A generalized density dissipation for weakly compressible smoothed particle hydrodynamics

Weakly compressible smoothed particle hydrodynamics (SPH) is known to suffer from numerical pressure noise, posing challenges to simulation stability and accuracy. To address this, the present study introduces a novel density dissipation scheme aimed at suppressing such unphysical noise. The proposed solution overcomes the limitation of traditional density dissipation schemes being ineffective at fluid interfaces in multiphase flow simulations. The novel scheme is generally applicable to the entire computational domain, encompassing both single-phase flow and multiphase flow. This advancement is achieved through two key components. First, the traditional density dissipation is replaced with a density increment dissipation approach that enables dissipation to cross interfaces separating different fluids. Second, based on dissipation volume conservation, a dissipation volume correction factor is employed to stabilize simulations characterized by large density ratios. The accuracy, stability, and robustness of our method are demonstrated through direct comparisons with experimental data or numerical results in four three-dimensional benchmarks: sloshing under external excitations, the rising of single and double bubbles, Rayleigh–Taylor instability, and Kelvin–Helmholtz instability. Additionally, our study reveals the relationship between SPH utilizing density dissipation and the approximate Riemann solver.