Numerical simulation of finite amplitude wave propagation in air using a realistic atmospheric absorption model

A nonlinear system of fluid dynamic equations is modeled that accounts for the effects of classical absorption, nitrogen and oxygen molecular relaxation, and relative humidity. Total variables rather than acoustic variables are used, which allow for the inclusion of frequency-independent terms. This system of equations is then solved in two dimensions using a fourth-order Runge-Kutta scheme in time and a dispersion-relation-preserving scheme in space. It is shown that the model accurately simulates wave steepening for propagation up to one shock formation distance. For a source amplitude of 157 dB re 20 μPa, the Fourier component amplitudes of the analytical and computed waveforms differ by 0.21% at most for the first harmonic in a lossless medium and 0.16% at most for the first harmonic in a medium that includes thermoviscous losses. It is shown that the absorption due to classical effects and molecular relaxation demonstrated by the model is within 1% of the analytical model and the computed dispersion due to molecular relaxation of nitrogen and oxygen is within 0.7% over a large frequency range. Furthermore, it is shown that the model can predict the amplification factor at a rigid boundary, which in a nonlinear system will be greater than two, to within 0.015%.