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.
Similar content being viewed by others
References
Higuera F.J., Succi S., Benzi R. (1989). Lattice gas ynamics with enhanced collisions. Europhys. Lett. 9(4): 345–349
Benzi R., Succi S., Vergassola M. (1992). The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197
Chen S., Chen H., Martinez D., Matthaeus W.H. (1991). Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys. Rev. Lett. 67, 3776–3779
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
Qian Y.H., D’Humieres D., Lallemand P. (1992). Lattice BGK models for Navier–Stokes equation. Europhys. Lett. 17(6): 479–484
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
Succi S. (2001). The Lattice Boltzmann Equation for fluid dynamics and beyond. Oxford University Press, Claredon press, Oxford
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
Chen H., Kandasamy S., Orszag S., Shock R., Succi S., Yakhot V. (2003), Extended Boltzmann Kinetic Equation for Turbulent Flows. Science 301, 633
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
Chen S., Doolen G. (1998). Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30, 329–364
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
He X., Li N. (2000). Lattice Boltzmann simulation of electrochemical systems. Comp. Phys.Comm. 129, 158–166
Watanabe T., Ebihara K. (2003). Numerical simulation of coalescence and breakup of rising droplets. Comput. Fluids 32, 823–834
Ansumali S., Karlin I.V. (2000). Stabilization of the lattice Boltzmann method by the H theorem: A numerical test. Phys. Rev. E 62: 7999
Boghosian B.M., Yepez J., Coveney P.V., Wagner A.J. (2001). Entropic lattice boltzmann methods. Proc. R. Soc. London, Ser. A 457, 717
Lallemand P., Luo L.-S. (2000). Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61: 6546
Ansumali S., Karlin I.V. (2002). Entropy function approach to the lattice boltzmann method. J. Stat. Phys. 107, 291–308
Karlin I.V., Gorban A.N., Succi S., Boffi V. (1998), Maximum entropy principle for lattice kinetic equations. Phys. Rev. Lett. 81, 6
Succi S., Karlin I., Chen H. (2002). Colloquium: role of the H-theorem in lattice Boltzmann hydrodynamic simulations. Rev. Mod. Phys. 74: 1203
Ansumali, S. Minimal kinetic modelling of hydrodynamics, PhD Thesis, No 15534, ETH Zürich, 2004.
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
Karlin I.V., Ferrante A., Öttinger H.C. (1999). Perfect entropy functions of the lattice boltzmann method. Europhys. Lett. 47(2): 182–188
Ansumali S., Karlin I.V., Öttinger H.C. (2003) Minimal entropic kinetic models for hydrodynamics. Europhys. Lett. 63(6): 798–804
Shan X., He X. (1998). Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 80, 65
Ansumali S., Karlin I.V. (2002) Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 66, 1–6
Ansumali S., Karlin I. (2002). Single relaxation time model for entropic lattice Boltzmann methods. Phys. Rev. E 65, 056312
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
Botella O., Peyret R. (1998). Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids. 27, 421–433
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
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10915-006-9097-5