayleigh-Taylor instability, and Kelvin Helmholtz instability. Additionally, our study reveals the relationship between SPH with the density dissipation and the approximate Riemann solver.