Review of Smoothed Particle Hydrodynamics: towards converged Lagrangian flow modelling

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This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original
applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed and since then the
weakly compressible form has been advanced reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing (MPC) and graphics processing units (GPUs). Applications are diverse and encompass wave-structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between first and the second-order theoretical limit. Recent advances are
improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.
Original languageEnglish
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Publication statusAccepted/In press - 7 Aug 2020


  • SPH


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