Title: Two routes from the Boltzmann equation to compressible flow of polyatomic gases

Authors: Paul J. Dellar

Addresses: Department of Mathematics, Imperial College London, London SW7 2AZ, UK

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.

Keywords: lattice Boltzmann method; discrete kinetic theory; gas dynamics; shock waves; splitting methods; compressible flow; polyatomic gases; particle velocities; simulation.

DOI: 10.1504/PCFD.2008.018081

Progress in Computational Fluid Dynamics, An International Journal, 2008 Vol.8 No.1/2/3/4, pp.84 - 96

Available online: 30 Apr 2008 *

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