Efficient p-multigrid spectral element model for water waves and marine offshore structures

TL;DR

This paper introduces an efficient p-multigrid spectral element method for simulating water waves and their interaction with offshore structures, significantly improving computational efficiency in marine engineering applications.

Contribution

It develops a novel geometric p-multigrid solver that enhances the efficiency of fully nonlinear potential flow simulations without requiring geometric mesh hierarchies.

Findings

The p-multigrid method achieves O(n) scalability.

Numerical benchmarks demonstrate improved run-time efficiency.

Successful simulation of wave-structure interactions with FPSO.

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 modellingapproach. We design and propose an efficientO(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 spectralelement 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 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.