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

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 totally Eulerian Finite Volume solver for multi-material fluid flows: Enhanced Natural Interface Positioning (ENIP)

28 pagesThis work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally Eulerian since the mesh is not moving and a sharp interface, separating two materials, evolves through the grid. A sliding boundary condition is enforced at the interface and mass, momentum and total energy are conserved. Although this former method performs well on 1D test cases, the interface reconstruction suffers of poor accuracy in conserving shapes for instance in linear advection. This situation leads to spurious instabilities of the interface. The method Enhanced-NIP presented in the present paper cures an inconsistency in the former NIP method that improves strikingly the results. It takes advantage of a more consistent description of the interface in the numerical scheme. Results for linear advection and compressible Euler equations for inviscid fluids are presented to assess the benefits of this new method

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

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

A two-fluid model for violent aerated flows

23 pages, 19 figures.Accepted to Computers and Fluids. Other authors publications and related animations can be downloaded at http://www.lama.univ-savoie.fr/~dutykhInternational audienceIn 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. 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 and analyze some of its properties. It is shown that this model can successfully mimic water wave impacts on coastal structures. The governing equations are discretized by a second-order finite volume method. Numerical results are presented for two examples: the dam break problem and the drop test problem. It is shown that this basic model can be used to study violent aerated flows, especially by providing fast qualitative estimates

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry.

International audienceIn this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable $\theta$), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity $u_{\theta}$