Lattice Boltzmann magnetohydrodynamics

Journal Article · Wed Jun 01 04:00:00 EDT 1994 · Physics of Plasmas; (United States)

DOI:https://doi.org/10.1063/1.870640· OSTI ID:7270288

Martinez, D O ^[1]; Chen, S ^[2]; Matthaeus, W H ^[1]

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1. Bartol Research Institute, University of Delaware, Newark, Delaware 19716 (United States)
2. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

Lattice gas and lattice Boltzmann methods are recently developed numerical schemes for simulating a variety of physical systems. In this paper a new lattice Boltzmann model for modeling two-dimensional (2-D) incompressible magnetohydrodynamics (MHD) is presented. The current model fully utilizes the flexibility of the lattice Boltzmann method in comparison with previous lattice gas and lattice Boltzmann MHD models, reducing the number of moving directions from 36 in other models to 12 only. To increase computational efficiency, a simple single time relaxation rule is used for collisions, which directly controls the transport coefficients. The bidirectional streaming process of the particle distribution function in this paper is similar to the original model [H. Chen and W. H. Matthaeus, Phys. Rev. Lett. [bold 58], 1845 (1987), S. Chen [ital et] [ital al]., Phys. Rev. Lett. [bold 67], 3776 (1991)], but has been greatly simplified, affording simpler implementation of boundary conditions and increasing the feasibility of extension into a workable three-dimensional (3-D) model. Analytical expressions for the transport coefficients are presented. Also, as example cases, numerical calculation for the Hartmann flow is performed, showing a good agreement between the theoretical prediction and numerical simulation, and a sheet-pinch simulation is performed and compared with the results obtained with a spectral method.

• OSTI ID: 7270288
• Journal Information: Physics of Plasmas; (United States), Journal Name: Physics of Plasmas; (United States) Vol. 1:6; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330 -- Plasma Kinetics
Transport
& Impurities-- (1992-)
700370* -- Plasma Fluid & MHD Properties-- (1992-)
BOLTZMANN EQUATION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
FLUID MECHANICS
FUNCTIONS
HYDRODYNAMICS
MAGNETOHYDRODYNAMICS
MECHANICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA SIMULATION
SIMULATION
TRANSPORT THEORY