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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 ℓ 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 ℓ 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 ℓ 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 ℓ and its asymptotic...

Instability of mixed finite elements for Richards' equation

Březina, Jan (2010)

Programs and Algorithms of Numerical Mathematics

Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.

Interaction of compressible flow with an airfoil

Česenek, Jan, Feistauer, Miloslav (2010)

Programs and Algorithms of Numerical Mathematics

The paper is concerned with the numerical solution of interaction of compressible flow and a vibrating airfoil with two degrees of freedom, which can rotate around an elastic axis and oscillate in the vertical direction. Compressible flow is described by the Navier-Stokes equations written in the ALE form. This system is discretized by the semi-implicit discontinuous Galerkin finite element method (DGFEM) and coupled with the solution of ordinary differential equations describing the airfoil motion....

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