  We develop an improved lattice-Boltzmann numerical scheme to solve
magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds
numbers, grounded on a manifestly Galilean covariant modeling of the
Navier-Stokes equations. The simulation of the magnetic induction equation
within the lattice-Boltzmann approach to MHD has been usually devised along the
lines of the simplest phenomenological description, the single relaxation time
(SRT) model. In order to deal with well-known stability difficulties of the SRT
framework, we introduce, alternatively, a multi-relaxation-time technique for
the solution of the magnetic induction equation, combined with a novel boundary
condition method to cope with the subtleties of magnetic Boltzmann-like
distributions on curved boundaries. As an application, we investigate open
issues related to the description of transient flow regimes in MHD pipe flows,
subject to non-uniform magnetic fields.
