SINGLE-LAYER FINITE ELEMENT APPROXIMATION OF 3D NAVIER–STOKES EQUATIONS WITH FREE BOUNDARIES FOR SHALLOW WATER FLOWS
✍ Scribed by GIOVANNI M. CORNETTI
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 988 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0271-2091
No coin nor oath required. For personal study only.
✦ Synopsis
In order to simulate flows in the shallow water limit, the full incompressible Navier-Stokes equations with free boundaries are solved using a single layer of finite elements. This implies a polynomial approximation of the velocity profile in the vertical direction, which in turn distorts the wave speed. This fact is verified by numerical results: the wave speed depends on the vertical discretization. When at least two layers of finite elements are used, the boundary layer at the bottom can be simulated and the comct solution for the shallow water limit is recovered. Then this algorithm is applied to the prediction of Tsunami event. KEY WORDS finite element; incompressible; Navier-Stokes; free surface flows; shallow watex 1. The approximated solution is obtained by a standard incompressible Navier-Stokes code (e.g. the methods proposed by Hughes et a1. ' Pironneau,' Patera and coworker^,^^^^^ Hansbo," Tezduyar et ~f . ' ~-' ~
and Cornetti16 could be applied). 2. The 3D Navier-Stokes equations with FEM discretization have more mathematical support than the asymptotic analysis, where assumptions on the dependence of the solution on the third co-ordinate may not always be satisfied.