Turbulence is one of the most challenging issues to track the detail in various engineering fields. In regard to turbulence in multiphase flow simulations, due to the complex flow fields at the phase interface, appropriate modeling of turbulence is of significant importance for the numerical accuracy. In this study, an enhanced solid-liquid multiphase MPS method, benefitting from a set of improved schemes, is incorporated with SPS turbulence model. It would be shown that the proposed method has potential applicability for multi-phase turbulence flow simulations.


Multiphase flows are widely encountered in coastal and ocean engineering fields, e.g. sediment transport, scouring, density driven currents at a river-mouth area, and so on. In general, multiphase flows have highly-deformed phase interface including density discontinuity, which may result in one of the most challenging issues in a numerical simulation, in particular, if it includes rigid bodies such as rubble stones dumped into the sea and slamming with entrapped air, etc. In this regard, one of the projection-based particle methods, namely MPS (Moving Particle Semi-implicit) method (Koshizuka et al., 1996), can be considered as an expectant candidate for simulation of multiphase flow owing to its fully Lagrangian framework and projection-based algorithm, i.e. an advantage in robustness for distinction to track the complex moving boundaries along with flexibility. On the other hand, the original MPS involves the numerical noises in pressure, and thus, much effort has been devoted to develop accurate multiphase particle method for more numerical stability and accuracy (Gotoh and Khayyer, 2016; Gotoh and Okayasu, 2017).

While, reproduction of turbulence is also one of the most important factor to guarantee the accuracy in the simulations. The pioneering work of turbulence modeling in the frame of particle method corresponds to the SPS (Sub-Particle-Scale) turbulence model by Gotoh et al. (2001). Although several studies have been carried out for development of turbulence modeling in the context of particle method so far, there have been few studies about application of SPS turbulent model into multiphase flow simulations. It stems from the difficult distinguishment of the SPS turbulent component from that of the pure numerical noises. However, in recent years, such pure noises have been effectively suppressed thanks to the development of the enhanced schemes. Considering the complex flow field in multiphase flow especially at the phase interface, the proper modeling of SPS turbulence is supposed to be of significant importance in order to achieve physically consistent multiphase simulations as a next step.

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