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Investigation of nonequilibrium effects across normal shock waves by means of a spectral-Lagrangian Boltzmann solver

par Munafò, Alessandro;Torres, Erik Matthias ;Haack, Jeffrey;Gamba, Irene;Magin, Thierry
Référence 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition(51: 2013-01-07), American Institute of Aeronautics and Astronautics Inc
Publication Publié, 2013

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Résumé :

A spectral-Lagrangian deterministic solver for the Boltzmann equation for rarefied gas flows is proposed. Numerical solutions are obtained for the flow across normal shock waves of pure gases and mixtures by means of a time-marching method. Operator splitting is used. The solution update is obtained as a combination of the operators for the advection (or transport) and homogeneous (or collision) problems. For the advection problem, the Finite volume method is considered. For the homogeneous problem, a spectral-Lagrangian numerical method is used. The latter is based on the weak form of the collision operator and can be used with any type of cross-section model. The conservation of mass, momentum and energy during collisions is enforced through the solution of a constrained optimization problem. Numerical results are compared with those obtained by means of the DSMC method. Very good agreement is found for the whole range of free-stream Mach numbers being considered. For the pure gas case, a comparison with experimentally acquired density profiles is also performed, allowing for a validation of the spectral-Lagrangian solver.