High-Order Numerical Methods for Nonlinear Wave and Wave-Structure Interaction for Engineering Applications

Date: 25.11.2020; UTC Time: 11:00 AM- 12:00 PM

Advances in numerical simulation and modelling fidelity of water waves go in hand with continued improvements in computational resources, efficient numerical 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 that complement conventional dispersive modelling approaches of Boussinesq-type and CFD. The research have targeted improvements in numerical efficiency, simulation at large spatial scales in practical times and with ability to handle offshore structures and marine environments in simulations. Highlights are given from research done for more than a decade with scopes towards engineering applications in renewables, and with the overall aim of delivering improved robustness and design new fast numerical methods for nonlinear and dispersive wave propagation modelling using high-order numerical methods. Historically, and perhaps surprisingly, spectral element methods appear to have been somewhat 'overlooked' in world-wide research for marine hydrodynamics applications. We therefore discuss and touch upon some of pros and cons as well as the recent years progress on the use of spectral element methods.

Refs:

Engsig-Karup, A.P. and Laskowski, W. Efficient p-multigrid spectral element model for water waves and marine offshore structures, arXiv:2009.00705, September 2020.

Engsig-Karup, A.P., Monteserin, C. and Eskilsson, C. A Mixed Eulerian-Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures, Water Waves, 1 : 315-342, 2019.

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Engsig-Karup, A. P., Eskilsson, C., and Bigoni, D. A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves. J. Comput. Phys. Volume 318, 1 August 2016, pp. 1-21, 2016.

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