High-Order Numerical Methods for Nonlinear Free Surface Wavesand Wave-Structure Interaction for Engineering Applications

Advances in numerical simulation and modelling fidelity of water waves go in hand with continued improvements in computational resources, improving the efficiency ofnumerical algorithms and the adoption of modern and emerging many-core hardware for massively parallel computations. We discuss trends in scientific computing and link these to recent research in addressing scientific gaps to be able to address nonlinear wave and wave-structure interaction problems through designing new high-order numerical schemes for both nonlinear and dispersive wave propagation and nonlinear wave-structure interaction based on potential flow theory and more recently also Navier-Stokes modelling. Through simple benchmarks of increasing complexities ourresearch targetimprovements in numerical efficiencythrough accelerated iterative solver strategies based on defect corrections / multigrid preconditioning, simulation at large spatial scales in practical times and with ability to handlethe geometric complexities ofoffshore structures and marine environments in simulations. Highlights are given from our research spanning nearly adecade with scopes towards engineering applications of high relevance for renewablesapplications.
Historically, and perhaps surprisingly, spectral element methods appear to have been somewhat ‘overlooked’ in world-wide research for marine hydrodynamics applications. We therefore given an overview of key scientific developments and benchmarks, and discuss some of the pros and cons, as well as the recent years progress on advancing theuse of high-order numerical schemes such as spectral element methods for free surface flows.