A new 2-D time-dependent model is used to simulate the propagation of an acoustic-gravity wave packet in the atmosphere. A Gaussian tropospheric heat source is assumed with a forcing period of 6.276 minutes. The atmospheric thermal structure creates three discrete wave ducts in the stratosphere, mesosphere, and lower thermosphere, respectively. The horizontally averaged vertical energy flux is derived over altitude and time in order to examine the time-resolved ducting. This ducting is characterized by alternating upward and downward energy fluxes within a particular duct, which clearly show the reflections occurring from the duct boundaries. These ducting simulations are the first that resolve the time-dependent vertical energy flux. They suggest that when ducted gravity waves are observed in the mesosphere they may also be observable at greater distances in the stratosphere.