Development of Advective Dynamic Stabilization scheme for ISPH simulations of free-surface fluid flows

Abstract

This study presents an enhanced version of a numerical stabilizing scheme, namely, the Dynamic Stabilization scheme (DS) by Tsuruta et al. (2013), referred to as the Advective DS scheme (ADS) for further enhancement of the numerical stability and accuracy in ISPH simulations of free-surface fluid flows. To ensure general stability of calculations, particle methods may benefit from particle regularization schemes including artificial repulsive force schemes to keep particles equally distanced. DS explicitly provides a stabilizing force based on the overlapped state of a target particle and its neighboring particle, resulting in a momentum-conservative repulsive force and stable simulations. However, DS may also result in numerical noises and numerical dissipation. Such numerical noises stem from the excess stabilizing forces because of consideration of the particle positions only. The approaching velocities of particles, corresponding to the divergence-free condition, are ignored. To precisely consider the dynamic states of particles in derivation of stabilizing forces, in ADS, the approaching velocities are additionally considered and the stabilizing forces are derived in a variationally consistent form based on time rate of particle overlapping state, to precisely recover the exact deteriorated particle regularity state. The enhanced performance of the proposed ADS scheme is shown through some benchmark tests including a Taylor-Green vortex, a dam break as a violent free-surface flow, an oscillating drop and a rotating square patch. The enhanced performance of ADS in terms of reproduced pressure and velocity fields, energy conservation and convergence are well demonstrated.