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3D monolithic finite element approach for aero-thermics processes in industrial furnaces⋆

E. Hachem, E. Massoni, T. Coupez (2011)

ESAIM: Proceedings

We consider in this paper a mathematical and numerical model to design an industrial software solution able to handle real complex furnaces configurations in terms of geometries, atmospheres, parts positioning, heat generators and physical thermal phenomena. A three dimensional algorithm based on stabilized finite element methods (SFEM) for solving the momentum, energy, turbulence and radiation equations is presented. An immersed volume method (IVM) for thermal coupling of fluids and solids is introduced...

A continuity property for the inverse of Mañé's projection

Zdeněk Skalák (1998)

Applications of Mathematics

Let X be a compact subset of a separable Hilbert space H with finite fractal dimension d F ( X ) , and P 0 an orthogonal projection in H of rank greater than or equal to 2 d F ( X ) + 1 . For every δ > 0 , there exists an orthogonal projection P in H of the same rank as P 0 , which is injective when restricted to X and such that ∥ P - P 0 ∥ < δ . This result follows from Mañé’s paper. Thus the inverse ( P | X ) - 1 of the restricted mapping P | X X → P X is well defined. It is natural to ask whether there exists a universal modulus of continuity for the inverse of Mañé’s...

A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence

Cédric Galusinski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system i ∂ t E + ∇ ( ∇ . E ) - α 2 ∇ × ∇ × E = - | E | 2 σ E , where E : ℝ 3 → ℂ 3 . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the H 1 ( ℝ 3 ) norm.

Influence of waves on Lagrangian acceleration in two-dimensional turbulent flows⋆⋆⋆⋆⋆⋆

Romain Nguyen van yen, Benjamin Kadoch, Vivek Kumar, Benjamin Ménétrier, Marie Farge, Kai Schneider, Diane Douady, Lionel Guez (2011)

ESAIM: Proceedings

The Lagrangian statistics in rotating Saint-Venant turbulence are studied by means of direct numerical simulation using a pseudo-spectral discretization fully resolving, both in time and space, all the inertio-gravity waves present in the system. To understand the influence of waves, three initial conditions are considered, one which is dominated by waves, one which is dominated by vortices, and one which is intermediate between these two extreme...

Remark on regularity of weak solutions to the Navier-Stokes equations

Zdeněk Skalák, Petr Kučera (2001)

Commentationes Mathematicae Universitatis Carolinae

Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space L 2 ( 0 , T , W 1 , 3 ( 𝛺 ) 3 ) are regular.

Simulations of gravity wave induced turbulence using 512 PE Cray T3E

Joseph Prusa, Piotr Smolarkiewicz, Andrzej Wyszogrodzki (2001)

International Journal of Applied Mathematics and Computer Science

A 3D nonhydrostatic, Navier-Stokes solver has been employed to simulate gravity wave induced turbulence at mesopause altitudes. This paper extends our earlier 2D study reported in the literature to three spatial dimensions while maintaining fine resolution required to capture essential physics of the wave breaking. The calculations were performed on the 512 processor Cray T3E machine at the National Energy Research Scientific Computing Center (NERSC) in Berkeley. The physical results of this study...

Sur le temps de vie de la turbulence bidimensionnelle

Thierry Gallay, Luis Miguel Rodrigues (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

On sait que toutes les solutions de l’équation de Navier-Stokes dans R 2 dont le tourbillon est intégrable convergent lorsque t → ∞ vers un écoulement autosimilaire appelé tourbillon d’Oseen. Dans cet article, nous donnons une estimation du temps nécessaire à la solution pour atteindre un voisinage du tourbillon d’Oseen à partir d’une donnée initiale arbitraire, mais bien localisée en espace. Nous obtenons ainsi une borne supérieure sur le temps de vie de la turbulence bidimensionnelle libre, en fonction...

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