On the Development and Application of Hybrid Numerical Models in Nonlinear Free Surface Hydrodynamics

In this article, we report on the development of hybrid numerical models used to simulate free surface, i.e., wave, hydrodynamics, wave-structure interactions, wave breaking and nearshore transformation, and wave-induced sediment transport. Specifically, a two(2D) or three-dimensional (3D) numerical wave tank (NWT), based on Fully Nonlinear Potential Flow (FNPF) equations, is used to simulate fully nonlinear wave generation and propagation from the far-field to the near-field, where a Navier-Stokes (NS) model is coupled with or nested within the NWT, to simulate near-field phenomena of more complex physics. In one presented application, a 2D-NWT is used to simulate periodic or irregular incident waves whose kinematics forces simulations of flow and sediment transport over the seabed and around partially buried obstacles. The suspended sediment transport is modeled in the near field in the NS model, using an immersed-boundary method and an embedded sediment transport model. Turbulence is represented by Large Eddy Simulation (LES) in the NS model, with a subgrid dynamic Smagorinsky scheme. The 2Dand 3D-NWTs are based on a higher-order Boundary Element Method (BEM), with an explicit second-order time stepping. Hence, only the NWT boundary is discretized. The solution for the velocity potential and its derivatives along the boundary is obtained in the BEM, which subsequently provides a solution at any required internal point within the domain. The NS-LES model domain is both initialized and driven for later time by the three-dimensional velocity field computed in the NWT. In the present formulation, the total velocity and pressure fields are expressed as the sum of irrotational (incident/far-field) and near-field viscous perturbations. The NS equations are formulated and solved for the perturbation fields, which are forced by the incident fields computed in the NWT. The feasibility of coupling the irrotational flow and NS solutions in an efficient hybrid manner is demonstrated.