Efficient P‐Multigrid Spectral Element Model for Water Waves and Marine Offshore Structures*

In marine offshore engineering, cost-efficient simulation of unsteady water wavesand their nonlinear interaction with bodies are important to address a broad range of engineeringapplications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF)model discretized using a Galerkin spectral element method to serve as a basis for handling both wavepropagation and wave-body interaction with high computational efficiency within a single modellingapproach. We design and propose an efficient O(n)-scalable computational procedure based ongeometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume andthe geometric features of complex bodies is represented accurately using high-order polynomial basisfunctions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectralelement model can take advantage of the high-order polynomial basis and thereby avoid generating ahierarchy of geometric meshes with changing number of elements as required in geometric h-multigridapproaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of theiterative geometric p-multigrid solver. Results of numerical experiments are presented for wavepropagation and for wave-body interaction in an advanced case for focusing design waves interactingwith a FPSO. Our study shows, that the use of iterative geometric p-multigrid methods for theLaplace problem can significantly improve run-time efficiency of FNPF simulators