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

M. R. Smith, H. M. Cave, Jong-Shinn Wu, M. N. Macrossan

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


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.

Original languageAmerican English
Pages (from-to)371-376
Number of pages6
JournalAIP Conference Proceedings
StatePublished - 13 Apr 2009
Event26th International Symposium on Rarefied Gas Dynamics, RGD26 - Kyoto, Japan
Duration: 20 Jul 200825 Jul 2008


  • CFD
  • DSMC
  • Direct simulation
  • EFM
  • EPSM
  • Euler equations
  • Kinetic Theory of Gasses
  • Rarefied gas dynamics


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