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Simulation of Cavity Flows by an Implicit Domain Decomposition Algorithm for the Lattice Boltzmann Equations

  • Jizu Huang
  • Chao Yang
  • Xiao-Chuan Cai
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

In this paper, we develop a fully implicit finite difference scheme for the lattice Boltzmann equations. A parallel, highly scalable Newton–Krylov–RAS algorithm is presented to solve the large sparse nonlinear system of equations arising at each time step. RAS is a restricted additive Schwarz preconditioner built with a cheaper discretization. The accuracy of the proposed method is carefully studied by comparing with other benchmark solutions. We show numerically that the nonlinearly implicit method is scalable on a supercomputer with more than 10,000 processors.

Keywords

Time Step Size Cavity Flow Krylov Subspace Method Particle Distribution Function Lattice Boltzmann Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The work was supported in part by NSFC grants 61170075 and 973 grant 2011CB309701.

References

  1. 1.
    S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M. Knepley, L.C. Mcinnes, B.F. Smith, H. Zhang, PETSc Users Manual (Argonne National Laboratory, Argonne, 2013)CrossRefGoogle Scholar
  2. 2.
    R. Benzi, S. Succi, M. Vergassola, The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197 (1992)CrossRefGoogle Scholar
  3. 3.
    O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 27, 421–433 (1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    C.H. Bruneau, C. Jouron, An efficient scheme for solving steady incompressible Navier-Stokes equations. J. Comput. Phys. 89, 389–413 (1990)CrossRefzbMATHGoogle Scholar
  5. 5.
    X.-C. Cai, M. Sarkis, A restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput. 21, 792–797 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    X.-C. Cai, W.D. Gropp, D.E. Keyes, M.D. Tidriri, Newton-Krylov-Schwarz methods in CFD, in Notes in Numerical Fluid Mechanics: Proceedings of the International Workshop on the Navier-Stokes Equations, ed. by R. Rannacher. (Vieweg Verlag, Braunschweig, 1994), pp. 123–135Google Scholar
  7. 7.
    X.-C. Cai, W.D. Gropp, D.E. Keyes, R.G. Melvin, D.P. Young, Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. SIAM J. Sci. Comput. 19, 246–265 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    G.B. Deng, J. Piquet, P. Queutey, M. Visonneau, Incompressible flow calculations with a consistent physical interpolation finite volume approach. Comput. Fluids 23, 1029–1047 (1994)CrossRefzbMATHGoogle Scholar
  9. 9.
    U. Ghia, K.N. Ghia, C.T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48, 387–411 (1982)CrossRefzbMATHGoogle Scholar
  10. 10.
    Z.L. Guo, T.S. Zhao, Explicit finite-difference lattice Boltzmann method for curvilinear coordinates. Phys. Rev. E 67, 066709(12p) (2003)Google Scholar
  11. 11.
    Z.L. Guo, C.G. Zheng, B.C. Shi, Non-equilibrium extrapolation method for velocity and boundary conditions in the lattice Boltzmann method. Chin. Phys. 11(4), 0366–0374 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    P. Luchini, Higher-order difference approximations of the Navier-Stokes equations. Int. J. Numer. Methods Fluids 12, 491–506 (1991)CrossRefzbMATHGoogle Scholar
  13. 13.
    R. Mei, W. Shyy, On the finite difference-based lattice Boltzmann method in curvilinear coordinates. J. Comput. Phys. 143, 426–448 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    H.W. Xi, G. W. Peng, S.-H. Chou, Finite-volume lattice Boltzmann method. Phys. Rev. E 59, 6202–6265 (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of SoftwareChinese Academy of SciencesBeijingP.R. China
  2. 2.Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina
  3. 3.State Key Laboratory of Computer ScienceChinese Academy of SciencesBeijingP.R. China
  4. 4.Department of Computer ScienceUniversity of Colorado BoulderBoulderUSA

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