A spectral element solution of the two-dimensional linearized potential flow radiation problem

We present a scalable two-dimensional Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in the time domain using a Gaussian displacement signal tailored to the discrete resolution. The added mass and damping coefficients are then obtained via Fourier transformation. The spectral element method is used to discretize the spatial fluid domain, whereas the classical explicit 4-stage fourth-order Runge-Kutta scheme is employed for the temporal integration. Spectral convergence of the proposed model is established for both affine and curvilinear elements, and the computational effort is shown to scale with O(N-p), with N being the total number of grid points and p approximate to 1.12. The solver is used to compute the hydrodynamic coefficients for several floating bodies and compared against known public benchmark results. The results show excellent agreement, ultimately validating the solver and emphasizing the geometrical flexibility and high accuracy and efficiency of the proposed solution strategy. Lastly, an extensive investigation of nonresolved energy from the pseudo-impulse is carried out to characterize the induced spurious oscillations of the free surface quantities leading to a robust strategy for tuning the pseudo-impulsivemotion to the spatial discretization.