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Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol, Francisco Ortegón Gallego (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity A ( θ , ϕ ) and nonlinear source terms of the form θ 2 | u | 2 and θ ϕ | u | 2 lying in L1. Some existence results are shown in this paper, including L -estimates and positivity for both θ and φ.

Dense Granular Poiseuille Flow

E. Khain (2011)

Mathematical Modelling of Natural Phenomena

We consider a dense granular shear flow in a two-dimensional system. Granular systems (composed of a large number of macroscopic particles) are far from equilibrium due to inelastic collisions between particles: an external driving is needed to maintain the motion of particles. Theoretical description of driven granular media is especially challenging for dense granular flows. This paper focuses on a gravity-driven dense granular Poiseuille flow...

Different boundary conditions for LES solver Palm 6.0 used for ABL in tunnel experiment

Řezníček, Hynek, Geletič, Jan, Bureš, Martin, Krč, Pavel, Resler, Jaroslav, Vrbová, Kateřina, Trush, Arsenii, Michálek, Petr, Beneš, Luděk, Sühring, Matthias (2023)

Programs and Algorithms of Numerical Mathematics

We tried to reproduce results measured in the wind tunnel experiment with a CFD simulation provided by numerical model PALM. A realistic buildings layout from the Prague-Dejvice quarter has been chosen as a testing domain because solid validation campaign for PALM simulation of Atmospheric Boundary Layer (ABL) over this quarter was documented in the past. The question of input data needed for such simulation and capability of the model to capture correctly the inlet profile and its turbulence structure...

Dissipation d’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles

Jean Duchon, Raoul Robert (1999/2000)

Séminaire Équations aux dérivées partielles

On étudie l’équation locale de l’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles tridimensionnelles. On explicite un terme de dissipation provenant de l’éventuel défaut de régularité de la solution. On donne au passage une preuve simple de la conjecture d’Onsager, améliorant un peu l’hypothèse de [1]. On propose une notion de solution dissipative pour de telles solutions faibles.

Dissipative Euler flows and Onsager's conjecture

Camillo De Lellis, László Székelyhidi (2014)

Journal of the European Mathematical Society

Building upon the techniques introduced in [15], for any θ < 1 10 we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent θ . A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent θ < 1 3 . Our theorem is the first result in this direction.

Estimate of vegetation efficiency on reducing dust concentration produced by a surface coal mine

Řezníček, Hynek, Beneš, Luděk (2019)

Programs and Algorithms of Numerical Mathematics

A new vegetative barrier can help to reduce dust concentration in a surface coal mine neighbourhood. The project reports about quantification of this effect. An air flow field is computed together with the dust transport driven by it using an in-house CFD solver. The 2D cuts of a real geometry of Bílina coal mine in north Bohemia are used. The vegetation is modelled as horizontally homogeneous porous medium which slows the air flow inside. An influence on turbulence and filtering the dust particles...

Finite element approximations for the stationary large eddy simulation model

Andrzej Warzyński (2010)

Applicationes Mathematicae

Some approximation procedures are presented for the system of equations arising from the large eddy simulation of turbulent flows. Existence of solutions to the approximate problems is proved. Discrete solutions generate a strongly convergent subsequence whose limit is a weak solution of the original problem. To prove the convergence theorem we use Young measures and related tools. We do not limit ourselves to divergence-free functions and our results are in particular valid for finite element approximations...

Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions

Piotr Szopa (2007)

Applicationes Mathematicae

This paper is devoted to proving the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate their number. We check how the distribution of the forces and moments through modes influences the estimate of the number of determining modes. We also estimate the dimension of the global attractor. Finally, we compare our results with analogous results for the Navier-Stokes equation.

Hydromagnetic stability of stratified shear flows in the presence of cross flow

Naresh Kumar Dua, Hari Kishan, Ruchi Goel (2011)

Annales Polonici Mathematici

The hydromagnetic stability of stratified shear flows in the presence of cross flows is discussed. The magnetic field is applied in the direction of the main flow. Some necessary conditions of instability, the growth rate of unstable modes and reduction of the unstable region are discussed.

Impact of the variations of the mixing length in a first order turbulent closure system

Françoise Brossier, Roger Lewandowski (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity ν t . The mixing length acts as a parameter which controls the turbulent part in ν t . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...

Impact of the variations of the mixing length in a first order turbulent closure system

Françoise Brossier, Roger Lewandowski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity  ν t . The mixing length acts as a parameter which controls the turbulent part in ν t . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...

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