Nonlinear progressive wave equation model for transient and steady-state sound beams

NPE is a nonlinear progressive wave equation and associated computer code that yields a time domain solution for propagation in an acoustic waveguide. In the present study, the NPE equation is modified to describe axisymmetric sound beams in the paraxial approximation. The modified version of NPE is employed to describe three cases of radiation from a baffled piston: linear transient propagation, linear cw propagation, and nonlinear cw propagation. Alternative schemes to initialize the moving window that is convected by NPE are discussed for each type of problem. The linear transient signal or linear cw signal evaluated by NPE is compared to the direct prediction of the transient or steady-state Rayleigh integral. The nonlinear signal evaluated by NPE is compared to experimental data in the near and far field. The results show that NPE gives good results for all three propagation problems, in some cases at close regions where the paraxial approximation was previously believed to be inaccurate.