Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.

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The present paper investigates properties of the solutions obtained with the equivalent sources method in scattering problems with the aim of identifying suitable monopole arrangements. Simple geometry scatterers--parallelepipeds with different aspect ratios--are considered and easy-to-implement source supports are tested: linear, circular, elliptical, and a "double linear" one. It was found that the supports providing best solutions differ according to the body geometry and the incidence angle of the impinging wave. Moreover, in the situations in which the other supports fail, it is shown that the double linear one provides satisfactory solutions with a minimum number of monopoles. Rules that furnish appropriate numbers of sources to use as well as their positioning are given for the different cases. A simple procedure based on these rules is proposed for scatterers with a more complex geometry, guaranteeing, still with a low number of monopoles, solutions with satisfactory accuracy.

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Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior. Mach waves are observed in the near sound field of the supersonic mixing layer computed by the LES. These waves show steepening typical to non-linear propagation. Further calculations using the Burgers equation support this finding, where the initial wave slope has a role in kicking them. No visible non-linear propagation effects were found for the subsonic mixing layers. The effects of geometrical spreading and viscosity are also considered.

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