Simulation of nonlinear random finite depth waves coupled with an elastic structure

Time accurate computation of random nonlinear shallow-water waves is required for the design of offshore wind turbines, and also in a multitude of other areas. Assuming the fluid to be inviscid and irrotational, nonlinear finite amplitude waves in a liquid body of finite depth are computed based on potential theory, i.e. the velocity potential must satisfy the Laplace equation at every instant in time. The free surface boundary conditions give a partial differential equation for the velocity potential and the free surface elevation on the free boundary. Similar coupling conditions are obtained at the boundary in contact with the deformable body. During the computation, the repeated solution of Laplace’s equation can be obtained by solving a boundary integral equation with the BEM and a fast multipole solver. The incident wave field is given by a stochastic wave process far from the structure, where the scattered (diffracted and radiated) wave field is comparatively small. This is finally coupled to another fluid description at the structure, which has a fully nonlinear description of both incident and scattered wave. The effect of the interacting flexible structure is included via a coupling computation. The chosen software architecture allows a modular coupling concept reflected in the algorithmically strong coupling of the various fluid domains, the structure, and the soil. As a numerical example, an offshore wind turbine is simulated, which has an additional fluid interaction with the stochastic wind field.