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Optimization Strategies for the Entropic Lattice Boltzmann Method

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The entropic formulation of the lattice Boltzmann method (LBM) features enhanced numerical stability due to its compliance with the Boltzmann H-theorem. This stability comes at the price of some computational overhead, associated with the need of adjusting the local relaxation time of the standard LBM in such a way as to secure compliance with the H-theorem. In this paper, we discuss a number of possible optimization strategies to reduce the computational overhead of entropic LBMs.

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References

  1. Higuera F.J., Succi S., Benzi R. (1989). Lattice gas ynamics with enhanced collisions. Europhys. Lett. 9(4): 345–349

    Google Scholar 

  2. Benzi R., Succi S., Vergassola M. (1992). The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197

    Article  Google Scholar 

  3. Chen S., Chen H., Martinez D., Matthaeus W.H. (1991). Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys. Rev. Lett. 67, 3776–3779

    Article  Google Scholar 

  4. Chen H., Chen S., Matthaeus W.H. (1992). Recovery of the Navier–Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A 45, 5339–5342

    Article  Google Scholar 

  5. Qian Y.H., D’Humieres D., Lallemand P. (1992). Lattice BGK models for Navier–Stokes equation. Europhys. Lett. 17(6): 479–484

    MATH  Google Scholar 

  6. Bhatnagar P.L., Gross E.P., Krook M. (1954). A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525

    Article  MATH  Google Scholar 

  7. Succi S. (2001). The Lattice Boltzmann Equation for fluid dynamics and beyond. Oxford University Press, Claredon press, Oxford

    MATH  Google Scholar 

  8. Li Y., Shock R., Zhang R., Chen H. (2004). Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method. J. Fluid Mech. 519, 273–300

    Article  MATH  Google Scholar 

  9. Chen H., Kandasamy S., Orszag S., Shock R., Succi S., Yakhot V. (2003), Extended Boltzmann Kinetic Equation for Turbulent Flows. Science 301, 633

    Article  Google Scholar 

  10. Rothman D.H., Zaleski S. (1994). Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow. Rev. Modern Phys. 66(4): 1417–1479

    Article  Google Scholar 

  11. Chen S., Doolen G. (1998). Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30, 329–364

    Article  MathSciNet  Google Scholar 

  12. Takada N., Misawa M., Tomiyama A., Hosokawa S. (2001). Simulation of bubble motion under gravity by lattice Boltzmann method. J. Nuc. Sci. Tech. 38(5): 330

    Article  Google Scholar 

  13. He X., Li N. (2000). Lattice Boltzmann simulation of electrochemical systems. Comp. Phys.Comm. 129, 158–166

    Article  MATH  MathSciNet  Google Scholar 

  14. Watanabe T., Ebihara K. (2003). Numerical simulation of coalescence and breakup of rising droplets. Comput. Fluids 32, 823–834

    Article  MATH  Google Scholar 

  15. Ansumali S., Karlin I.V. (2000). Stabilization of the lattice Boltzmann method by the H theorem: A numerical test. Phys. Rev. E 62: 7999

    Article  Google Scholar 

  16. Boghosian B.M., Yepez J., Coveney P.V., Wagner A.J. (2001). Entropic lattice boltzmann methods. Proc. R. Soc. London, Ser. A 457, 717

    Article  MATH  MathSciNet  Google Scholar 

  17. Lallemand P., Luo L.-S. (2000). Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61: 6546

    Article  MathSciNet  Google Scholar 

  18. Ansumali S., Karlin I.V. (2002). Entropy function approach to the lattice boltzmann method. J. Stat. Phys. 107, 291–308

    Article  MATH  Google Scholar 

  19. Karlin I.V., Gorban A.N., Succi S., Boffi V. (1998), Maximum entropy principle for lattice kinetic equations. Phys. Rev. Lett. 81, 6

    Article  Google Scholar 

  20. Succi S., Karlin I., Chen H. (2002). Colloquium: role of the H-theorem in lattice Boltzmann hydrodynamic simulations. Rev. Mod. Phys. 74: 1203

    Article  Google Scholar 

  21. Ansumali, S. Minimal kinetic modelling of hydrodynamics, PhD Thesis, No 15534, ETH Zürich, 2004.

  22. Love Peter J., Boghosian Bruce M. (2004). On the dependence of the Navier Stokes equations on the distribution of molecular velocities. Phys. A 332, 47–59

    Article  MathSciNet  Google Scholar 

  23. Karlin I.V., Ferrante A., Öttinger H.C. (1999). Perfect entropy functions of the lattice boltzmann method. Europhys. Lett. 47(2): 182–188

    Article  Google Scholar 

  24. Ansumali S., Karlin I.V., Öttinger H.C. (2003) Minimal entropic kinetic models for hydrodynamics. Europhys. Lett. 63(6): 798–804

    Article  Google Scholar 

  25. Shan X., He X. (1998). Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 80, 65

    Article  Google Scholar 

  26. Ansumali S., Karlin I.V. (2002) Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 66, 1–6

    Article  MathSciNet  Google Scholar 

  27. Ansumali S., Karlin I. (2002). Single relaxation time model for entropic lattice Boltzmann methods. Phys. Rev. E 65, 056312

    Article  MathSciNet  Google Scholar 

  28. Hou S., Zou Q., Chen S., Doolen G., Cogley A.C. (1995). Simulation of cavity flow by the lattice Boltzmann method. J. Comp. Phys. 11, 329–347

    Article  Google Scholar 

  29. Botella O., Peyret R. (1998). Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids. 27, 421–433

    Article  MATH  Google Scholar 

  30. Erturk E., Corke T.C., Gökçöl C. (2005). Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Methods Fluids 48(7): 747–774

    Article  MATH  Google Scholar 

  31. Ansumali S., Karlin I.V. (2000). Stabilization of the lattice Boltzmann method by the H theorem: A numerical test. Phys. Rev. E 62(6): 7999–8003

    Article  Google Scholar 

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Correspondence to Francesca Tosi.

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Tosi, F., Ubertini, S., Succi, S. et al. Optimization Strategies for the Entropic Lattice Boltzmann Method. J Sci Comput 30, 369–387 (2007). https://doi.org/10.1007/s10915-006-9097-5

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  • DOI: https://doi.org/10.1007/s10915-006-9097-5

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