Microscopic statistical description of incompressible Navier-Stokes granular fluids

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19240%2F17%3AA0000018" target="_blank" >RIV/47813059:19240/17:A0000018 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1140%2Fepjp%2Fi2017-11472-2" target="_blank" >https://link.springer.com/article/10.1140%2Fepjp%2Fi2017-11472-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/i2017-11472-2" target="_blank" >10.1140/epjp/i2017-11472-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Microscopic statistical description of incompressible Navier-Stokes granular fluids

Popis výsledku v původním jazyce

Based on the recently established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic 1-body PDF evolving in time by means of MMKE necessarily exhibits the phenomenon of Decay to Kinetic Equilibrium (DKE), whereby the same 1-body PDF asymptotically relaxes to a stationary and spatially uniform Maxwellian PDF.

Název v anglickém jazyce

Microscopic statistical description of incompressible Navier-Stokes granular fluids

Popis výsledku anglicky

Based on the recently established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic 1-body PDF evolving in time by means of MMKE necessarily exhibits the phenomenon of Decay to Kinetic Equilibrium (DKE), whereby the same 1-body PDF asymptotically relaxes to a stationary and spatially uniform Maxwellian PDF.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10305 - Fluids and plasma physics (including surface physics)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

European Physical Journal Plus

ISSN

2190-5444

e-ISSN

—

Svazek periodika

132

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

18

Strana od-do

'213-1'-'213-18'

Kód UT WoS článku

000400908700001

EID výsledku v databázi Scopus

2-s2.0-85019111722