An approximate method for solving rarefied and transitional flows using TDEFM with isotropic mesh adaptation

Smith, M. R., Cave, H. M., Wu, J. S. and Macrossan, M. N. (2009). An approximate method for solving rarefied and transitional flows using TDEFM with isotropic mesh adaptation. In: Takashi Abe, AIP Conference Proceedings. Rarefied gas dynamics : Proceedings of the 26th International Symposium on Rarefied Gas Dynamics : RGD26. 26th International Symposium on Rarefied Gas Dynamics, Kyoto, Japan, (371-376). 20-25 July 2008.

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Author Smith, M. R.
Cave, H. M.
Wu, J. S.
Macrossan, M. N.
Title of paper An approximate method for solving rarefied and transitional flows using TDEFM with isotropic mesh adaptation
Conference name 26th International Symposium on Rarefied Gas Dynamics
Conference location Kyoto, Japan
Conference dates 20-25 July 2008
Proceedings title AIP Conference Proceedings. Rarefied gas dynamics : Proceedings of the 26th International Symposium on Rarefied Gas Dynamics : RGD26   Check publisher's open access policy
Journal name Rarefied Gas Dynamics   Check publisher's open access policy
Place of Publication New York , U.S.A.
Publisher American Institute of Physics
Publication Year 2009
Year available 2009
Sub-type Fully published paper
DOI 10.1063/1.3076504
ISBN 9780735406155
0735406154
ISSN 0094-243X
1551-7616
1935-0465
Editor Takashi Abe
Volume 1084
Issue 1
Start page 371
End page 376
Total pages 6
Collection year 2010
Language eng
Abstract/Summary DSMC [1] can become increasingly expensive when extended to the near-continuum regime. Because of the statistical nature of the results, long run times are required to build up samples of simulator particles large enough to reduce the statistical scatter to acceptable levels. Here we adapt a kinetic theory based flux method to produce a quick approximate solver for transition and near-continuum flows. The results have no statistical scatter. The CPU times are similar to those of traditional continuum (Navier-Stokes or Euler) solvers. The True Direction Equilibrium Flux Method (TDEFM) [2, 3] is a generalisation of Pullin's kinetic theory based EFM [4]. TDEFM can transfer fluxes of mass, momentum and energy in physically realistic directions from any source cell to any destination cell, even if the cells do not share an interface. TDEFM, as an Euler solver, has been shown to provide good results on a Cartesian grid for flows where standard continuum methods produce unphysical asymmetries apparently because the continuum fluxes are constrained (in one time step) to flow in the grid coordinate directions rather than the correct physical direction. [2, 3] The new method for rarefied flow does not try to produce the correct velocity distribution function, but does ensure that mass, momentum and energy are transported within the flow over the physically correct distances between “pseudo-collisions.” To ensure this, (1) the time step is restricted so that mass, momentum and energy are exchanged between contiguous cells only in one time step, and (2) the cells sizes are adapted, as steady state is approached, to be approximately equal to the local mean free path. The results for Mach 5 flow over a flat plate for varying Knudsen numbers show an average difference (compared to DSMC) in the X-velocity profile near the surface of the plate of less than 6 percent. TDEFM, employing adaptive mesh refinement, required less than 9 percent of the computational time required by DSMC for the same flow. Thus the approximate method could be useful for quick “first-estimate” solutions of otherwise time consuming design problems. ©2009 American Institute of Physics
Subjects E1
970109 Expanding Knowledge in Engineering
880305 Space Transport
091399 Mechanical Engineering not elsewhere classified
Keyword Kinetic theory of gases
CFD
DSMC
EPSM
EFM
TDEFM
Direct simulation
Euler equations
Rarefied gas dynamics
Q-Index Code E1
Q-Index Status Confirmed Code
Additional Notes Series title: AIP conference proceedings, no. 1084.

 
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