Accurate true direction solutions to the euler equations using a uniform distribution equilibrium method

Alex Ferguson*, Matthew R. Smith, Jong-Shinn Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A novel approach for the use of multiple continuous uniform distributions for reconstruction of the Maxwell-Boltzmann equilibrium probability distribution function is used for the solution of one and two dimensional Euler equations. The Uniform distribution Equilibrium Flux Method (UEFM) is a kinetic-theory based flux solver which calculates true directional, volume to volume fluxes based on integration (over velocity space and physical space) of a sum of uniform probability distribution functions working to approximate the equilibrium distribution function. The resulting flux expressions contain only the Heaviside unit step function and do not require the evaluation of the Exponential or Error Functions. The proposed method is verified using a series of one and two dimensional benchmarks and is shown to provide a higher level of accuracy (for a given computational expense) when compared to the similar Quiet Direct Simulation (QDS) method.

Original languageAmerican English
Pages (from-to)79-100
Number of pages22
JournalCMES - Computer Modeling in Engineering and Sciences
Volume63
Issue number1
DOIs
StatePublished - 2010

Keywords

  • CFD.
  • Computational Fluid Dynamics
  • Euler Equations
  • Kinetic Theory of Gases

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