This paper proposes a means of simulating directional sources in Finite Difference Time Domain (FDTD) based acoustic models for impulse response (IR) calculation which, unlike other currently available methods, is able to accommodate highly irregular directivity patterns. Weighted numerical free-field IRs are applied to the simulation of first-order reflections at the boundaries of a modeled acoustic domain such that the continuing interior wave field is that which would be produced by a directional sound source. Numerical results demonstrate the application of this approach for a 2-Dimensional wave field, implementing both simple and irregular (e.g. highly directional, discontinuous) sound source directivity patterns.