On removing the numerical instability induced by negative pressures in SPH simulations of typical fluid–structure interaction problems in ocean engineering

Abstract

This paper is dedicated to (1) emphasizing the importance of removing the Tensile Instability (TI) induced by negative pressures in Smoothed Particle Hydrodynamics (SPH) simulations, and (2) proposing new modifications for the Tensile Instability Control (TIC) and Particle Shifting Technique (PST) to simulate Fluid–Structure Interaction (FSI) phenomena with violent free-surface evolutions. Four numerical benchmarks associated with classical FSI problems characterized by negative pressures are simulated to show how the tensile instability destroys an SPH simulation without any TI prevention strategies. Therefore, PST and TIC are adopted into the SPH simulations for the sake of suppressing the tensile instability. However, different combinations of TI prevention strategies, i.e. different combinations of PST and TIC, lead to different results, and hence detailed investigations and discussions are provided. It is demonstrated that when negative pressures are moderate, solely using either PST or TIC works well. Nonetheless, it is in favor of using both PST and TIC if an SPH simulation is characterized by extremely strong negative pressures. Furthermore, for the problems with a convex-shaped structure penetrating a free-surface, special modifications are necessary for both PST and TIC in order to obtain accurate SPH results.