@article{Pirner2021,
  author    = {Pirner, Marlies},
  title     = {A review on BGK models for gas mixtures of mono and polyatomic molecules},
  series = {Fluids},
  volume    = {6},
  journal   = {Fluids},
  number    = {11},
  issn      = {2311-5521},
  doi       = {10.3390/fluids6110393},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-250161},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{HaackHauckKlingenbergetal.2021,
  author    = {Haack, J. and Hauck, C. and Klingenberg, C. and Pirner, M. and Warnecke, S.},
  title     = {A Consistent BGK Model with Velocity-Dependent Collision Frequency for Gas Mixtures},
  series = {Journal of Statistical Physics},
  volume    = {184},
  journal   = {Journal of Statistical Physics},
  number    = {3},
  issn      = {1572-9613},
  doi       = {10.1007/s10955-021-02821-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269146},
  pages     = {31},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}