Boltzmann collision operator for polyatomic gases in agreement with experimental data and DSMC method

Continuum Mechanics and Thermodynamics, vol. 35, pp. 103–119

Abstract

Abstract This paper is concerned with the Boltzmann equation based on a continuous internal energy variable to model polyatomic gases with constant specific heats. We propose a family of models for the collision kernel and evaluate the nonlinear Boltzmann collision operator to get explicit expressions for transport coefficients like shear and bulk viscosities, thermal conductivity, depending on the collision kernel parameters. This model is shown to contain as a special case the collision kernel used in the direct simulation Monte Carlo method with the variable hard sphere cross section. Then, we show that it is possible to choose parameters in such a way that we recover various physical phenomena, in particular, experimental data for the shear viscosity, Prandtl number and the ratio of bulk and shear viscosities at the same time.

Authors 4

1. Vladimir Djordjić corresponding Aachen Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Applied and Computational Mathematics, RWTH Aachen University, Schinkelstr. 2, 52062, Aachen, Germany

2. Georgii Oblapenko

   Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

   Affiliation as printed

   German Aerospace Center (DLR), Bunsenstrasse 10, 37073, Göttingen, Germany

3. Milana Pavić‐Čolić

   University of Novi Sad

   Affiliation as printed

   Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000, Serbia

4. Manuel Torrilhon Aachen Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Applied and Computational Mathematics, RWTH Aachen University, Schinkelstr. 2, 52062, Aachen, Germany