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Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

Published online by Cambridge University Press:  03 June 2015

L. M. Yang ,
C. Shu  and
J. Wu
L. M. Yang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, Jiangsu, China
C. Shu*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
J. Wu
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, Jiangsu, China
*
Corresponding author. URL:http://serve.me.nus.edu.sg/shuchang/, Email: [email protected]
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Abstract

This paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.

Keywords

76T10FV-LBMnon-free parameter modelscompressible inviscid flows
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 4 , August 2012 , pp. 454 - 472
Copyright
Copyright © Global-Science Press 2012

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