Modeling of Wave Breaking and Wave-Structure Interactions by Coupling of Fully Nonlinear Potential Flow and Lattice-Boltzmann Models

In this work, we report on the development and initial validation of a new hybrid numerical model for strongly nonlinear free surface flows, including wave breaking and wave-structure interactions. Specifically, a two-dimensional numerical wave tank (NWT) based on Fully Nonlinear Potential Flow (FNPF) theory, and a higher-order Boundary Element Method (BEM), is used to simulate fully nonlinear wave generation and far-field propagation over a possibly complex, but generally sloping, bottom bathymetry. A particle-based Lattice Boltzmann (LB) model is coupled with (or nested within) the FNPF-NWT, in the region where breaking would normally occur (e.g., upper part of a slope) and interrupt FNPF simulations. The coupled model is able to capture breaking and post-breaking (or wave-interaction) phenomena that involve more complex physics than represented by FNPF theory. Turbulence, in particular, is represented in the LB model by a Large Eddy Simulation (LES) scheme, based on a Smagorinsky model. In applications, we first validate the model for a one-way weakly coupled scheme, in which the LB model is initialized in the near-field, and then possibly driven on its boundary, by the wave-induced far-field velocity and pressure and their derivatives, computed within the NWT. In the paper, we formulate a fully (or strongly) coupled approach, in which the flow is first decomposed into irrotational and viscous perturbation parts. The latter lead to new terms that, by analogy with Navier-Stokes (NS) equations, are expressed as volume forces, that drive LB simulations of the perturbation fields. Applications of this strong coupling approach will be presented at the conference.