We present a compressible gasdynamic numerical model that utilizes a three-dimensional adaptive grid to provide high spatial resolution of an expanding compression wave. We apply this model to recent explosions of Popocatepetl volcano in Mexico by incorporating both high resolution topography for a lower boundary and atmospheric stratification based upon climatological thermodynamic soundings. Explosions are simulated by the instantaneous release of an overpressure in a prescribed volume over the volcano's crater. The results show a compression wave that propagates as a supersonic shock close to the explosion, transforming into a sonic compression wave at larger distances. We validate the model predictions by comparing them to pressure-time series measured by a microbarograph located 11 km away from the crater. With the model validation we estimate the equivalent initial internal energy of the explosions to range from 2 × 10¹³ J to 1.1 × 10¹⁵ J.