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

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

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: Jun 5, 2019
• 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
• Contract Date: Jun 5, 2019