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

We present a new parallel spectral element solver, FNPF-SEM, for simulating linear and fully nonlinear potential-flow-based water waves and their interactions with offshore structures. The tool is designed as a general-purpose wave model for offshore engineering applications. Built on the open-source Firedrake framework, the new FNPF-SEM model is a computational tool capable of capturing both linear and nonlinear wave phenomena with high accuracy and efficiency, supporting high-order (spectral) finite elements. Additionally, Firedrake provides native support for MPI-based parallelism, enabling efficient multi-CPU distributed computations for large-scale simulations. We demonstrate the capabilities of the high-order model through h - and p -convergence studies, and weak and strong scaling tests. Verification is performed against analytical and numerical solutions and verified against experimental data, including nonlinear high-order harmonic generation and 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.