Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441256" target="_blank" >RIV/00216208:11320/21:10441256 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cQlilzT31R" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cQlilzT31R</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218202521500391" target="_blank" >10.1142/S0218202521500391</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
Popis výsledku v původním jazyce
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is decreasing with a certain rate, the rescaled velocity and pressure of the microscopic system converges to the solution of an effective equation which is given by Darcy's law. The range of sizes of particles we consider is exactly the same which leads to Darcy's law in the homogenization limit of incompressible fluids. Unlike previous results for the Darcy regime we estimate the deficit related to the pressure approximation via the Bogovskii operator. This allows for more flexible estimates of the pressure in Lebesgue and Sobolev spaces and allows to proof convergence results for all barotropic exponents gamma > 3/2.
Název v anglickém jazyce
Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
Popis výsledku anglicky
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is decreasing with a certain rate, the rescaled velocity and pressure of the microscopic system converges to the solution of an effective equation which is given by Darcy's law. The range of sizes of particles we consider is exactly the same which leads to Darcy's law in the homogenization limit of incompressible fluids. Unlike previous results for the Darcy regime we estimate the deficit related to the pressure approximation via the Bogovskii operator. This allows for more flexible estimates of the pressure in Lebesgue and Sobolev spaces and allows to proof convergence results for all barotropic exponents gamma > 3/2.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2021
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Mathematical Models and Methods in Applied Sciences
ISSN
0218-2025
e-ISSN
—
Svazek periodika
31
Číslo periodika v rámci svazku
09
Stát vydavatele periodika
SG - Singapurská republika
Počet stran výsledku
33
Strana od-do
1787-1819
Kód UT WoS článku
000698444200003
EID výsledku v databázi Scopus
2-s2.0-85112640168