TY  - JOUR
A1  - Pirner, Marlies
T1  - A review on BGK models for gas mixtures of mono and polyatomic molecules
JF  - Fluids
N2  - We consider the Bathnagar–Gross–Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisfying the same two main properties (conservation properties and entropy inequality). However, in practical applications, one often has to deal with two additional physical issues. First, a gas often does not consist of only one species, but it consists of a mixture of different species. Second, the particles can store energy not only in translational degrees of freedom but also in internal degrees of freedom such as rotations or vibrations (polyatomic molecules). Therefore, here, we will present recent BGK models for gas mixtures for mono- and polyatomic particles and the existing mathematical theory for these models.
KW  - multi-fluid mixture
KW  - kinetic model
KW  - BGK approximation
KW  - degrees of freedom in internal energy
KW  - existence of solutions
KW  - large-time behaviour
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-250161
SN  - 2311-5521
VL  - 6
IS  - 11
ER  - 
TY  - JOUR
A1  - Haack, J.
A1  - Hauck, C.
A1  - Klingenberg, C.
A1  - Pirner, M.
A1  - Warnecke, S.
T1  - A Consistent BGK Model with Velocity-Dependent Collision Frequency for Gas Mixtures
JF  - Journal of Statistical Physics
N2  - We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies. Moreover, we prove that the model satisfies an H-Theorem and characterize the form of equilibrium.
KW  - plasma physics
KW  - multi-fluid mixture
KW  - kinetic model
KW  - BGK approximation
KW  - velocity-dependent collision frequency
KW  - entropy minimization
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-269146
SN  - 1572-9613
VL  - 184
IS  - 3
ER  -