Picture of boy being examining by doctor at a tuberculosis sanatorium

Understanding our future through Open Access research about our past...

Strathprints makes available scholarly Open Access content by researchers in the Centre for the Social History of Health & Healthcare (CSHHH), based within the School of Humanities, and considered Scotland's leading centre for the history of health and medicine.

Research at CSHHH explores the modern world since 1800 in locations as diverse as the UK, Asia, Africa, North America, and Europe. Areas of specialism include contraception and sexuality; family health and medical services; occupational health and medicine; disability; the history of psychiatry; conflict and warfare; and, drugs, pharmaceuticals and intoxicants.

Explore the Open Access research of the Centre for the Social History of Health and Healthcare. Or explore all of Strathclyde's Open Access research...

Image: Heart of England NHS Foundation Trust. Wellcome Collection - CC-BY.

A fast spectral method for the Boltzmann equation for monatomic gas mixtures

Wu, Lei and Zhang, Jun and Reese, Jason M. and Zhang, Yonghao (2015) A fast spectral method for the Boltzmann equation for monatomic gas mixtures. Journal of Computational Physics, 298. pp. 602-621. ISSN 0021-9991

[img]
Preview
Text (Wu-etal-J-Comp-Phys-2015-A-fast-spectral-method-Boltzmann-equation-monatomic-gas-mixtures)
Wu_etal_J_Comp_Phys_2015_A_fast_spectral_method_Boltzmann_equation_monatomic_gas_mixtures.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (3MB) | Preview

Abstract

Although the fast spectral method has been established for solving the Boltzmann equation for single-species monatomic gases, its extension to gas mixtures is not easy because of the non-unitary 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- Krook-Wu solutions for the spatially-homogeneous relaxation problem, for mr up to 36. In spatially-inhomogeneous 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 two-dimensional temperature-driven 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.