Long duration SPH simulations of sloshing in tanks with a low fill ratio and high stretching

Achieving stable and accurate simulations of long duration sloshing with low fill ratios using smooth particle hydrodynamics (SPH) is a challenging problem. Its solution requires a judicious choice of SPH formulation to minimize the effect of errors introduced into the simulation by boundary conditions, dissipation terms or computer arithmetic. We assess the difficulties and common pitfalls of such simulations and propose a SPH method to deal with them effectively. The formulation combines an efficient use of double precision, wall boundary conditions using ghost particles, and a δ-SPH scheme for stability with minimal energy dissipation. The proposed SPH formulation accurately matches the experimental data, both in terms of surface elevations and forces on the tank, of the study of tuned liquid dampers by Reed et al. 1998, later reproduced by ESA/ESTEC, over a wide range of frequencies.