skip to main content

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

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-Lagrangianmore » method.« less
Authors:
 [1] ;  [2] ;  [2] ;  [3] ;  [1]
  1. Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640 Rhode-Saint-Genèse (Belgium)
  2. Department of Mathematics, The University of Texas at Austin, 201 E. 24th Street, Austin, TX 78712 (United States)
  3. (ICES), The University of Texas at Austin, 201 E. 24th Street, Austin, TX 78712 (United States)
Publication Date:
OSTI Identifier:
22314862
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 264; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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