A high-order shifted boundary method for water waves and floating bodies

Jens Visbech*, Allan P. Engsig-Karup, Harry B. Bingham, Mostafa Amini-Afshar, Mario Ricchiuto

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Abstract

We consider the setting of fully nonlinear potential flow when simulating free surface waves using finite volume/cell/element methods. Here, the fluid domain is bounded by arbitrarily complex boundaries in topology and shape but also time-dependent (deforming or/and moving). Therefore, modeling such problems can be challenging and time-consuming from a meshing-point-of-view. If mesh updates are required [1], the domain should be re-meshed at each discrete time step, which provides a heavy computational burden. One way to circumvent this challenge is to consider unfitted/embedded/immersed boundary-type methods, where a simple – easy-to-generate – regular-shaped mesh is constructed once. Hereafter, the true domain is placed– and freely moved –on top of this background mesh. Enforcing boundary conditions is how unfitted methods differ from each other. One – relatively new – unfitted boundary method is the shifted boundary method (SBM), which we define more thoroughly in the upcoming section. Unfitted approaches have been developed for wave problems in recent years, where we highlight a few: The harmonic polynomial cell method with immersed type boundaries and/or overlapping grids in [2]. The same techniques have also been applied to the finite difference method in [3]. This abstract presents our recent developments toward modeling water waves and floating bodies using the SBM combined with a high-order spectral element method (SEM). Ultimately, we aim to model highly nonlinear wave-wave and wave-structure interactions using these techniques.
Original languageEnglish
Title of host publicationProceedings of 39th International Workshop on Water Waves and Floating Bodies
Number of pages4
PublisherIWWWFB
Publication date2024
Publication statusPublished - 2024
EventThe 39th International Workshop on Water Waves and Floating Bodies - St. Andrews, United Kingdom
Duration: 14 Apr 202417 Apr 2024
https://sites.dundee.ac.uk/iwwwfb2024/

Conference

ConferenceThe 39th International Workshop on Water Waves and Floating Bodies
Country/TerritoryUnited Kingdom
CitySt. Andrews
Period14/04/202417/04/2024
Internet address

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