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Title: On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules

The high Mach number shock structure singularity arising in moment equations of the Boltzmann equation was investigated. The source of the singularity is shown to be the unbalanced treatment between two high order kinematic and dissipation terms caused by the overreach of Maxwellian molecule assumption. In compressive gaseous flow, the high order stress-strain coupling term of quadratic nature will grow far faster than the strain term, resulting in an imbalance with the linear dissipation term and eventually a blow-up singularity in high thermal nonequilibrium. On the other hand, the singularity arising from unbalanced treatment does not occur in the case of velocity shear and expansion flows, since the high order effects are cancelled under the constraint of the free-molecular asymptotic behavior. As an alternative method to achieve the balanced treatment, Eu's generalized hydrodynamics, consistent with the second law of thermodynamics, was revisited. After introducing the canonical distribution function in exponential form and applying the cumulant expansion to the explicit calculation of the dissipation term, a natural platform suitable for the balanced treatment was derived. The resulting constitutive equation with the nonlinear factor was then shown to be well-posed for all regimes, effectively removing the high Mach number shock structure singularity.
Authors:
 [1]
  1. Department of Aerospace and System Engineering and Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22256996
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 5; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; BOLTZMANN EQUATION; COUPLING; DISTRIBUTION FUNCTIONS; HYDRODYNAMICS; LIMITING VALUES; MACH NUMBER; MOLECULES; SHEAR; SINGULARITY; THERMODYNAMICS