publication . Preprint . 2018

Stabilization of the Lattice Boltzmann Method Using Information Theory

Wilson, Tyler L; Pugh, Mary; Dawson, Francis;
Open Access English
  • Published: 11 Jan 2018
Abstract
A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow simulations are carried out and compared to Single Relaxation Time LBM, Two Relaxation Time LBM, Multiple Relaxation Time LBM and Eherenfest Step LBM.
Subjects
arXiv: Nonlinear Sciences::Cellular Automata and Lattice GasesPhysics::Computational PhysicsComputer Science::PerformanceComputer Science::Computational Engineering, Finance, and Science
free text keywords: Physics - Computational Physics, Physics - Fluid Dynamics
Download from
73 references, page 1 of 5

[1] H. Liu, Q. Kang, C. R. Leonardi, S. Schmieschek, A. Narvaez, B. D. Jones, J. R. Williams, A. J. Valocchi, and J. Harting, Computational Geosciences 20, 1 (2015).

[2] G. R. McNamara and G. Zanetti, Physical Review Letters 61, 2332 (1988).

[3] F. J. Higuera, S. Succi, and R. Benzi, EPL (Europhysics Letters) 345, 345 (1989).

[4] F. J. Higuera and J. Jimenez, EPL (Europhysics Letters) 9, 663 (1989).

[5] S. Chen, H. Chen, D. Martnez, and W. Matthaeus, Physical Review Letters 67, 3776 (1991).

[6] R. Benzi, S. Succi, and M. Vergassola, Physics Reports 222, 145 (1992).

[7] H. Chen, S. Chen, and W. H. Matthaeus, Physical Review A 45, R5339 (1992).

[8] Y. Qian, D. D'Humieres, and P. Lallemand, EPL (Europhysics Letters) 479 (1992).

[9] J.-P. Rivet and J. P. Boon, Lattice Gas Hydrodynamics (Cambridge University Press, 2005) p. 312.

[10] B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, 2005) p. 341.

[11] X. He and L. Luo, Physical Review E 55, 6333 (1997).

[12] X. He and L.-S. Luo, Journal of Statistical Physics 88, 927 (1997).

[13] X. He and L.-S. Luo, Physical Review E 56, 6811 (1997).

[14] M. K. Banda, W. A. Yong, and A. Klar, SIAM Journal on Scienti c Computing 27, 2098 (2006).

[15] J. Sterling and S. Chen, Journal of Computational Physics 206, 196 (1996).

73 references, page 1 of 5
Any information missing or wrong?Report an Issue