Abstract: By using the spectral allocation method, a fully-nonlinear dynamical numerical model for the propagation of disturbance in the mesosphere is found. Applying the newly founded numerical model, the evolution and propagation of an initially given Gassian wave-like temperature disturbance in a compressible atmosphere were simulated. The simulation results show that the temperature disturbance excites two gravity-wave packets soon, one propagates upward and another propagates downward. The energy propagation paths of these two packets are slightly different from the ray paths predicted by the linear theory. A further numerical analysis indicates that after 3 hours' evolution of the initially given temperature disturbance, the disturbance converts entirely to wave motion, and during the conversion, only 79% disturbance energy is converted to be wave-associated energy.