In organic photovoltaic (OPV) systems, exciton dissociation and ultrafast charge separation at donor-acceptor heterojunctions both play a key role in controlling the efficiency of the conversion of excitation energy into free charge carriers. In this work, nonadiabatic dynamics simulations based on the quantum-classical Liouville equation are employed to study the real-time dynamics of exciton dissociation and charge separation at a model donor-acceptor interface. Benchmark comparisons for a variety of low dimensional donor-acceptor chain models are performed to assess the accuracy of the quantum classical dynamics technique referred to as the forward-backward trajectory solution (FBTS). Although not always quantitative, the FBTS approach offers a reasonable balance between accuracy and computational cost. The short-time dynamics of exciton dissociation in related higher-dimensional lattice models for the interface are also investigated to assess the effect of the dimensionality on the first steps in the mechanism of charge carrier generation.