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A Review on a General Multi-Species BGK Model: Modelling, Theory and Numerics

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From Kinetic Theory to Turbulence Modeling (INdAM 2021)

Part of the book series: Springer INdAM Series ((SINDAMS,volume 51))

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Abstract

In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular, we consider an approximation of the Boltzmann equation, the Bhatnagar–Gross–Krook (BGK) equation. This equation is used in many applications because it is very efficient in numerical simulations. In this article, we recall a general BGK equation for gas mixtures which has free parameters. Specific choices of these free parameters lead to special cases in the literature. For this model, we provide an overview concerning modelling, theoretical results and numerics.

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Acknowledgement

Marlies Pirner is supported by the Alexander von Humboldt foundation.

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Authors and Affiliations

  1. Julius-Maximilians-Universität Würzburg, Würzburg, Germany

    Marlies Pirner & Sandra Warnecke

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  1. Marlies Pirner
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  2. Sandra Warnecke
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Correspondence to Marlies Pirner .

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Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Paolo Barbante

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Francesco D. Belgiorno

  3. Dipartimento di Matematica, Politecnico di Milano, MIlano, Italy

    Silvia Lorenzani

  4. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Lorenzo Valdettaro

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Pirner, M., Warnecke, S. (2023). A Review on a General Multi-Species BGK Model: Modelling, Theory and Numerics. In: Barbante, P., Belgiorno, F.D., Lorenzani, S., Valdettaro, L. (eds) From Kinetic Theory to Turbulence Modeling. INdAM 2021. Springer INdAM Series, vol 51. Springer, Singapore. https://doi.org/10.1007/978-981-19-6462-6_17

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