Two routes from the Boltzmann equation to compressible flow of
polyatomic gases
P. J. Dellar (2008) Two routes from the Boltzmann equation to
compressible flow of polyatomic gases Progress in
Computational Fluid Dynamics 8
84-96
Reprint available (TwoRoutesPoly.pdf
322K)
Abstract
This paper presents a systematic approach to simulating compressible
flow of polyatomic gases using the Boltzmann equation for a discrete
set of particle velocities. We derive the complete system of moment
equations needed to recover the Navier-Stokes-Fourier equations. One
may either circumvent the usual relation between pressure and internal
energy density by assigning additional energies to the particles, or
introduce an entirely separate set of particle distribution functions
to simulate the macroscopic energy equation. The latter permits the use
of longer timesteps, and may generalise more easily to multiple space
dimensions. However, the momentum and energy equations must be coupled
to obtain correct viscous heating for realistic values of the Prandtl
number. Numerical experiments are presented for the standard one
dimensional Sod shock tube benchmark for monatomic and diatomic gases
using both unified 7 velocity and split 4 + 3 velocity formulations.
@article{Dellar08poly,
Author =
{Dellar, P. J.},
Title = {Two routes from the Boltzmann equation
to compressible flow of polyatomic gases},
Journal =
{Progress in CFD},
Year = {2008},
Volume =
{8},
Pages = {94--96},
DOI = {doi:10.1504/PCFD.2008.018081},
URL = {http://www.inderscience.com/link.php?id=18081}
}