  We present a numerical scheme to solve the Wigner equation, based on a
lattice discretization of momentum space. The moments of the Wigner function
are recovered exactly, up to the desired order given by the number of discrete
momenta retained in the discretisation, which also determines the accuracy of
the method. The Wigner equation is equipped with an additional collision
operator, designed in such a way as to ensure numerical stability without
affecting the evolution of the relevant moments of the Wigner function. The
lattice Wigner scheme is validated for the case of quantum harmonic and
anharmonic potentials, showing good agreement with theoretical results. It is
further applied to the study of the transport properties of one and two
dimensional open quantum systems with potential barriers. Finally, the
computational viability of the scheme for the case of three- dimensional open
systems is also illustrated.
