We present a Spectral Element Fully Nonlinear Potential Flow (FNPFSEM) model developed for the simulation of wave-body interactions between nonlinear free surface waves and impermeable structures. The solver is accelerated using an iterative p-multigrid algorithm. Two cases are considered: (i) a surface piercing box forced into vertical motion creating radiated waves and (ii) a rectangular box released above its equilibrium resulting in freely decaying heave motion. The FNPF-SEM model is validated by comparing the computed hydrodynamic forces against those obtained by a Navier-Stokes solver. Although not perfect agreement is observed the results are promising, a significant speedup due to the iterative algorithm is however seen.


The demand for renewable energy is increasing worldwide to which the ocean offers great possibilities. Wave Energy Converters (WEC) covers a range of different structures built to transform some of the endless energy found in moving waters into electricity, see e.g. Li and Yu (2012) for an overview. Designing durable o shore bodies or structures that are able to withstand the continuous forcing from the water masses as well as finding optimal shapes for energy extraction requires precise modelling of nonlinear wave-body interactions. Specially important are the accurate predictions of the hydrodynamic loads exerted onto the structures during longer periods of time. In addition to high accuracy it is desirable to have models with low computational cost allowing for fast simulations. Computational fluid dynamic tools (CFD) are increasingly used in the industry due to their high fidelity, they are however computationally expensive even with advanced high-performance computing techniques (HPC) available (Davidson & Costello, 2020).

Focusing on creating a model with high accuracy we have chosen to employ a high-order finite element method, namely the Spectral Element Method (SEM), see e.g. Kopriva (2009) for a general overview and Xu et al. (2018) for a recent review on SEM for water waves. Besides providing high accuracy, finite element frameworks are flexible regarding the domain geometry. Using SEM to discretize the Fully Nonlinear Potential Flow (FNPF) equations we aim to provide a medium fidelity tool with a significant speedup over conventional CFD tools. Engsig-Karup et al. (2016) outline the SEM discretization of the FNPF equations for wave propagation.

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