Numerical simulation of shock wave propagation in flows

19th International Symposium on Nonlinear Acoustics (ISNA), Waseda Univ, Tokyo, JAPAN, MAY 21-24, 2012International audienceAcoustical shock waves propagate through flows in many situations. The sonic boom produced by a supersonic aircraft influenced by winds, or the so-called Buzz-Saw-Noise produced by turbo-engine fan blades when rotating at supersonic speeds, are two examples of such a phenomenon. In this work, an original method called FLHOWARD, acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction, is presented. It relies on a scalar nonlinear wave equation, which takes into account propagation in a privileged direction (one-way approach), with diffraction, flow, heterogeneous and nonlinear effects. Theoretical comparison of the dispersion relations between that equation and parabolic equations (standard or wide angle) shows that this approach is more precise than the parabolic approach because there are no restrictions about the angle of propagation. A numerical procedure based on the standard split-step technique is used. It consists in splitting the nonlinear wave equation into simpler equations. Each of these equations is solved thanks to an analytical solution when it is possible, and a finite differences scheme in other cases. The advancement along the propagation direction is done with an implicit scheme. The validity of that numerical procedure is assessed by comparisons with analytical solutions of the Lilley's equation in waveguides for uniform or shear flows in linear regime. Attention is paid to the advantages and drawbacks of that method. Finally, the numerical code is used to simulate the propagation of sonic boom through a piece of atmosphere with flows and heterogeneities. The effects of the various parameters are analysed