General higher order extension to the Quiet Direct Simulation method

Y. J. Lin, M. R. Smith, H. M. Cave, J. C. Huang, Jong-Shinn Wu*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Presented is the multi-dimensional extension of the Quiet Direct Simulation (QDS) method to general, higher order spatial accuracy. Due to the true directional nature of QDS, where volume-to-volume fluxes are computed as opposed to fluxes at cell interfaces, a volumetric reconstruction is required. In this approach, the conserved quantities are permitted to vary (according to a polynomial expression) across all simulated dimensions. Prior to flux computation, QDS particles are introduced using properties based on weighted moments taken over the polynomial reconstruction of conserved quantity fields. The resulting flux expressions are shown to exactly reproduce existing 2 nd order extensions (for one-dimensional flows) while providing means for true multi-dimensional reconstruction and general higher order extensions. Here we will show a typical comparison among different spatial order extensions of QDS and other WENO (5th order accurate) based numerical scheme. The extension is demonstrated up to 5th order spatial accuracy and is shown to be comparable to or more accurate than the other higher order schemes.

Original languageEnglish
Title of host publication27th International Symposium on Rarefied Gas Dynamics - 2010, RGD27
Number of pages6
EditionPART 1
StatePublished - 20 May 2011
Event27th International Symposium on Rarefied Gas Dynamics, RGD27 - Pacific Grove, CA, United States
Duration: 10 Jul 201115 Jul 2011

Publication series

NameAIP Conference Proceedings
NumberPART 1
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Conference27th International Symposium on Rarefied Gas Dynamics, RGD27
Country/TerritoryUnited States
CityPacific Grove, CA


  • CFD
  • Euler equations
  • QDS
  • The kinetic theory of gases


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