Nonlinear time‐domain wave‐structure interaction: A parallel fast integral equation approach

We report on the development and validation of a new numerical wave tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three‐dimensional overturning waves over arbitrary bottom. Int J Numer Methods Fluids. 2001; 35:829‐867], which was successful at modeling many wave phenomena, including landslide‐generated tsunamis, rogue waves, and the initiation of wave breaking over slopes. This earlier NWT combined a three dimensional MII (mid‐interval interpolation) boundary element method (BEM) to an explicit mixed Eulerian–Lagrangian time integration. The latter was based on second‐order Taylor series expansions for the mesh geometry and Dirichlet free surface boundary condition for the potential, requiring high‐order derivatives to be computed in space and time. Here, to be able to solve large scale wave‐structure interaction problems for surface‐piercing bodies of complex geometry, of interest for ocean engineering and naval hydrodynamics applications, the NWT is reformulated to use cubic B‐spline meshes and the BEM solution is accelerated with a parallelized fast multipole method (FMM) based on ExaFMM, one of the fastest open source FMM to date. The NWT accuracy, convergence, and scaling are first assessed for simple cases, by comparing results with those of the earlier MII‐NWT as a function of mesh size and other model parameters. The relevance of the new NWT for solving the targeted applications is then demonstrated for surface piercing fixed cylinders, for which we show that results agree well with theoretical and experimental data for wave elevation and hydrodynamic forces. An efficient three‐dimensional numerical wave tank, solving for fully nonlinear potential flow, is presented for wave‐structure interactions. This boundary element method using cubic B‐splines shows high‐order convergence and is shown to accurately predict both wave propagation and hydrodynamic forces on submerged or floating fixed structures. The method is accelerated in parallel and with an efficient fast multipole method.