  A numerical method, suitable for the simulation of the time evolution of
quantum spin models of arbitrary lattice dimension, is presented. The method
combines sampling of the Wigner function with evolution equations obtained from
the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Going to higher
orders of the BBGKY hierarchy allows for a systematic refinement of the method.
Quantum correlations are treated through both, the Wigner function sampling and
the BBGKY evolution, bringing about highly accurate estimates of correlation
functions. The method is particularly suitable for long-range interacting
systems, and we demonstrate its power by comparing with exact results as well
as other numerical methods. As an application we compute spin squeezing in a
two-dimensional lattice with power-law interactions and a transverse field,
which should be accessible in future ion trap experiments.
