scholarly journals Numerical and Experimental Investigation of Wave Overtopping of Barriers

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 451 ◽  
Author(s):  
Cannata ◽  
Tamburrino ◽  
Ferrari ◽  
Badas ◽  
Querzoli
Keyword(s):  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Integral Form ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Wave Overtopping

We present a study of wave overtopping of barriers. The phenomenon of the wave overtopping over emerged structures is reproduced both numerically and experimentally. The numerical simulations are carried out by a numerical scheme for three-dimensional free-surface flows, which is based on the solution of the Navier–Stokes equations in a novel integral form on a time-dependent coordinate system. In the adopted numerical scheme, a novel wet–dry technique, based on the exact solution of the Riemann problem over the dry bed, is proposed. The experimental tests are carried out by adopting a nonintrusive and continuous-in-space image-analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves. A comparison between numerical and experimental results, for several wave and water-depth conditions, is shown.

Modélisation tridimensionnelle de l'écoulement au voisinage d'un aménagement portuaire

1989 ◽  
Vol 16 (6) ◽  
pp. 829-844
Author(s):  
A. Soulaïmani ◽  
Y. Ouellet ◽  
G. Dhatt ◽  
R. Blanchet
Keyword(s):  
Free Surface ◽  
Computational Analysis ◽  
Stokes Equations ◽  
A Priori ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Solution Algorithm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Flows

This paper is devoted to the computational analysis of three-dimensional free surface flows. The model solves the Navier-Stokes equations without any a priori restriction on the pressure distribution. The variational formulation along with the solution algorithm are presented. Finally, the model is used to study the hydrodynamic regime in the vicinity of a projected harbor installation. Key words: free surface flows, three-dimensional flows, finite element method.

The Application of Numerical Methods for the Solution of Some Problems in Free-Surface Hydrodynamics

2005 ◽  
Vol 49 (04) ◽  
pp. 288-301
Author(s):  
U. P. Bulgarelli
Keyword(s):  
Free Surface ◽  
Numerical Methods ◽  
Stokes Equations ◽  
Level Set Methods ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Robust Algorithms ◽  
Ship Waves ◽  
Particle Hydrodynamics

The aim of this contribution is to present some of the recent developments achieved at INSEAN in the context of accurate and robust algorithms for the solutions of the system of partial differential equations governing complex free-surface flows. The paper addresses several problems of relevant interest in naval hydrodynamics, for example, sloshing, water on deck, microscale breaking waves, bow-stern flows, ship waves, steady and unsteady ship flows. Each problem is solved through the most appropriate numerical method, which is selected on the basis of the approximations that can be done for the particular problem and of the kind of result that the analysis has to provide. Numerical methods adopted involve classical boundary element approaches, smoothed particle hydrodynamics, heterogeneous domain decomposition techniques, level-set methods, steady and unsteady Reynolds averaged Navier-Stokes equations. Validation versus experimental data are presented. Comparisons among different numerical approaches are also established in a few cases with the aim of highlighting their limits and/or capabilities.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Numerical Modeling of Flow Over a Dam Spillway

2006 ◽  
Author(s):  
Iraj Saeedpanah ◽  
M. Shayanfar ◽  
E. Jabbari ◽  
Mohammad Haji Mohammadi
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Iterative Solution ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
Water Jets ◽  
Pressure Fields ◽  
Good Agreement

Free surface flows are frequently encountered in hydraulic engineering problems including water jets, weirs and around gates. An iterative solution to the incompressible two-dimensional vertical steady Navier-Stokes equations, comprising momentum and continuity equations, is used to solve for the priori unknown free surface, the velocity and the pressure fields. The entire water body is covered by a unstructured finite element grid which is locally refined. The dynamic boundary condition is imposed for the free surface where the pressure vanishes. This procedure is done continuously until the normal velocities components vanish. To overcome numerical errors and oscillations encountering in convection terms, the SUPG (streamline upwinding Petrov-Galerkin) method is applied. The solution method is tested for different discharges onto a standard spillway geometries. The results shows good agreement with available experimental data.

scholarly journals Hydrodynamic Effects Produced by Submerged Breakwaters in a Coastal Area with a Curvilinear Shoreline

2019 ◽  
Vol 7 (10) ◽  
pp. 337 ◽  
Author(s):  
Francesco Gallerano ◽  
Giovanni Cannata ◽  
Federica Palleschi
Keyword(s):  
Coastal Area ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Integral Form ◽  
Navier Stokes ◽  
Hydrodynamic Effect ◽  
Riemann Solver ◽  
Three Dimensional Model ◽  
Navier Stokes Equations

A three-dimensional numerical study of the hydrodynamic effect produced by a system of submerged breakwaters in a coastal area with a curvilinear shoreline is proposed. The three-dimensional model is based on an integral contravariant formulation of the Navier-Stokes equations in a time-dependent curvilinear coordinate system. The integral form of the contravariant Navier-Stokes equations is numerically integrated by a finite-volume shock-capturing scheme which uses Monotonic Upwind Scheme for Conservation Laws Total Variation Diminishing (MUSCL-TVD) reconstructions and an Harten Lax van Leer Riemann solver (HLL Riemann solver). The numerical model is used to verify whether the presence of a submerged coastal defence structure, in the coastal area with a curvilinear shoreline, is able to modify the wave induced circulation pattern and the hydrodynamic conditions from erosive to accretive.

Numerical Simulation of Transient Free Surface Flows Using a Moving Mesh Technique

2006 ◽  
Vol 73 (6) ◽  
pp. 1017-1025 ◽  
Author(s):  
Laura Battaglia ◽  
Jorge D’Elía ◽  
Mario Storti ◽  
Norberto Nigro
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Surface Flows ◽  
Flow Domain ◽  
Convection Dominated

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of the moving type that involve geometrical nonlinearities. In contrast to more conventional computational fluid dynamics problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult as it generates large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a streamline upwind/Petrov-Galerkin (SUPG) scheme (Hughes, T. J. R., and Brooks, A. N., 1979, “A Multidimensional Upwind Scheme With no Crosswind Diffusion,” in Finite Element Methods for Convection Dominated Flows, ASME ed., 34. AMD, New York, pp. 19–35, and Brooks, A. N., and Hughes, T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259) combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one (Tezduyar, T. E., 1992, “Stablized Finite Element Formulations for Incompressible Flow Computations,” Adv. Appl. Mech., 28, pp. 1–44, and Tezduyar, T. E., Mittal, S., Ray, S. E., and Shih, R., 1992, “Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements,” Comput. Methods Appl. Mech. Eng., 95, pp. 221–242). At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in the PETSc-FEM code (PETSc-FEM: a general purpose, parallel, multi-physics FEM program. GNU general public license (GPL), http://www.cimec.org.ar/petscfem) by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented.

scholarly journals A convergent FV–FE scheme for the stationary compressible Navier–Stokes equations

2020 ◽  
Author(s):  
Charlotte Perrin ◽  
Khaled Saleh
Keyword(s):  
Finite Element ◽  
Numerical Scheme ◽  
Space Dimension ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Convergence Result ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Industrial Software

Abstract In this paper we prove a convergence result for a discretization of the three-dimensional stationary compressible Navier–Stokes equations assuming an ideal gas pressure law $p(\rho )=a \rho ^{\gamma }$ with $\gamma> \frac{3}{2}$. It is the first convergence result for a numerical method with adiabatic exponents $\gamma $ less than $3$ when the space dimension is 3. The considered numerical scheme combines finite volume techniques for the convection with the Crouzeix–Raviart finite element for the diffusion. A linearized version of the scheme is implemented in the industrial software CALIF3S developed by the French Institut de Radioprotection et de Sûreté Nucléaire.

Sign in / Sign up

Export Citation Format

Share Document