Abstract: By using the alternative-direction-implicit scheme, a two-dimensional fully nonlinear compressible atmospheric dynamic model is established, with which, the responses of the mesosphere and lower thermosphere to a localized and time-variable thermal source and a momentum forcing source in the troposphere are numerically simulated respectively. And then the energy density, the horizontal and vertical wavenumber and the frequency of the response are analyzed. The numerical results show that the response carrying the energy propagates from the troposphere and lower stratosphere upward to the mesosphere and lower thermosphere within a relatively narrow horizontal field which is symmetrical about the horizontal location of the heat source. The effect of the heat source upon the response is much stronger than that of the momentum forcing source. It is different in affecting the frequency, the horizontal wave length and the vertical wave length of the induced gravity wave. The horizontal wave length can be determined by the horizontal scale of the heat source, the frequency of the response is almost the same with the heat source with high frequency in the simulation, but the vertical wave length of the response is much larger than the vertical scale of the source. Usually, the longer the horizontal scale of the thermal source is, the larger the vertical wave length of the induced gravity wave.