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Abstract
Although the fast spectral method has been established for solving the Boltzmann equation for singlespecies monatomic gases, its extension to gas mixtures is not easy because of the nonunitary mass ratio between the di↵erent molecular species. The conventional spectral method can solve the Boltzmann collision operator for binary gas mixtures but with a computational cost of the order m3rN6, where mr is the mass ratio of the heavier to the lighter species, and N is the number of frequency nodes in each frequency direction. In this paper, we propose a fast spectral method for binary mixtures of monatomic gases that has a computational cost O(pmrM2N4 logN), where M2 is the number of discrete solid angles. The algorithm is validated by comparing numerical results with analytical Bobylev
KrookWu solutions for the spatiallyhomogeneous relaxation problem, for mr up to 36. In spatiallyinhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo methods. As an application, a twodimensional temperaturedriven flow is investigated, for which other numerical methods find it difficult to resolve the flow field at large Knudsen numbers. The fast spectral method is accurate and elective in simulating highly rarefied gas flows, i.e. it captures the discontinuities and fine structures in the velocity distribution functions.
KrookWu solutions for the spatiallyhomogeneous relaxation problem, for mr up to 36. In spatiallyinhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo methods. As an application, a twodimensional temperaturedriven flow is investigated, for which other numerical methods find it difficult to resolve the flow field at large Knudsen numbers. The fast spectral method is accurate and elective in simulating highly rarefied gas flows, i.e. it captures the discontinuities and fine structures in the velocity distribution functions.
Original language  English 

Pages (fromto)  602621 
Number of pages  10 
Journal  Journal of Computational Physics 
Volume  298 
Early online date  30 Jun 2015 
DOIs  
Publication status  Published  1 Oct 2015 
Keywords
 Boltzmann equation
 gas mixtures
 Fourier spectral method
 rarefied gas dynamics
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Dive into the research topics of 'A fast spectral method for the Boltzmann equation for monatomic gas mixtures'. Together they form a unique fingerprint.Projects
 2 Finished

Multiscale Simulation of Micro and Nano Gas Flows
Zhang, Y. & Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/08/11 → 31/01/15
Project: Research

NonEquilibrium Fluid Dynamics for Micro/Nano Engineering Systems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/11 → 16/02/16
Project: Research