Lattice Boltzmann method for shallow water flow with wave radiation stress

The protection of the marine environment is of growing concern, and the development of hydrodynamic models is required to study ocean processes. In this work, a two-dimensional hydrodynamic lattice Boltzmann model was developed to study wave–current coupling problems that combine wave radiation, bed shear stress and wind shear stress. The model is based on nonlinear shallow water equations and two different forms are developed to model wave radiation stress. The first form uses an additional external force term, including a weight factor in the lattice Boltzmann equation at the streaming step. The second form modifies a local equilibrium distribution function at the collision step. Von Neumann stability method is used to study the two schemes. This model was verified by three classic cases: waves diffracted by a straight vertical wall, waves diffracted by two breakwaters, and waves in a circular channel. The numerical results demonstrate the validity of the proposed model, indicating that it can accurately describe the characteristics of water flow with interactions between waves and currents.