2023 Volume 79 Issue 17 Article ID: 23-17116
The ISPH method is a projection-based particle method which potentially enables robust simulations of free-surface fluid flows including violent ones. However, in case of violent flows such as wave breaking, numerical instabilities may arise due to so-called tensile instability and rank deficiency. Therefore, careful enhancement of the method’s reliability would be indispensable. In this research, we have proposed two new schemes for the ISPH method to ensure the resolution of the continuity equation in discrete level which is of significant importance not only in satisfaction of incompressibility conditions (density invariance and null divergence velocity field), but also in reliability of the discretized form of the commonly applied Navier-Stokes equation derived from the Reynolds Transport Theorem. The new schemes, referred to as VEM/VCS clearly improve the invariant density and null velocity divergence conditions, and result in an enhanced numerical resolution of the continuity equation in an ISPH simulation of violent wave breaking on a steep slope.
