Gagarina, E, Ambati, VR, van der Vegt, JJW et al. (1 more author) (2014) Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves. Journal of Computational Physics, 275. pp. 459-483. ISSN 0021-9991
Abstract
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time. One novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis-à-vis the mesh deformation being geometrically dependent on free surface evolution. Another key feature is the use of a variational (dis)continuous Galerkin finite element discretization in time. Moreover, in the absence of a wave maker, it is shown to be equivalent to the second order symplectic Störmer-Verlet time stepping scheme for the free-surface degrees of freedom. These key features add to the stability of the numerical method. Finally, the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the Maritime Research Institute Netherlands. © 2014 Elsevier Inc.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Nonlinear water waves;; Finite element Galerkin method; Variational formulation; Symplectic time integration; Deforming grids |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Mar 2017 09:23 |
Last Modified: | 17 Mar 2017 09:23 |
Published Version: | https://doi.org/10.1016/j.jcp.2014.06.035 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jcp.2014.06.035 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109062 |