Lattice kinetic simulations in three-dimensional magnetohydrodynamics

A lattice kinetic algorithm to simulate three-dimensional (3D) incompressible magnetohydrodynamics is presented. The fluid is monitored by a distribution function, which obeys a scalar kinetic equation, subject to an external force due to the imposed magnetic field. Following the work of Dellar [J. Comput. Phys. 179, 95 (2002)] , the magnetic field is represented by a different three-component vector distribution function, which obeys a corresponding vector kinetic equation. Discretization of the 3D phase space is based on a 19-bit scheme for the hydrodynamic part and on a 7-bit scheme for the magnetic part. Numerical results for magnetohydrodynamic (MHD) flow in a rectangular duct with insulating and conducting walls provide excellent agreement with corresponding analytical solutions. The scheme maintains in all cases tested the MHD constraint del.B=0 within machine round-off error.