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 language | English |
|---|---|
| Pages (from-to) | 7493-7503 |
| Number of pages | 11 |
| Journal | Applied Mathematical Modelling |
| Volume | 40 |
| Issue number | 17-18 |
| Early online date | 16 Mar 2016 |
| DOIs | |
| Publication status | Published - Sep 2016 |
| Externally published | Yes |
| Event | Workshop on Advances in Numerical Modelling of Hydrodynamics - Sheffield, United Kingdom Duration: 24 Mar 2015 → 25 Mar 2015 |
Keywords
- Shallow water waves
- Hele-Shaw
- Damped wave motion
- Finite element method