Solving the complete pseudo-impulsive radiation and diffraction problem using a spectral element method

This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a solution to a pseudo-impulsive formulation in the time domain, where the frequency-dependent quantities, such as added mass, radiation damping, and wave excitation force for arbitrary heading angle, β, are evaluated using Fourier transforms from the tailored time-domain responses. The spatial domain is tessellated by an unstructured high-order hybrid configured mesh and with solutions represented by piece-wise polynomial basis functions in the spectral element space. Fourth-order accurate time integration is employed, making the entire numerical scheme a high-order scheme. The model can use symmetry boundaries in the spatial representation to reduce the computational burden. The key piece of the numerical model – the discrete Laplace solver – is verified through p- and h-convergence studies. Moreover, to highlight the capabilities of the proposed model, we present proof-of-concept examples of simple floating bodies (a hemisphere and a box). Also, an oscillating water column is considered, including generalized modes representing the piston motion and wave sloshing effects inside the wave energy converter chamber. In this case, the spectral element model trivially computes the infinite-frequency added mass, which is a singular problem for conventional boundary element-type solvers. The proposed model serves its practical purpose within the field of offshore engineering for simulations of floating offshore wind turbines, wave energy converters, and much more. [Display omitted] •A spectral element solution to linear impulsive radiation/diffraction problems.•Computation of added mass, damping, and excitation force for simple geometries.•Simulation of an oscillating water column with generalized modes.•The spectral element discretization is supported by unstructured meshes.