Large data analysis for Kolmogorov's two-equation model of turbulence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401799" target="_blank" >RIV/00216208:11320/19:10401799 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pmfE99QZX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pmfE99QZX</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.nonrwa.2019.04.008" target="_blank" >10.1016/j.nonrwa.2019.04.008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Large data analysis for Kolmogorov's two-equation model of turbulence

Popis výsledku v původním jazyce

Kolmogorov seems to have been the first to recognize that a two-equation model of turbulence might be used as the basis of turbulent flow prediction. Nowadays, a whole hierarchy of phenomenological two-equation models of turbulence is in place. The structure of their governing equations is similar to the Navier-Stokes equations for incompressible fluids, the difference is that the viscosity is not constant but depends on two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velocity fluctuations (i.e. the turbulent energy) and the measure related to the length scales of turbulence. For these two scalar quantities two additional evolutionary convection-diffusion equations are added to the generalized Navier-Stokes system. Although Kolmogorov&apos;s model has so far been almost unnoticed, it exhibits interesting features. First of all, in contrast to other two-equation models of turbulence, there is no source term in the equation for the frequency. Consequently, nonhomogeneous Dirichlet boundary conditions for the quantities measuring the effect of turbulence are assigned to a part of the boundary. Second, the structure of the governing equations is such that one can find an &quot;equivalent&quot; reformulation of the equation for turbulent energy that eliminates the presence of the energy dissipation acting as the source in the original equation for turbulent energy and which is merely an L-1 quantity. Third, the material coefficients such as the viscosity and turbulent diffusivities may degenerate, and thus the a priori control of the derivatives of the quantities involved is unclear. We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov&apos;s two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stick-slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications. (C) 2019 Elsevier Ltd. All rights reserved.

Název v anglickém jazyce

Large data analysis for Kolmogorov's two-equation model of turbulence

Popis výsledku anglicky

Kolmogorov seems to have been the first to recognize that a two-equation model of turbulence might be used as the basis of turbulent flow prediction. Nowadays, a whole hierarchy of phenomenological two-equation models of turbulence is in place. The structure of their governing equations is similar to the Navier-Stokes equations for incompressible fluids, the difference is that the viscosity is not constant but depends on two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velocity fluctuations (i.e. the turbulent energy) and the measure related to the length scales of turbulence. For these two scalar quantities two additional evolutionary convection-diffusion equations are added to the generalized Navier-Stokes system. Although Kolmogorov&apos;s model has so far been almost unnoticed, it exhibits interesting features. First of all, in contrast to other two-equation models of turbulence, there is no source term in the equation for the frequency. Consequently, nonhomogeneous Dirichlet boundary conditions for the quantities measuring the effect of turbulence are assigned to a part of the boundary. Second, the structure of the governing equations is such that one can find an &quot;equivalent&quot; reformulation of the equation for turbulent energy that eliminates the presence of the energy dissipation acting as the source in the original equation for turbulent energy and which is merely an L-1 quantity. Third, the material coefficients such as the viscosity and turbulent diffusivities may degenerate, and thus the a priori control of the derivatives of the quantities involved is unclear. We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov&apos;s two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stick-slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications. (C) 2019 Elsevier Ltd. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamická a matematická analýza proudění strukturovaných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Nonlinear Analysis: Real World Applications

ISSN

1468-1218

e-ISSN

—

Svazek periodika

50

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

40

Strana od-do

104-143

Kód UT WoS článku

000477783900008

EID výsledku v databázi Scopus

2-s2.0-85065230859