On Bgk Approximation for Reactive and Nonreactive Flows

Abstract

In the framework of recently introduced consistent Bhatnagar‐Gross‐Krook (BGK) approximations of the Boltzmann equations for both reactive and nonreactive gas mixtures, the problem of an appropriate choice of relaxation times, which represent the crucial parameters of the model, is addressed. In this first approach, BGK results are tested versus the only exact analytical solutions available in the literature for mixtures, namely the Bobylev‐Krook‐Wu (BKW) modes for space‐homogeneous inert Maxwellian molecules. Results indicate, as expected, that using the actual average collision times in the BGK equations produces a too‐fast dissipation (entropy production) with respect to the Boltzmann description, and that the best fit in that trend is obtained if such times are amplified by a suitable factor, roughly of order two in the cases run.

Keywords:

• Kinetic theory
• Gas mixtures
• BGK model
• BKW modes

Acknowledgments

This work was performed in the frame of the activities sponsored by MIUR (Project “Mathematical Problems of Kinetic Theories”), by INdAM, by GNFM, by the University of Parma (Italy), and by the European TMR Network “Hyperbolic and Kinetic Equations: Asymptotics, Numerics, Analysis.”