A two-dimensional nonlinear numerical model has been developed to study atmospheric coupling due to vertically propagating Gravity Waves (GWs) on different planets. The model is able to simulate both acoustic and gravity waves due to inclusion of compressibility. The model also considers dissipative effects due to viscosity, conduction and radiative damping. The hyperbolic inviscid advection equations are solved using the Lax-Wendroff method. The parabolic diffusion terms are solved implicitly using a linear algebra-based Direct method. The model is validated by comparing numerical solutions against analytical results for linear propagation, critical level absorption and breaking. A case study of tsunami-generated GWs is presented for the 2004 Sumatra earthquake whereby the model is forced through tsunamigenic sea-surface displacement. The properties of simulated GWs closely match those derived from ionospheric sounding observations reported in literature. Another application for Martian ice cloud formation is discussed where GWs from topographic sources are shown to create cold pockets with temperatures below the CO2 condensation threshold. The simulated cold pockets coincide with the cloud echo observations from the Mars Orbiting Laser Altimeter (MOLA) aboard Mars Global Survey (MGS) spacecraft.