2018/06/27 by Christian Klingenberg, Klingenberg, Christian, Marlies Pirner +3
Mathematics · Physics and Astronomy · #35Q20 #35Q79 #65Z05 #82C40 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Optical properties and cooling technologies in crystalline materials
paper · pdf · doi:10.48550/arxiv.1806.11486
openalex publication_date 2018/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a multi component gas mixture with translational and internal\nenergy degrees of freedom assuming that the number of particles of each species\nremains constant. We will illustrate the derived model in the case of two\nspecies, but the model can be easily generalized to multiple species. The two\nspecies are allowed to have different degrees of freedom in internal energy and\nare modelled by a system of kinetic ES-BGK equations featuring two interaction\nterms to account for momentum and energy transfer between the species. We prove\nconsistency of our model: conservation properties, positivity of the\ntemperature, H-theorem and convergence to a global equilibrium in the form of a\nglobal Maxwell distribution. Thus, we are able to derive the usual macroscopic\nconservation laws. For numerical purposes we apply the Chu reduction to the\ndeveloped model for polyatomic gases and give an application for a gas\nconsisting of a mono atomic and a diatomic species.\n