Maximum principle for the mass fraction in a system with two mass balance equations

Gauthier Lazare; Qingqing Feng; Philippe Helluy; Jean-Marc Hérard; Frank Hulsemann; Stéphane Pujet

doi:10.5802/crmeca.244

Article de recherche

Maximum principle for the mass fraction in a system with two mass balance equations
[Principe du maximum pour le titre massique d’un système incluant deux bilans de masse]

Gauthier Lazare ^1,² ; Qingqing Feng ¹ ; Philippe Helluy ² ; Jean-Marc Hérard ^1,³ ; Frank Hulsemann ¹ ; Stéphane Pujet ¹

¹ EDF R&D Chatou - 6 quai Waltier, 78400, Chatou, France.
² IRMA, UMR 7501, 7 rue Descartes, 67000 Strasbourg, France.
³ I2M - Institut de Mathématiques de Marseille, Aix Marseille Université, France.

Comptes Rendus. Mécanique, Volume 352 (2024), pp. 81-98.

Résumé
Abstract

Dans cette note, trois schémas Volumes Finis sont proposés pour respecter le principe du maximum du titre massique, solution d’une équation de bilan instationnaire, incluant un déséquilibre en vitesse avec une vitesse relative non nulle et un terme source. Le principe du maximum continu est d’abord étudié puis les schémas discrets linéaires implicites sont détaillés dans un cadre multi-dimensionnel non structuré.

Three Finite Volume schemes are proposed in this note to satisfy the maximum principle for the mass fraction $y$ , solution of an unsteady balance equation, including a relative velocity between phases and a source term. The continuous maximum principle is examined first. Then, linear implicit discrete schemes are detailed in a multi-dimensional and unstructured framework.

Reçu le : 2023-11-10
Révisé le : 2024-02-26
Accepté le : 2024-02-27
Publié le : 2024-04-04

DOI : 10.5802/crmeca.244

Keywords: maximum principle, Finite Volume scheme, two-phase flow, non-equilibrium velocity
Mot clés : Principe du maximum, schéma Volumes Finis, écoulement diphasique, déséquilibre en vitesse

Affiliations des auteurs :

Gauthier Lazare ^{1, 2} ; Qingqing Feng ¹ ; Philippe Helluy ² ; Jean-Marc Hérard ^{1, 3} ; Frank Hulsemann ¹ ; Stéphane Pujet ¹

¹ EDF R&D Chatou - 6 quai Waltier, 78400, Chatou, France.
² IRMA, UMR 7501, 7 rue Descartes, 67000 Strasbourg, France.
³ I2M - Institut de Mathématiques de Marseille, Aix Marseille Université, France.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Maximum principle for the mass fraction in a system with two mass balance equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {81--98},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2024},
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     language = {en},
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Gauthier Lazare; Qingqing Feng; Philippe Helluy; Jean-Marc Hérard; Frank Hulsemann; Stéphane Pujet. Maximum principle for the mass fraction in a system with two mass balance equations. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 81-98. doi : 10.5802/crmeca.244. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.244/

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