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A New Equilibrium Distribution Function of the Lattice Boltzmann Method

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High Performance Computing and Applications (HPCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9576))

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Abstract

According to the conventional Maxwell distribution function, a new equilibrium distribution function based on a discrete velocity model (D2Q13) is proposed. A parallel lattice Boltzmann algorithm based on this new function is used for simulating the lid-driven cavity flow. The experimental results validate the correctness of the new equilibrium distribution function.

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References

  1. Raabe, D.: Overview of the lattice Boltzmann method for nano- and micro-scale fluid dynamics in materials science and engineering. Model. Simul. Mater. Sci. Eng. 12(6), 13–46 (2004)

    Article  Google Scholar 

  2. Tang, G., Tao, W., He, Y.: Gas slippage effect on micriscale porous flow using the lattice Boltzmann method. Phys. Rev. E 72(5), 056301 (2005)

    Article  Google Scholar 

  3. Guo, Z.L., Zhao, T.S.: Lattice Boltzmann model for incompressible flows through porous media. Phys. Rev. E 66(32B), 036301–036304 (2002)

    Google Scholar 

  4. Grunau, D., Chen, S., Eggert, K.: A lattice Boltzmann model for multiphase fluid-flows. Phys. Fluids 5(10), 2557–2562 (1993)

    Article  MATH  Google Scholar 

  5. Thömesa, G., Beckera, J., Junkb, M., Vaikuntama, A.K., Kehrwalda, D., Klarc, A., Steinera, K., Wiegmann, A.: A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. J. Comput. Phys. 228(4), 1139–1156 (2009)

    Article  MathSciNet  Google Scholar 

  6. Qu, K., Shu, C., Chew, Y.T.: Alternative method to construct equilibrium distribution functions in lattice-Boltzmann method simulation of inviscid compressible flows at high Mach number. Phys. Rev. E 75(3), 036706 (2007)

    Article  MathSciNet  Google Scholar 

  7. Alexander, F.J., Chen, S., Sterling, J.D.: Lattice Boltzmann thermodynamics. Phys. Rev. E 47(8), 2249–2252 (1993)

    Article  Google Scholar 

  8. Kataoka, T., Tsutahara, M.: Lattice Boltzmann method for the compressible Euler equations. Phys. Rev. E 69(5), 056702 (2004)

    Article  MathSciNet  Google Scholar 

  9. Cottet, G.-H., Koumoutsakos, P.: Vortex Methods: Theory and Practice. Cambridge University Press, Cambridge, England (2000)

    Book  MATH  Google Scholar 

  10. He, Y.L., Wang, Y., Li, Q.: Lattice Boltzmann Method: Theory and Applications. Science Press, Beijing (2009)

    Google Scholar 

  11. Vanka, S.P.: Block-implicit multi-grid solution of Navier-Stokes equations in primitive variables. J. Comput. Phys. 65, 138–158 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ghia, U., Ghia, K.N., Shin, C.T.: High-Re solutions for incompressible flow using the Navier-Stokes equations and a multi-grid method. J. Comput. Phys. 48(3), 387–410 (1982)

    Article  MATH  Google Scholar 

  13. Hou, S., Zou, Q., Chen, S.: Simulation of cavity flow by the lattice Boltzmann method. J. Comput. Phys. 118(2), 329–347 (1995)

    Article  MATH  Google Scholar 

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Acknowledgments

This work was supported by National Nature Science Foundation of China (No. 91330116).

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Correspondence to Wu Zhang .

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Xu, W., Liu, Z., Zhu, W., Zhang, W. (2016). A New Equilibrium Distribution Function of the Lattice Boltzmann Method. In: Xie, J., Chen, Z., Douglas, C., Zhang, W., Chen, Y. (eds) High Performance Computing and Applications. HPCA 2015. Lecture Notes in Computer Science(), vol 9576. Springer, Cham. https://doi.org/10.1007/978-3-319-32557-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-32557-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32556-9

  • Online ISBN: 978-3-319-32557-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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