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Variational finite element methods for waves in a Hele-Shaw tank

Kalogirou, Anna; Moulopoulou, Erietta E.; Bokhove, Onno

Authors

Erietta E. Moulopoulou

Onno Bokhove



Abstract

The damped motion of driven water waves in a Hele-Shaw tank is investigated variationally and numerically. The equations governing the hydrodynamics of the problem are derived from a variational principle for shallow water. The variational principle includes the effects of surface tension, linear momentum damping due to the proximity of the tank walls and incoming volume flux through one of the boundaries representing the generation of waves by a wave pump. The model equations are solved numerically using (dis)continuous Galerkin finite element methods and are compared to exact linear wave sloshing and driven wave sloshing results. Numerical solutions of the nonlinear shallow water-wave equations are also validated against laboratory experiments of artificially driven waves in the Hele-Shaw tank.

Citation

Kalogirou, A., Moulopoulou, E. E., & Bokhove, O. (2016). Variational finite element methods for waves in a Hele-Shaw tank. Applied Mathematical Modelling, 40(17-18), 7493-7503. https://doi.org/10.1016/j.apm.2016.02.036

Journal Article Type Article
Acceptance Date Mar 2, 2016
Online Publication Date Mar 16, 2016
Publication Date 2016-09
Deposit Date Jun 4, 2019
Publicly Available Date Mar 28, 2024
Journal Applied Mathematical Modelling
Print ISSN 0307-904X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 40
Issue 17-18
Pages 7493-7503
DOI https://doi.org/10.1016/j.apm.2016.02.036
Keywords Modelling and Simulation; Applied Mathematics
Public URL https://nottingham-repository.worktribe.com/output/2138159
Publisher URL https://www.sciencedirect.com/science/article/pii/S0307904X1630110X

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