  We present a general framework to design Godunov-type schemes for
multidimensional ideal magnetohydrodynamic (MHD) systems, having the
divergence-free relation and the related properties of the magnetic field B as
built-in conditions. Our approach mostly relies on the 'Constrained Transport'
(CT) discretization technique for the magnetic field components, originally
developed for the linear induction equation, which assures div(B)=0 and its
preservation in time to within machine accuracy in a finite-volume setting. We
show that the CT formalism, when fully exploited, can be used as a general
guideline to design the reconstruction procedures of the B vector field, to
adapt standard upwind procedures for the momentum and energy equations,
avoiding the onset of numerical monopoles of O(1) size, and to formulate
approximate Riemann solvers for the induction equation. This general framework
will be named here 'Upwind Constrained Transport' (UCT). To demonstrate the
versatility of our method, we apply it to a variety of schemes, which are
finally validated numerically and compared: a novel implementation for the MHD
case of the second order Roe-type positive scheme by Liu and Lax (J. Comp.
Fluid Dynam. 5, 133, 1996), and both the second and third order versions of a
central-type MHD scheme presented by Londrillo and Del Zanna (Astrophys. J.
530, 508, 2000), where the basic UCT strategies have been first outlined.
