324 research outputs found
Simulation of Free Surface Compressible Flows Via a Two Fluid Model
The purpose of this communication is to discuss the simulation of a free
surface compressible flow between two fluids, typically air and water. We use a
two fluid model with the same velocity, pressure and temperature for both
phases. In such a numerical model, the free surface becomes a thin three
dimensional zone. The present method has at least three advantages: (i) the
free-surface treatment is completely implicit; (ii) it can naturally handle
wave breaking and other topological changes in the flow; (iii) one can easily
vary the Equation of States (EOS) of each fluid (in principle, one can even
consider tabulated EOS). Moreover, our model is unconditionally hyperbolic for
reasonable EOS.Comment: 8 pages, 10 figures; OMAE2008, 27th International Conference on
Offshore Mechanics and Arctic Engineering. Other authors papers and
animations related to this work can be downloaded from:
http://www.cmla.ens-cachan.fr/fileadmin/Membres/dutykh/ The paper was
slightly modified according to referees comment
A lower bound on the blow-up rate for the Davey-Stewartson system on the torus
We consider the hyperbolic-elliptic version of the Davey-Stewartson system
with cubic nonlinearity posed on the two dimensional torus. A natural setting
for studying blow up solutions for this equation takes place in . In this paper, we prove a lower bound on the blow up rate for these
regularities
Long time behaviour of solutions of abstract inequalities: Applications to thermo-hydraulic and magnetohydrodynamic equations
AbstractWe study some scalar inequalities of parabolic type and we give the leading term of an asymptotic expansion as t → ∞ for solutions of thermo-hydraulic equations without external excitation. A phenomenon of resonance is pointed out. We also treat M. H. D. equations and Navier-Stokes equations on a Riemannian manifold
Global attractors for the one dimensional wave equation with displacement dependent damping
We study the long-time behavior of solutions of the one dimensional wave
equation with nonlinear damping coefficient. We prove that if the damping
coefficient function is strictly positive near the origin then this equation
possesses a global attractor
On the effect of compressibility on the impact of a falling jet
At the first World Sloshing Dynamics Symposium that took place during the Nineteenth (2009) International Offshore and Polar Engineering (ISOPE) Conference in Osaka, Japan, it was made clear that simplified academic problems have an important role to play in the understanding of liquid impacts. The problem of the impact of a mass of liquid on a solid structure is considered. First the steady two-dimensional and irrotational flow of an inviscid and incompressible fluid falling from a vertical pipe, hitting a horizontal plate and flowing sideways, is considered. A parametric study shows that the flow can either leave the pipe tangentially or detach from the edge of the pipe. Two dimensionless numbers come into play: the Froude number and the aspect ratio between the falling altitude and the pipe width. When the flow leaves tangentially, it can either be diverted immediately by the plate or experience squeezing before being diverted. The profile of the pressure exerted on the plate is computed and discussed. Then the same problem is revisited with the inclusion of compressibility effects, both for the falling liquid and for the gas surrounding it. An additional dimensionless number comes into play, namely the Mach number. Finally, a discussion on the differences between the incompressible and compressible cases is provided
Tsunami generation by dynamic displacement of sea bed due to dip-slip faulting
In classical tsunami-generation techniques, one neglects the dynamic sea bed
displacement resulting from fracturing of a seismic fault. The present study
takes into account these dynamic effects. Earth's crust is assumed to be a
Kelvin-Voigt material. The seismic source is assumed to be a dislocation in a
viscoelastic medium. The fluid motion is described by the classical nonlinear
shallow water equations (NSWE) with time-dependent bathymetry. The
viscoelastodynamic equations are solved by a finite-element method and the NSWE
by a finite-volume scheme. A comparison between static and dynamic
tsunami-generation approaches is performed. The results of the numerical
computations show differences between the two approaches and the dynamic
effects could explain the complicated shapes of tsunami wave trains.Comment: 16 pages, 10 figures, Accepted to Mathematics and Computers in
Simulation. Other author's papers can be downloaded at
http://www.cmla.ens-cachan.fr/~dutyk
Finite volume methods for unidirectional dispersive wave models
We extend the framework of the finite volume method to dispersive
unidirectional water wave propagation in one space dimension. In particular we
consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods
are used for time discretizations. The fully discrete schemes are validated by
direct comparisons to analytic solutions. Invariants conservation properties
are also studied. Main applications include important nonlinear phenomena such
as dispersive shock wave formation, solitary waves and their various
interactions.Comment: 25 pages, 12 figures, 51 references. Other authors papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh
A compressible two-fluid model for the finite volume simulation of violent aerated flows. Analytical properties and numerical results
In the study of ocean wave impact on structures, one often uses Froude
scaling since the dominant force is gravity. However the presence of trapped or
entrained air in the water can significantly modify wave impacts. When air is
entrained in water in the form of small bubbles, the acoustic properties in the
water change dramatically and for example the speed of sound in the mixture is
much smaller than in pure water, and even smaller than in pure air. While some
work has been done to study small-amplitude disturbances in such mixtures,
little work has been done on large disturbances in air-water mixtures. We
propose a basic two-fluid model in which both fluids share the same velocities.
It is shown that this model can successfully mimic water wave impacts on
coastal structures. Even though this is a model without interface, waves can
occur. Their dispersion relation is discussed and the formal limit of pure
phases (interfacial waves) is considered. The governing equations are
discretized by a second-order finite volume method. Numerical results are
presented. It is shown that this basic model can be used to study violent
aerated flows, especially by providing fast qualitative estimates.Comment: 38 pages, 22 figures; CMLA research report; Other authors papers and
animations related to this work can be downloaded from:
http://www.lama.univ-savoie.fr/~dutykh
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