FNPF-SEM: A parallel spectral element model in Firedrake for fully nonlinear water wave simulations

TL;DR

FNPF-SEM is a parallel spectral element solver in Firedrake designed for accurate, efficient, large-scale simulations of linear and nonlinear water waves and their interactions with structures, validated against analytical and experimental benchmarks.

Contribution

The paper introduces a novel high-order spectral element model within Firedrake for fully nonlinear water wave simulations, supporting complex geometries and scalable parallel computations.

Findings

High-order spectral element method achieves high accuracy in wave simulations.

Model demonstrates excellent scalability on parallel computing architectures.

Validation confirms the model's effectiveness against analytical and experimental data.

Abstract

We present a new parallel spectral element solver, FNPF-SEM, for simulating linear and fully nonlinear potential flow-based water waves and their interaction with offshore structures. The tool is designed as a general-purpose wave model for offshore engineering applications. Built within the open-source framework Firedrake, the new FNPF-SEM model is designed as a computational tool capable of capturing both linear and nonlinear wave phenomena with high accuracy and efficiency, with support for high-order (spectral) finite elements. Additionally, Firedrake provides native support for MPI-based parallelism, allowing for efficient multi-CPU distributed computations needed for large-scale simulations. We demonstrate the capabilities of the high-order spectral element model through h- and p-convergence studies, and weak and strong scaling tests. Validation is performed against analytical solutions and experimental data for several benchmark cases, including nonlinear high-order harmonic generation and linear and nonlinear wave interactions with a cylinder and a breakwater. The new FNPF-SEM model offers a numerical framework for simulating wave propagation and wave-structure interactions, with the following key features: i) the ability to represent complex geometries through flexible, unstructured finite element meshes; ii) reduced numerical diffusion and dispersion by using high-order polynomial expansions; and iii) scalability to full- and large-scale simulations over long time periods through a parallel implementation.