Abstract
Lattice Boltzmann Method (LBM) is a novel numerical method for flows simulations. Compared with classic methods of Finite Difference Method, Finite Volume Method and Finite Element Method, LBM has numerous advantages, including inherent parallelization and simplicity of boundary condition treatment. The LBM usually has a constraint of incompressible fluid (Mach number less than 0.4). A variant of the LBM is studied and used to deal with compressible fluid with Mach number up to 0.9 in this paper. Special emphasis is placed on mesh generation of 3-D complete geometry in Cartesian coordinate system. Numerical experiments are fulfilled in 2-D and 3-D compressible flows. Performance evaluation of the algorithm demonstrates high parallel efficiency and prefect scalability. Numerical results indicate that the LBM is successful with the simulation of compressible fluid.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Qian, Y.H., d’Humieres, D., Lallemand, P.: Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17, 479 (1992)
Alexander, F.J., Chen, H., Doolen, G.D.: Lattice Boltzmann model for compressible fluids. Phys. Rev. A 46(4), 1967–1970 (1992)
Alexander, F., Chen, H., Chen, S., et al.: Lattice Boltzmann model for compressible fluids. Physical Review A 46(4), 1967–1970 (1992)
Yu, H., Zhao, K.: Lattice Boltzmann method for compressible flows with high Mach numbers. Physical Review E 61(4), 3867–3870 (2000)
Palmer, B., Rector, D.: Lattice Boltzmann algorithm for simulating thermal flow in compressible fluids. J. Comput. Phys. 161(1), 1–20 (2000)
He, X., Chen, S., Doolen, G.D.: A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit. Journal of Computational Physics 146(1), 282–300 (1998)
Qu, K., Shu, C., Chew, Y.: Alternative method to construct equilibrium distribution functions in lattice-Boltzmann method simulation of inviscid compressible flows at high Mach number. Physical Review EÂ 75(3), 036706 (2007)
Li, Q., He, Y., Wang, Y., et al.: Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 76(5), 056705–056735 (2007)
Sun, C., Hsu, A.: Multi-level lattice Boltzmann model on square lattice for compressible flows. Computers and Fluids 33(10), 1363–1385 (2004)
Yan, G., Zhang, J., Liu, Y., et al.: A multi-energy-level lattice Boltzmann model for the compressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 55(1), 41–56 (2007)
Shan, X., Yuan, X.F., Chen, H.: Kinetic theory representation of hydrodynamics: A way beyond the Navier-Stokes equation. Journal of Fluid Mechanics 550, 413–441 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feng, W., He, B., Song, A., Wang, Y., Zhang, M., Zhang, W. (2010). Compressible Lattice Boltzmann Method and Applications. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11842-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-11842-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11841-8
Online ISBN: 978-3-642-11842-5
eBook Packages: Computer ScienceComputer Science (R0)