The research reported is directed at developing a computational model for assessing the importance of nonlinear propagation in the near field of jet engines. In order to attain accurate results, more complete models of acoustic wave propagation are required. The goal of the current research is to develop a two-dimensional time domain solution to the Navier–Stokes equations that includes the effects of classical absorption, relative humidity, and molecular relaxation of diatomic nitrogen and oxygen. Using fluid dynamics equations from Pierce [Acoustics: An Introduction to Its Physical Principals and Applications (ASA, New York, 1989)], a system of equations is created and solved using finite difference schemes. Benchmark cases will be discussed to show that the code is capable of reproducing the physical phenomena associated with atmospheric absorption and the relative importance of the various attenuation mechanisms will be discussed. [Work supported by ONR.]