scholarly journals Numerical solution of a free surface flow problem over an obstacle

2019 ◽  
Vol 106 (120) ◽  
pp. 135-148
Author(s):  
Samira Beyoud ◽  
Dahbia Boukari-Hernane
Keyword(s):  
Free Surface ◽  
Flow Problem ◽  
Vries Equation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Inviscid Fluid ◽  
Subcritical Case ◽  
Runge Kutta Method ◽  
Different Shapes ◽  
Gravity Acceleration

We consider a free surface flow problem of an incompressible and inviscid fluid, perturbed by a topography placed on the bottom of a channel. We suppose that the flow is steady, bidimensional and irrotational. We neglect the effects of the superficial tension but we take into account the gravity acceleration g. The main unknown of our problem is the equilibrium free surface of the flow; its determination is based on the Bernoulli equation which is transformed as the forced Korteweg-de Vries equation. The problem is solved numerically via the fourth-order Runge-Kutta method for the subcritical case, and the finite difference method for the supercritical case. The results obtained are illustrated by several figures, where the height h of the obstacle, and the value of the Froude number F of the flow, are varied. Note that different shapes of the obstacle have been considered.

Solvability of a supercritical free surface flow problem under gravity-capillarity

2017 ◽  
Vol 97 (10) ◽  
pp. 1701-1716
Author(s):  
N. Foukroun ◽  
R. Ait-Yahia-Djouadi ◽  
D. Hernane-Boukari
Keyword(s):  
Free Surface ◽  
Flow Problem ◽  
Free Surface Flow ◽  
Surface Flow

On the free-surface flow of very steep forced solitary waves

2013 ◽  
Vol 739 ◽  
pp. 1-21 ◽  
Author(s):  
Stephen L. Wade ◽  
Benjamin J. Binder ◽  
Trent W. Mattner ◽  
James P. Denier
Keyword(s):  
Free Surface ◽  
Solitary Waves ◽  
Flow Problem ◽  
Nonlinear Approximation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Boundary Integral ◽  
Weakly Nonlinear ◽  
Nonlinear Solutions

AbstractThe free-surface flow of very steep forced and unforced solitary waves is considered. The forcing is due to a distribution of pressure on the free surface. Four types of forced solution are identified which all approach the Stokes-limiting configuration of an included angle of $12{0}^{\circ } $ and a stagnation point at the wave crests. For each type of forced solution the almost-highest wave does not contain the most energy, nor is it the fastest, similar to what has been observed previously in the unforced case. Nonlinear solutions are obtained by deriving and solving numerically a boundary integral equation. A weakly nonlinear approximation to the flow problem helps with the identification and classification of the forced types of solution, and their stability.

Steady free-surface flow over spatially periodic topography

2015 ◽  
Vol 781 ◽  
Author(s):  
B. J. Binder ◽  
M. G. Blyth ◽  
S. Balasuriya
Keyword(s):  
Free Surface ◽  
Bound States ◽  
Asymptotic Theory ◽  
Vries Equation ◽  
Solution Space ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Bed Topography ◽  
Spatially Periodic ◽  
Autonomous Dynamical Systems

Two-dimensional free-surface flow over a spatially periodic channel bed topography is examined using a steady periodically forced Korteweg–de Vries equation. The existence of new forced solitary-type waves with periodic tails is demonstrated using recently developed non-autonomous dynamical-systems theory. Bound states with two or more co-existing solitary waves are also identified. The solution space for varying amplitude of forcing is explored using a numerical method. A rich bifurcation structure is uncovered and shown to be consistent with an asymptotic theory based on small forcing amplitude.

Transcritical flow over obstacles and holes: forced Korteweg–de Vries framework

2019 ◽  
Vol 881 ◽  
pp. 660-678 ◽  
Author(s):  
Roger H. J. Grimshaw ◽  
Montri Maleewong
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Vries Equation ◽  
Solitary Wave Solution ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Main Concern ◽  
Oncoming Flow ◽  
Transcritical Flow ◽  
De Vries

This paper extends a previous study of free-surface flow over two localised obstacles using the framework of the forced Korteweg–de Vries equation, to an analogous study of flow over two localised holes, or a combination of an obstacle and a hole. Importantly the terminology obstacle or hole can be reversed for a stratified fluid and refers more precisely to the relative polarity of the forcing and the solitary wave solution of the unforced Korteweg–de Vries equation. As in the previous study, our main concern is with the transcritical regime when the oncoming flow has a Froude number close to unity. In the transcritical regime at early times, undular bores are produced upstream and downstream of each forcing site. We then describe the interaction of these undular bores between the forcing sites, and the outcome at very large times.

scholarly journals Fully implicit time discretization for a free surface flow problem

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 619-620 ◽  
Author(s):  
Eberhard Bänsch ◽  
Stephan Weller
Keyword(s):  
Free Surface ◽  
Flow Problem ◽  
Free Surface Flow ◽  
Time Discretization ◽  
Surface Flow ◽  
Implicit Time ◽  
Fully Implicit

scholarly journals THE EFFECT OF SURFACE TENSION ON FREE-SURFACE FLOW INDUCED BY A POINT SINK

2016 ◽  
Vol 57 (4) ◽  
pp. 417-428
Author(s):  
G. C. HOCKING ◽  
H. H. N. NGUYEN ◽  
L. K. FORBES ◽  
T. E. STOKES
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Axisymmetric Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Limiting Factor ◽  
Inviscid Fluid ◽  
Steady Solutions ◽  
Determining Factor ◽  
Effect Of Surface

The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.

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