A unified approach to an augmented Burgers equation for the propagation of sonic booms

Nonlinear propagation through a relaxing atmosphere of pressure disturbances extracted from a computational fluid dynamics (CFD) solution of the flow around a supersonic aircraft is simulated using an augmented Burgers equation. The effects of nonlinearity, geometrical spreading, atmospheric inhomogeneity, thermoviscous attenuation, and molecular vibration relaxation are taken into account. The augmented Burgers equation used for sonic boom propagation calculations is often solved by the operator splitting method, but numerical difficulties arise with this approach when dissipation is not effective. By re-examining the solution algorithms for the augmented Burgers equation, a stable method for handling the relaxation effect has been developed. This approach can handle the Burgers equation in a unified manner without operator splitting and, therefore, the resulting scheme is twice as fast as the original one. The approach is validated by comparing it with an analytical solution and a detailed CFD of dispersed plane wave propagation. In addition, a rise time prediction of low-boom supersonic aircraft is demonstrated.