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

Anna Kalogirou, Erietta E. Moulopoulou, Onno Bokhove

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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. (C) 2016 The Authors. Published by Elsevier Inc.

Original languageEnglish
Pages (from-to)7493-7503
Number of pages11
JournalApplied Mathematical Modelling
Volume40
Issue number17-18
Early online date16 Mar 2016
DOIs
Publication statusPublished - Sep 2016
Externally publishedYes
EventWorkshop on Advances in Numerical Modelling of Hydrodynamics - Sheffield
Duration: 24 Mar 201525 Mar 2015

Keywords

  • Shallow water waves
  • Hele-Shaw
  • Damped wave motion
  • Finite element method

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