A new mixed Boltzmann-BGK model for gas mixtures
speaker: Maria Groppi (Università di Parma)abstract: Relaxation-time approximations of BGK-type for gas mixtures description constitute the most used simplified kinetic models of the Boltzmann equations, since they retain the most significant mathematical and physical features of the Boltzmann description, but are computationally more manageable. The BGK models for mixtures available in the literature may be divided into two classes, the former assuming the kinetic equation for each species governed by a unique relaxation operator 1,2, and the latter showing a sum of binary relaxation operators, preserving thus the structure of the original Boltzmann system 3. In order to preserve as much as possible the accuracy of the Boltzmann description, but with a kinetic system manageable from the computational point of view, we propose a mixed Boltzmann-BGK model for an inert gas mixture of monoatomic gases. In this setting, collisions occurring within the same species (intra-species) are modelled by Boltzmann operators, while interactions between different components (inter-species) are described by the BGK operators given in 3, that represent the relaxation model for mixtures with the closest structure to the Boltzmann one. We prove consistency of the model, in particular a Boltzmann H-Theorem holds true, prescribing convergence of solutions to equilibrium Maxwellians with all species sharing a common mean velocity and a common temperature. The structure of the model allows us to formally derive hydrodynamic equations in different collisional regimes, namely with all collisions dominant, or with only collisions within the same species playing the dominant role, the latter leading to multitemperature and multivelocity Euler and Navier Stokes equations. Some results relevant to the particular case of a two-species mixture 4 are presented. This is a joint work with M. Bisi, E. Lucchin, G. Martalò (University of Parma- Italy).
REFERENCES 1 P. Andries, K. Aoki, B. Perthame, Journal of Statistical Physics, 106, pp. 993-1018 (2002). 2 M. Bisi, M. Groppi, G. Spiga, Physical Review E, 81, 036327 (2010). 3 A. V. Bobylev, M. Bisi, M. Groppi, G. Spiga, I. F. Potapenko, Kinetic and Related Models, 11, pp. 1377-1393 (2018). 4 M. Bisi, W. Boscheri, G. Dimarco, M. Groppi, G. Martalò, Applied Mathematics and Computation, 433, 127416 (2022).
timetable:
Tue 29 Nov, 14:30 - 15:30, Sala Azzurra
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