We have developed Lagrangian methods such as Smooth Particle Hydrodynamics (SPH) and Moving Largrangin Patric-Galerkin (MLPG) Methods to simulate immiscible fluids and sediment transport in the fluid especially those involving violent water surfaces, e.g. breaking waves, violent flow interaction with structures, and sediment tracking.
Kernel function approximation - basis of the Lagrangian method
MLPG simulation of heavy fluid (in blue) mixed with light fluid (in red)
SPH simulation of dam break on a movable bed
The group also developed the Eulerian-Lagrangian method, having flow simulated in fixed meshes and sediments moved by Lagrangian particles representing each single sediment grain. The particle-in-cell approach is used to resolve sediment-fluid interplay for particularly large amount of particles. This method is intended to capture the fundamental sediment suspension and transport under complex free surface flow in coastal seas, including beach ripple dynamics, scouring and onshore/offshore transport and liquefaction around offshore structure foundations.
Selected references:
Shi, H., Si, P., Dong, P. et al. (2019). A two-phase SPH model for massive sediment motion in free surface flows, Advances in water resources, 129, 80-98
Xu, C. and Dong, P. (2017). Two-phase flow modeling of sediment suspension in the EMS/ Dollard estuary, Estuarine, Coastal and Shelf Science, 191, 115-124
Zhou, Y. (2017). A sharp-interface treatment technique for two-phase flows in meshless methods. Computers & Fluids, 147, 90-101.
Zhou, Y., Ma, Q., Yan, S. (2017). MLPG_R method for modelling 2D flows of two immiscible fluids. International Journal for Numerical Methods in Fluids, 84(7), 385-408.
Finn, J. R., Li, M., and Apte, S. V. (2016). Particle based modelling and simulation of naturals and dynamics in the wave bottom boundary layer. Journal of Fluid Mechanics, 796, 340-385.
Chen, X., Li, M., Chen, D. and Yu, X. (2011). A general two-phase turbulent flow model applied to the study of sediment transport in open channels. International Journal of Multiphase Flow, 37, 1099-1108.
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