Asymptotic Relaxation of Moment Equations for a Multi-species, Homogeneous BGK Model

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially nontrivial velocity distributions. Here, in this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large times.. Authors: Habbershaw, Evan [Univ. of Tennessee, Knoxville, TN (United States)]; Glasby, Ryan S. [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)]; Haack, Jeffrey Robert [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000220440885); Hauck, Cory D. [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)]; Wise, Steven M. [Univ. of Tennessee, Knoxville, TN (United States)] (ORCID:0000000338242075). DOE Contract: 89233218CNA000001; AC05-00OR22725. Subjects: 97 MATHEMATICS AND COMPUTING; kinetic theory; moment equations; multi-species BGK; rarefied gas dynamics