  The non-commutative theory of charge transport in mesoscopic aperiodic
systems under magnetic fields, developed by Bellissard, Shulz-Baldes and
collaborators in the 90's, is complemented with a practical numerical
implementation. The scheme, which is developed within a $C^*$-algebraic
framework, enable efficient evaluations of the non-commutative Kubo formula,
with errors that vanish exponentially fast in the thermodynamic limit.
Applications to a model of a 2-dimensional Quantum spin-Hall insulator are
given. The conductivity tensor is mapped as function of Fermi level, disorder
strength and temperature and the phase diagram in the plane of Fermi level and
disorder strength is quantitatively derived from the transport simulations.
Simulations at finite magnetic field strength are also presented.
