A spectral boundary integral method for inviscid water waves in a finite domain

Im, Jeon-Sook; Billingham, John

Abstract

In this paper, we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls, and also how it can be modified to take into account water of finite depth with a spatially varying bottom. In each case, we use Chebyshev polynomials as the basis of our representation of the solution and filtering to remove spurious high-frequency modes. We show that spectral accuracy can be achieved until wave breaking, plunging or wall impingment occurs in two model problems.

Citation

Im, J.-S., & Billingham, J. (2016). A spectral boundary integral method for inviscid water waves in a finite domain. International Journal for Numerical Methods in Fluids, 82(7), 437-448. https://doi.org/10.1002/fld.4225

• Journal Article Type: Article
• Acceptance Date: Feb 1, 2016
• Publication Date: Mar 7, 2016
• Deposit Date: Jun 27, 2016
• Publicly Available Date: Jun 27, 2016
• Journal: International Journal for Numerical Methods in Fluids
• Print ISSN: 0271-2091
• Electronic ISSN: 1097-0363
• Publisher: Wiley
• Peer Reviewed: Not Peer Reviewed
• Volume: 82
• Issue: 7
• Pages: 437-448
• DOI: https://doi.org/10.1002/fld.4225
• Public URL: https://nottingham-repository.worktribe.com/output/781179
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1002/fld.4225/abstract
• Additional Information: This is the pre-peer reviewed version of the following article: Im, J.-S., and Billingham, J. (2016) A spectral boundary integral method for inviscid water waves in a finite domain. Int. J. Numer. Meth. Fluids, which has been published in final form at http://dx.doi.org/10.1002/fld.4225. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.