Commun. Comput. Phys.,
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Volume 4.


Simulation of MHD Flows Using a Hybrid Lattice-Boltzmann Finite-Difference Method

Huayu Li 1, Hyungson Ki 1*

1 Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA.

Received 26 June 2007; Accepted (in revised version) 8 December 2007
Available online 18 March 2008

Abstract

A hybrid lattice-Boltzmann finite-difference method is presented to simulate incompressible, resistive magnetohydrodynamic (MHD) flows. The lattice Boltzmann equation (LBE) with the Lorentz force term is solved to update the flow field while the magnetic induction equation is solved using the finite difference method to calculate the magnetic field. This approach is methodologically intuitive because the governing equations for MHD are solved in their respective original forms. In addition, the extension to $3$-$D$ is straightforward. For validation purposes, this approach was applied to simulate the Hartmann flow, the Orszag-Tang vortex system ($2$-$D$ and $3$-$D$) and the magnetic reconnection driven by doubly periodic coalescence instability. The obtained results agree well with analytical solutions and simulation results available in the literature.


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PACS: 47.11.-j, 47.65.-d
Key words: Lattice Boltzmann method, LBM, hybrid, finite difference method, Magnetohydrodynamics, MHD.

*Corresponding author.
Email: lihuayu@egr.msu.edu (H. Li), hski@msu.edu (H. Ki)
 

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