Title: Non-uniform grid Lattice Boltzmann simulations of 1-D dissipative magnetohydrodynamics

Authors: Angus I.D. Macnab, George Vahala, Linda Vahala

Addresses: Center for Scientific Computation and Mathematical Modelling, University of Maryland, 4119 CSIC Building 406, College Park, MD, USA. ' Department of Physics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187, USA. ' Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529, USA

Abstract: Lattice Boltzmann methods (LBMs) provide a kinetic simulation technique for solving systems governed by non-linear conservation equations. Most LBMs use the linearised single time relaxation form of the Boltzmann equation to temporally evolve particle distribution functions on a discrete spatial lattice. These kinetic simulation techniques are computationally efficient and highly parallelisable. The use of non-uniform distributions of the spatial grid further enhances the computational efficiency of these algorithms by focusing computational effort around structures of interest such as velocity shocks and current sheets. Here, we apply a non-uniform grid LBM to one-dimensional magnetohydrodynamic systems. Simulations are presented for three sets of initial conditions in order to analyse the effects of the presence of the magnetic induction equation and compare the results to Burger|s turbulence.

Keywords: Lattice Boltzmann method; 1-D magnetohydrodynamics; resistive magnetohydrodynamics; non-uniform grids; Lattice B.G.K equation; simulation; turbulence; Lattice Boltzmann equation; Lattice Boltzmann model.

DOI: 10.1504/PCFD.2005.005816

Progress in Computational Fluid Dynamics, An International Journal, 2005 Vol.5 No.1/2, pp.37 - 49

Published online: 08 Dec 2004 *

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