Study of a variable step network and comparison between the radii method and the parabolic equations, applied to the acoustic propagation in the atmosphere

A variable step network for solving the parabolic equation using the finite element method is developed. The convergence of the network is investigated. It is shown that one calculation step, which variates in a parabolic way with the propagation distance, improves the calculation time by a factor of five, when compared to a fixed step. Moreover, the error of discretization is not increased. The results obtained with the radii and the parabolic methods are compared. The presence of low wind and low pressure gradients are considered. Similar results are given by both methods in the range of 100 to 1000 Hz and in a propagation distance of about 100 m.