A hybrid particle-continuum method applied to shock waves

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147 Scopus citations


A hybrid numerical scheme designed for hypersonic non-equilibrium flows is presented which solves the Navier-Stokes equations in regions of near-equilibrium and uses the direct simulation Monte Carlo method where the flow is in non-equilibrium. Detailed analysis of each stage of the hybrid cycle illustrates the difficulty in defining physically correct DSMC boundary conditions in regards to both macroscopic state and velocity distribution. However, results also show that DSMC boundary conditions have little effect on a previously initialized interior particle domain. A sub-relaxation technique capable of determining macroscopic, hydrodynamic properties in a DSMC simulation is used to determine low-scatter boundary conditions for the NS domain. Particle and continuum domains adapt during the hybrid simulation through application of a continuum breakdown parameter based on the gradient-length Knudsen number. The hybrid code reproduces experimental results and full DSMC simulations in half the time for a large range of 1D shock waves in argon and diatomic nitrogen gas.

Original languageEnglish (US)
Pages (from-to)402-416
Number of pages15
JournalJournal of Computational Physics
Issue number2
StatePublished - Jul 1 2006

Bibliographical note

Funding Information:
This work is sponsored by the Space Vehicle Transportation Institute, under NASA Grant NCC3-989 with joint sponsorship from the Department of Defense.


  • Direct simulation Monte Carlo
  • Hybrid particle-continuum
  • Hypersonics
  • Non-equilibrium
  • Re-entry vehicles


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