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, $\beta$, 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 represented by piece-wise polynomial basis functions in the spectral element space. Fourth-order accurate time integration is employed through an explicit four-stage Runge-Kutta method and complemented by fourth-order finite difference approximations for time differentiation. To reduce the computational burden, the model can make use of symmetry boundaries in the domain representation. The key piece of the numerical model -- the discrete Laplace solver -- is validated through $p$- and $h$-convergence studies. Moreover, to highlight the capabilities of the proposed model, we present prof-of-concept examples of simple floating bodies (a sphere and a box). Lastly, a much more involved case is performed of an oscillating water column, including generalized modes resembling 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.

翻译：本文提出了一种新颖、高效、高阶精确且稳定的基于谱元法的模型，用于计算漂浮式海上结构物的完整三维线性辐射与绕射问题。我们在时域中提出了一种伪脉冲公式的解，其中依赖于频率的量，如附加质量、辐射阻尼和任意航向角β的波浪激励力，通过傅里叶变换从定制时域响应中评估。空间域由非结构化高阶混合配置网格划分，并在谱元空间中用分段多项式基函数表示。通过显式四阶龙格-库塔方法实现四阶精度时间积分，并辅以四阶有限差分近似进行时间微分。为减少计算负担，模型可利用域表示中的对称边界。数值模型的关键部分——离散拉普拉斯求解器——通过p收敛和h收敛研究进行了验证。此外，为突出所提出模型的能力，我们展示了简单浮体（球体和箱体）的概念验证示例。最后，针对振荡水柱进行了更复杂的案例，包括广义模态，模拟波能转换器腔体内的活塞运动和波浪晃荡效应。在此案例中，谱元模型轻松计算了无限频率附加质量，而这对传统边界元求解器而言是一个奇异问题。