A Lattice Boltzmann method for free surface flows over partially submerged structures

The Lattice Boltzmann method (LBM) has been extensively developed to efficiently simulate free surface flows and interactions between single-phase flows and fully immersed structures. However, few studies have focused on modelling partially submerged structures, particularly on accurately evaluating their hydrodynamic forces under gravity and wave dynamic conditions. To advance the application of LBM in this area, this study presents a dynamic-pressure Lattice Boltzmann model tailored for simulating partially submerged stationary structures in free surface flows. In the free surface section, the volume-of-fluid method is implemented and the advection of volume fraction is governed by the streaming of intrinsic density distribution functions. For the fluid-structure interface, an interpolated bounce-back scheme is imposed on the no-slip fluid-structure boundary and an improved momentum exchange method is employed to assess the fluid loads, accounting for the effects of gravity and external sources. This paper details the implementation of modelling framework and presents the outcomes of five benchmark simulations conducted for model verification and validation. These cases include flows over a circular cylinder and a square cylinder, Rider-Kothe single vortex evolution, dam-break flows, and wave impact on two partially submerged fixed boxes. The developed numerical model yields satisfactory agreement with experimental and numerical results in terms of the hydrodynamic force evaluation and free surface deformation. The final case demonstrates the capability of the LBM model in investigating frequency response of wave impact on partially submerged structures, highlighting its potential for broader applications in coastal and ocean engineering.