Active liquid crystals or active gels are soft materials which can be physically realised, e.g. by preparing a solution of cytoskeletal filaments interacting with molecular motors. We study the hydrodynamics of an active liquid crystal in a slab-like geometry with various boundary conditions, by solving numerically its equations of motion via lattice Boltzmann simulations. In all cases we find that active liquid crystals can sustain spontaneous flow in steady state contrarily to their passive counterparts, and in agreement with recent theoretical predictions. We further find that conflicting anchoring conditions at the boundaries lead to spontaneous flow for any non-zero value of the 'activity' parameter, while with unfrustrated anchoring at all boundaries spontaneous flow only occurs when the activity exceeds a critical threshold. We finally discuss the dynamic pathway leading to steady state in a few selected cases. (c) 2007 Elsevier B.V. All fights reserved.