We consider a multi component gas mixture with translational and internal energy degrees of freedom assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but the model can be easily generalized to multiple species. The two species are allowed to have different degrees of freedom in internal energy and are modelled by a system of kinetic ES-BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the temperature, H-theorem and convergence to a global equilibrium in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. For numerical purposes we apply the Chu reduction to the developed model for polyatomic gases and give an application for a gas consisting of a monoatomic and a diatomic species.

A consistent kinetic model for a two-component mixture of polyatomic molecules / Klingenberg, C.; Pirner, M.; Puppo, G.. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - 17:1(2019), pp. 149-173. [10.4310/cms.2019.v17.n1.a6]

A consistent kinetic model for a two-component mixture of polyatomic molecules

Puppo G.
2019

Abstract

We consider a multi component gas mixture with translational and internal energy degrees of freedom assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but the model can be easily generalized to multiple species. The two species are allowed to have different degrees of freedom in internal energy and are modelled by a system of kinetic ES-BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the temperature, H-theorem and convergence to a global equilibrium in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. For numerical purposes we apply the Chu reduction to the developed model for polyatomic gases and give an application for a gas consisting of a monoatomic and a diatomic species.
2019
ES-BGK approximation; kinetic model; multi-fluid mixture; polyatomic molecules
01 Pubblicazione su rivista::01a Articolo in rivista
A consistent kinetic model for a two-component mixture of polyatomic molecules / Klingenberg, C.; Pirner, M.; Puppo, G.. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - 17:1(2019), pp. 149-173. [10.4310/cms.2019.v17.n1.a6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1366495
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