Rarefied hypersonic flow simulations using the Navier-Stokes equations with non-equilibrium boundary conditions

Christopher J. Greenshields, Jason M. Reese*

*Corresponding author for this work

Research output: Contribution to journalLiterature reviewpeer-review


This paper investigates the use of Navier-Stokes-Fourier equations with non-equilibrium boundary conditions (BCs) for simulation of rarefied hypersonic flows. It revisits a largely forgotten derivation of velocity slip and temperature jump by Patterson, based on Grad's moment method. Mach 10 flow around a cylinder and Mach 12.7 flow over a flat plate are simulated using both computational fluid dynamics using the temperature jump BCs of Patterson and Smoluchowski and the direct simulation Monte-Carlo (DSMC) method. These flows exhibit such strongly non-equilibrium behaviour that, following Patterson's analysis, they are strictly beyond the range of applicability of the BCs. Nevertheless, the results using Patterson's temperature jump BC compare quite well with the DSMC and are consistently better than those using the standard Smoluchowski temperature jump BC. One explanation for this better performance is that an assumption made by Patterson, based on the flow being only slightly non-equilibrium, introduces an additional constraint to the resulting BC model in the case of highly non-equilibrium flows.

Original languageEnglish
Pages (from-to)80-87
Number of pages8
JournalProgress in Aerospace Sciences
Publication statusPublished - Jul 2012


  • high-speed flow
  • thermodynamic non-equilibrium
  • boundary conditions
  • compressible flows
  • numerical simulation
  • rarefied gas dynamics
  • temperature jump
  • velocity slip
  • aerodynamics
  • hypersonics
  • supersonic flow
  • kinetic theory
  • extended hydrodynamics
  • Knudsen number


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