Simulation of MHD Flows Using a Hybrid Lattice-Boltzmann Finite-Difference Method (Communications in Computational Physics, 2018)
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 fieldwhile the magnetic induction equation is solved using the finite difference method tocalculate the magnetic field. This approach is methodologically intuitive because thegoverning equations for MHD are solved in their respective original forms. In addition, the extension to 3-D is straightforward. For validation purposes, this approachwas applied to simulate the Hartmann flow, the Orszag-Tang vortex system (2-D and3-D) and the magnetic reconnection driven by doubly periodic coalescence instability. The obtained results agree well with analytical solutions and simulation resultsavailable in the literature.