A spectral-Lagrangian Boltzmann solver for a multi-energy level gas

Journal Article · Thu May 01 04:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.01.036· OSTI ID:22314862

Munafò, Alessandro ^[1]

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1. Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640 Rhode-Saint-Genèse (Belgium)

In this paper a spectral-Lagrangian method is proposed for the full, non-linear Boltzmann equation for a multi-energy level gas typical of a hypersonic re-entry flow. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and relaxation) are accounted for. The formulation developed can also be used for the case of a gas mixture made of monatomic gases without internal energy (where only elastic collisions occur). The advantage of the spectral-Lagrangian method lies in the generality of the algorithm in use for the evaluation of the elastic and inelastic collision operators, as well as the conservation of mass, momentum and energy during collisions. The latter is realized through the solution of constrained optimization problems. The computational procedure is based on the Fourier transform of the partial elastic and inelastic collision operators and exploits the fact that these can be written as weighted convolutions in Fourier space with no restriction on the cross-section model. The feasibility of the proposed approach is demonstrated through numerical examples for both space homogeneous and in-homogeneous problems. Computational results are compared with those obtained by means of the DSMC method in order to assess the accuracy of the proposed spectral-Lagrangian method.

• OSTI ID: 22314862
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 264; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BOLTZMANN EQUATION
COMPARATIVE EVALUATIONS
CROSS SECTIONS
ENERGY LEVELS
EXCITATION
FOURIER TRANSFORMATION
GASES
LAGRANGIAN FUNCTION
MASS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
OPTIMIZATION
RELAXATION
SPACE
SUPERSONIC FLOW