Stability-Enhanced ISPH Method with Accurate Velocity Divergence for Robust Computation of Wave Breaking Resultant Violent Flows

For the design of coastal structures, it is necessary to simulate violent free-surface flows by wave breaking with high accuracy. The particle method, a Lagrangian-type method, is suitable for simulating free-surface flows with violent motions. Among particle methods, the ISPH method is expected to provide accurate solutions since the incompressibility condition of flow is mathematically guaranteed by the Helmholtz–Leray decomposition. However, it may still contain numerical noises in pressure field and may become unstable, especially in violent fluid cases. In addition, as a result of numerical approximations and discretizations, the numerical resolution of the continuity equation, i.e., incompressibility conditions, namely divergence-free velocity and invariant density fields, may not be ensured. To our best knowledge, there is no research on how well the ISPH calculation results satisfy the incompressibility conditions. There is a possibility that numerical errors may result in some deviations from the incompressibility conditions, and if these deviations are noticeable, it is necessary to reduce them. Furthermore, since the numerical resolution of the continuity equation is a precondition for the Navier–Stokes equation for incompressible fluids, this measure also improves the reliability of the solution of the Navier–Stokes equation. In this paper, two numerical schemes, namely, Velocity-divergence Error Mitigating (VEM) and Volume Conservation Shifting (VCS) schemes are incorporated, to further improve the numerical resolution of the continuity equation in the context of ISPH and to further enhance the numerical stability. The effectiveness of the proposed schemes is validated through a benchmark test including violent free-surface flow.