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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]
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Database: Engineering Source
Description
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]
ISSN:00219991
DOI:10.1016/j.jcp.2023.112259