A three-dimensional model of wave interactions with permeable structures using the lattice Boltzmann method.

• A novel lattice Boltzmann scheme corresponding to the volume-averaged Navier-Stokes equations is derived. • A 3D multi-relaxation-time lattice Boltzmann model for the interaction of waves and porous structures is established. • The present lattice Boltzmann model is capable of handling spatially varying porous medium cases. To simulate the three-dimensional interaction of waves and porous structures using the lattice Boltzmann method, a novel multi-relaxation-time lattice Boltzmann scheme corresponding to the volume-averaged Navier-Stokes equations incorporating porous flow is developed. The porosity is introduced into the equilibrium distribution function, and the frictional forces produced by the porous media are added by the discrete force model. Through the Maxwell iteration, the relation between the mesoscopic lattice Boltzmann scheme and the macroscopic governing equations is established. Large eddy simulation and the single-phase volume-of-fluid techniques are modified to take porous media into account. The friction parameters in this model are calibrated using the experimental data of two-dimensional dam-break waves interacting with porous media composed of crushed rocks. Validations are carried out by comparing the simulation result of the proposed model with the laboratory data of three-dimensional dam-break waves impacting a prism and three-dimensional surface gravity waves (solitary waves and cnoidal waves) interacting with a vertical permeable breakwater. Furthermore, the interaction of regular waves and a rubble mound breakwater is used to test the capability of the model to handle spatially varying porous media. The different simulation results strongly agree with the experimental data, which prove that the lattice Boltzmann model has the ability to simulate complex wave motions near porous structures. [ABSTRACT FROM AUTHOR]