Commun. Comput. Phys.,
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Volume 4.

MHD Turbulence Studies using Lattice Boltzmann Algorithms

G. Vahala 1*, B. Keating 2, M. Soe 3, J. Yepez 4, L. Vahala 5, J. Carter 6, S. Ziegeler 7

1 Department of Physics, William and Mary, Williamsburg, VA 23185, USA.
2 Department of Physics, William and Mary, Williamsburg, VA 23185, USA; and Department of Ocean and Resources Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA.
3 Department of Mathematics and Physics, Rogers State University, Claremore, OK 74017, USA.
4 Air Force Research Laboratory, Hanscom AFB, Bedford, MA 01731, USA.
5 Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529, USA.
6 NERSC Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
7 High Performance Computing Modernization Program, Mississippi State University, MS 39762, USA.

Received 31 October 2007; Accepted (in revised version) 4 December 2007
Available online 21 April 2008


Three dimensional free-decaying MHD turbulence is simulated by lattice Boltzmann methods on a spatial grid of $8000^3$ for low and high magnetic Prandtl number. It is verified that $\nabla \cdot B = 0$ is automatically maintained to machine accuracy throughout the simulation. Isosurfaces of vorticity and current show the persistence of many large scale structures (both magnetic and velocity) for long times --- unlike the velocity isosurfaces of Navier-Stokes turbulence.

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PACS: 52.65.Kj, 52.35.Ra, 47.27.-i
Key words: Turbulence, lattice Boltzmann method, entropy, MHD.

*Corresponding author.
Email: (G. Vahala), (B. Keating), (M. Soe), (J. Yepez), (L. Vahala), (J. Carter), (S. Ziegeler)

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