An efficient p ‐multigrid spectral element model for fully nonlinear water waves and fixed bodies

Abstract In marine offshore engineering, cost‐efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications 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 wave propagation and wave‐body interaction with high computational efficiency within a single modeling approach. We design and propose an efficient ( n ) ‐scalable computational procedure based on geometric p ‐multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high‐order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p ‐multigrid spectral element model can take advantage of the high‐order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h ‐multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p ‐multigrid solver. Results of numerical experiments are presented for wave propagation and for wave‐body interaction in an advanced case for focusing design waves interacting with a floating production storage and offloading. Our study shows, that the use of iterative geometric p ‐multigrid methods for the Laplace problem can significantly improve run‐time efficiency of FNPF simulators.