Sloshing simulations with the smoothed particle hydrodynamics (SPH) method

Abstract

The main aims of this work are to identify, verify, and validate a smoothed particle hydrodynamics (SPH) method for simulating long duration transient and steady- state fluid sloshing in complex geometries. The validation will be carried out by comparing the SPH simulations against experimental data provided by ESA/ESTEC for transient and steady-state sloshing in a rectangular tank with a low filling ratio and of transient sloshing in a pill-shaped tank that exhibits transition from swaying to swirling waves. The experimental tests proved to be extremely challenging due to the low fill ratio of the rectangular tank and the long duration of both experiments. The main challenge is to devise a SPH scheme that balances spatial and temporal accuracy with an efficient computer implementation to produce accurate simulations at a reasonable computing cost. The investigation highlighted three issues of critical importance: the treatment of solid boundaries in order to limit the introduction numerical errors into the system; the application of a correct numerical dissipation scheme to reduce existing numerical errors; and the need for a massively parallel implementation.. Careful examination of the most suitable techniques led to the adoption a cor- rected δ-SPH scheme that provides numerical dissipation to reduce spurious pressure oscillations, and a fixed ghost particle boundary condition to accurately impose wall boundary conditions. The proposed SPH methods were coded in the open source parallel code DualSPHysics. The implementation showed significant improvements in energy conservation and solution accuracy when compared to state-of-the-art SPH methods, and accurately reproduced known analytical solutions to linear sloshing. The validation against the ESA/ESTEC experimental data showed excellent agreement between the SPH simulations and experiments, accurately reproducing the time history of wave heights and sloshing forces as well as capturing the full free-surface shapes. Only the careful selection of appropriate boundary conditions, artificial dissipation and a massively parallel GPU architecture allowed to accurately simulate these experiments.