  Nonlinear conservation laws such as the system of ideal magnetohydrodynamics
(MHD) equations may develop singularities over time. In these situations,
viscous regularization is a common approach to regain regularity of the
solution. In this paper, we present a new viscous flux to regularize the MHD
equations which holds many attractive properties. In particular, we prove that
the proposed viscous flux preserves positivity of density and internal energy,
satisfies the minimum entropy principle, is consistent with all generalized
entropies, and is Galilean and rotationally invariant. We also provide a
variation of the viscous flux that conserves angular momentum. To make the
analysis more useful for numerical schemes, the divergence of the magnetic
field is not assumed to be zero. Using continuous finite elements, we show
several numerical experiments including contact waves and magnetic
reconnection.
