Vertically Integrated Non-hydrostatic Free Surface Flow Equations

Author(s):  
Oscar Castro-Orgaz ◽  
Willi H. Hager
2000 ◽  
Vol 126 (6) ◽  
pp. 425-436 ◽  
Author(s):  
Alexander G. Panagiotopoulos ◽  
Johannes V. Soulis

Author(s):  
Saira F. Pineda ◽  
Armando J. Blanco ◽  
Luis Rojas-Solo´rzano

Open flow channel is very common in engineering applications. Traditional approaches solve shallow-water flow equations, known as Saint-Venant equations, when one or two dimension solutions can be adequate for obtaining most of the important flow characteristics. However, complex situations can require solving Navier-Stokes equations. The arrival of high performance computers and commercial software packages offers new possibilities in the field of numerical hydraulics. However, commercial software packages should be tested on some specific cases; so that these can be used with confidence. In this paper we solve several cases of free surface flow that consider subcritical, supercritical, critical, oscillatory depth profiles and hydraulic jumps using a commercial package, CFX™. Most of these cases are proposed as benchmark solutions for non-prismatic cross section, non-uniform bed slope and transition between subcritical and supercritical flow. Other cases as Hydraulic jump consist of experimental data of hydraulics jumps for incident flow with Froude numbers up to 4.23. Both types of cases allow us to perform the verification and validation of the commercial package used. Results obtained with CFX™ show excellent agreement with analytical solutions, for subcritical, supercritical, transitional and hydraulic jump cases. Special care with grid selection and entrance boundary condition is crucial to simulate with accuracy these types of flows. In particular, when a proper structured mesh is used, quality results are highly improved. Finally, results show to be insensitive to entrance turbulence conditions.


2010 ◽  
Vol 647 ◽  
pp. 187-200 ◽  
Author(s):  
J. EGGERS ◽  
A. F. SMITH

We rederive and expand upon a method for finding solutions to the two-dimensional irrotational (inviscid) flow equations in the presence of a free surface, found by Hopkinson. This method allows the flow to be driven by placing singularities, like sources or vortices, in the interior of the flow domain. We then apply the method to find a number of novel solutions: separated flow driven by a source, vortices behind a plate and free-surface flow stirred by a double vortex. Free surfaces generically exhibit cusp singularities with a 2/3 power index, similar to those found in very viscous flow.


1975 ◽  
Vol 3 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Thomas G. Smith ◽  
J.O. Wilkes

Author(s):  
Arthur E. P. Veldman ◽  
Henk Seubers ◽  
Peter van der Plas ◽  
Joop Helder

The simulation of free-surface flow around moored or floating objects faces a series of challenges, concerning the flow modelling and the numerical solution method. One of the challenges is the simulation of objects whose dynamics is determined by a two-way interaction with the incoming waves. The ‘traditional’ way of numerically coupling the flow dynamics with the dynamics of a floating object becomes unstable (or requires severe underrelaxation) when the added mass is larger than the mass of the object. To deal with this two-way interaction, a more simultaneous type of numerical coupling is being developed. The paper will focus on this issue. To demonstrate the quasi-simultaneous method, a number of simulation results for engineering applications from the offshore industry will be presented, such as the motion of a moored TLP platform in extreme waves, and a free-fall life boat dropping into wavy water.


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