Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future

ABSTRACT

This paper assesses some recent trends in the novel numerical meshless method smoothed particle hydrodynamics, with particular focus on its potential use in modelling free-surface flows. Due to its Lagrangian nature, smoothed particle hydrodynamics (SPH) appears to be effective in solving diverse fluid-dynamic problems with highly nonlinear deformation such as wave breaking and impact, multi-phase mixing processes, jet impact, sloshing, flooding and tsunami inundation, and fluid–structure interactions. The paper considers the key areas of rapid progress and development, including the numerical formulations, SPH operators, remedies to problems within the classical formulations, novel methodologies to improve the stability and robustness of the method, boundary conditions, multi-fluid approaches, particle adaptivity, and hardware acceleration. The key ongoing challenges in SPH that must be addressed by academic research and industrial users are identified and discussed. Finally, a roadmap is proposed for the future developments.

Keywords:

• Environmental fluid mechanics
• free-surface flows
• numerical methods
• smoothed particle hydrodynamics
• SPH

Acknowledgements

The authors would like to thank the editors of the Journal of Hydraulic Research, and in particular Professor Vladimir Nikora, for their valuable input to improve the quality of the paper.

Notes

1. There are several conventions about SPH notations in the literature (particles are often labelled as i and j). Here we follow the original notations of Monaghan (1992).

2. Using implicit time integration schemes in SPH have been poorly addressed in the literature. See e.g. Cueille (2005).

3. https://research.nvidia.com/content/cuda-research-centers