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Mathematical justification of a compressible bi-fluid system with different pressure laws: A semi-discrete approach and numerical illustrations.

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Title: Mathematical justification of a compressible bi-fluid system with different pressure laws: A semi-discrete approach and numerical illustrations.
Authors: Bresch, Didier1 (AUTHOR) didier.bresch@univ-smb.fr, Burtea, Cosmin2 (AUTHOR) cosmin.burtea@imj-prg.fr, Lagoutière, Frédéric1,3 (AUTHOR) lagoutiere@math.univ-lyon1.fr
Source: Journal of Computational Physics. Oct2023, Vol. 490, pN.PAG-N.PAG. 1p.
Subjects: Asymptotic homogenization, Fractions, Velocity
Abstract: In this paper we obtain a one velocity macroscopic description of a mixture of two viscous compressible fluids by homogenization/averaging. The paper is written in two parts that can be read independently one of the other. In the first part, we propose two numerical schemes respectively for a two-fluid immiscible system, (i.e. two fluids separated by sharp interfaces) and for a bifluid mixture system (diffuse interface description via volume fractions). We present various simulations that suggest that the two systems of equations describe the same mixture at different scales and, as a consequence, that averaged velocity, density and pressure of the first model match with the respective velocity, density and pressure of the second model. In a second part, we show how to mathematically formalize the previous assertion via kinetic equations verified by the Young measures associated to oscillatory solutions of the model describing the finer scale. • A justification of a semi-discrete Baer-Nunziato-type bi-fluid model is provided. • It is obtained via homogenization techniques from the Navier-Stokes system. • The mixture is thus understood as the limit of a sequence of unmixed fluids. • Numerical experiments help understand the weak convergence process. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Mathematical justification of a compressible bi-fluid system with different pressure laws: A semi-discrete approach and numerical illustrations.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Oct2023, Vol. 490, pN.PAG-N.PAG. 1p.
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  Data: In this paper we obtain a one velocity macroscopic description of a mixture of two viscous compressible fluids by homogenization/averaging. The paper is written in two parts that can be read independently one of the other. In the first part, we propose two numerical schemes respectively for a two-fluid immiscible system, (i.e. two fluids separated by sharp interfaces) and for a bifluid mixture system (diffuse interface description via volume fractions). We present various simulations that suggest that the two systems of equations describe the same mixture at different scales and, as a consequence, that averaged velocity, density and pressure of the first model match with the respective velocity, density and pressure of the second model. In a second part, we show how to mathematically formalize the previous assertion via kinetic equations verified by the Young measures associated to oscillatory solutions of the model describing the finer scale. • A justification of a semi-discrete Baer-Nunziato-type bi-fluid model is provided. • It is obtained via homogenization techniques from the Navier-Stokes system. • The mixture is thus understood as the limit of a sequence of unmixed fluids. • Numerical experiments help understand the weak convergence process. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jcp.2023.112259
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Asymptotic homogenization
        Type: general
      – SubjectFull: Fractions
        Type: general
      – SubjectFull: Velocity
        Type: general
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      – TitleFull: Mathematical justification of a compressible bi-fluid system with different pressure laws: A semi-discrete approach and numerical illustrations.
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            – D: 01
              M: 10
              Text: Oct2023
              Type: published
              Y: 2023
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              Value: 490
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