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A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows

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Post-edited
Auteurs : Furfaro, Damien (Auteur de la Conférence)
CIRM (Editeur )

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two-phase flow model the discrete equations method basis two-phase flow model rewriting locally constant interfacial variables local conservative formulation two-phase Riemann problem solver entropy preserving Godunov type scheme
Résumé : A simple, robust and accurate HLLC-type Riemann solver for two-phase 7-equation type models is built. It involves 4 waves per phase, i.e. the three conventional right- and left-facing and contact waves, augmented by an extra "interfacial" wave. Inspired by the Discrete Equations Method (Abgrall and Saurel, 2003), this wave speed $u_I$ is assumed function only of the piecewise constant initial data. Therefore it is computed easily from these initial data. The same is done for the interfacial pressure $P_I$. Interfacial variables $u_I$ and $P_I$ are thus local constants in the Riemann problem. Thanks to this property there is no difficulty to express the non-conservative system of partial differential equations in local conservative form. With the conventional HLLC wave speed estimates and the extra interfacial speed $u_I$, the four-waves Riemann problem for each phase is solved following the same strategy as in Toro et al. (1994) for the Euler equations. As $u_I$ and $P_I$ are functions only of the Riemann problem initial data, the two-phase Riemann problem consists in two independent Riemann problems with 4 waves only. Moreover, it is shown that these solvers are entropy producing. The method is easy to code and very robust. Its accuracy is validated against exact solutions as well as experimental data.

Codes MSC :
76Mxx - Basic methods in fluid mechanics, See also {65-XX}
 76TXX - Two-phase and multiphase flows
    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 26/08/14
    Date de captation : 21/08/14
    Sous collection : Research talks
    arXiv category : Mathematical Physics
    Domaine : Mathematical Physics
    Format : QuickTime (.mov) Durée : 00:45:05
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2014-08-21_Furfaro.mp4
Informations sur la Rencontre

Nom de la rencontre : CEMRACS : Numerical modeling of plasmas / CEMRACS : Modèles numériques des plasmas
Organisateurs de la rencontre : Campos Pinto, Martin ; Charles, Frédérique ; Guillard, Hervé ; Nkonga, Boniface
Dates : 21/07/14 - 29/08/14
Année de la rencontre : 2014
URL Congrès : http://smai.emath.fr/cemracs/cemracs14/

Données de citation

DOI : 10.24350/CIRM.V.18557003
Citer cette vidéo: Furfaro, Damien (2014). A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18557003
URI : http://dx.doi.org/10.24350/CIRM.V.18557003

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