Qualitative Simulation (QSIM) reasons about the behaviour of dynamic physical systems as they evolve over time. The system is represented by a coarse qualitative model rather than precise numerical models. However, for large complex domains, such as robotics for Urban Search and Rescue, existing QSIM implementations are inefficient. ASPQSIM is a novel formulation of the QSIM algorithm in Answer Set Programming that takes advantage of the similarities between qualitative simulation and constraint satisfaction problems. ASPQSIM is compared against an existing QSIM implementation on a variety of domains that demonstrate ASPQSIM provides a significant improvement in efficiency especially on complex domains, and producing simulations in domains that are not solvable by the procedural implementation.