The self-action of a laser beam incident on a liquid crystal cell can cause the refracted beam to exhibit singularities in the optical wave field. We present here a self-consistent study of this phenomenon using a Finite Difference Time Domain (FDTD) solver for non-linear optical devices. The self-consistent liquid crystal director-optics FDTD method treats both the full three-dimensional spatial structures of the refracted beam and the director. This paper presents the algorithm and tests the method by examining the output from a incident Gaussian beam. We discuss quantitative differences between these results and the earlier work, and further investigate the short and long wavelength limits.