Picture offshore wind farm

Open Access research that is improving renewable energy technology...

Strathprints makes available scholarly Open Access content by researchers across the departments of Mechanical & Aerospace Engineering (MAE), Electronic & Electrical Engineering (EEE), and Naval Architecture, Ocean & Marine Engineering (NAOME), all of which are leading research into aspects of wind energy, the control of wind turbines and wind farms.

Researchers at EEE are examining the dynamic analysis of turbines, their modelling and simulation, control system design and their optimisation, along with resource assessment and condition monitoring issues. The Energy Systems Research Unit (ESRU) within MAE is producing research to achieve significant levels of energy efficiency using new and renewable energy systems. Meanwhile, researchers at NAOME are supporting the development of offshore wind, wave and tidal-current energy to assist in the provision of diverse energy sources and economic growth in the renewable energy sector.

Explore Open Access research by EEE, MAE and NAOME on renewable energy technologies. Or explore all of Strathclyde's Open Access research...

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

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

Download (3MB) | Preview


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.