Some comments on modeling the linearized Boltzmann equation

• Published in: Journal of quantitative spectroscopy & radiative transfer Vol. 77; no. 1; pp. 43 - 59
• Main Authors: Barichello, L.B, Siewert, C.E
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.02.2003
• Subjects: Boltzmann equation; Rarefied-gas dynamics; Synthetic kernels; Rarefied-gas dynamics; Synthetic kernels; Boltzmann equation
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/S0022-4073(02)00074-2

Some exact solutions of the homogeneous and the inhomogeneous linearized Boltzmann equation (LBE) for rigid-sphere collisions are used to define two model equations in the general area of rarefied-gas dynamics. These equations are obtained from a systematic development of two synthetic scattering kernels that yield model equations that have as exact solutions certain known exact solutions of the homogeneous and of the inhomogeneous LBE. The first model established is defined in terms of the collisional invariants and the Chapman–Enskog integral equations for viscosity and for heat conduction. An extended model is defined also in terms of the collisional invariants and the Chapman–Enskog functions for viscosity and heat conduction, but the first and second Burnett functions are also included in the model. The variable collision frequency or generalized BGK model is also obtained as a special case. In addition, the exact mean-free paths defined, for rigid-sphere collisions and the LBE, in terms of viscosity or heat conduction are employed to define approximations of these quantities that are consistent with the use of the variable collision frequency model.