Existence analysis of a single-phase flow mixture with van der Waals pressure

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00319358" target="_blank" >RIV/68407700:21340/18:00319358 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/16M1107024" target="_blank" >http://dx.doi.org/10.1137/16M1107024</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/16M1107024" target="_blank" >10.1137/16M1107024</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence analysis of a single-phase flow mixture with van der Waals pressure

Popis výsledku v původním jazyce

The transport of single-phase fluid mixtures in porous media is described by cross- diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy’s law, and the van der Waals equation of state for mixtures. The model consists of parabolic equations with cross diffusion with a hypocoercive diffusion operator. The global-in-time existence of weak solutions in a bounded domain with equilibrium boundary conditions is proved, extending the boundedness-by-entropy method. Based on the free energy inequality, the large-time convergence of the solution to the constant equilibrium mass density is shown. For the two-species model and specific diffusion matrices, an integral inequality is proved, which reveals a minimum principle for the mass fractions. Without mass diffusion, the two-dimensional pressure is shown to converge exponentially fast to a constant. Numerical examples in one space dimension illustrate this convergence.

Název v anglickém jazyce

Existence analysis of a single-phase flow mixture with van der Waals pressure

Popis výsledku anglicky

The transport of single-phase fluid mixtures in porous media is described by cross- diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy’s law, and the van der Waals equation of state for mixtures. The model consists of parabolic equations with cross diffusion with a hypocoercive diffusion operator. The global-in-time existence of weak solutions in a bounded domain with equilibrium boundary conditions is proved, extending the boundedness-by-entropy method. Based on the free energy inequality, the large-time convergence of the solution to the constant equilibrium mass density is shown. For the two-species model and specific diffusion matrices, an integral inequality is proved, which reveals a minimum principle for the mass fractions. Without mass diffusion, the two-dimensional pressure is shown to converge exponentially fast to a constant. Numerical examples in one space dimension illustrate this convergence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

1095-7154

Svazek periodika

50

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

1367-1395

Kód UT WoS článku

000426630900043

EID výsledku v databázi Scopus

2-s2.0-85043526119