A Kirchhoff approximation-based numerical method to compute multiple acoustic scattering of a moving source

• We present an approximate method to compute noise propagation from a moving source.
• This method uses the Kirchhoff–Helmholtz equation and the Kirchhoff assumption.
• This method can handle a moving source and multiple scattering.
• Three test cases are led to evaluate the validity of the method.
• Results are good and show that the method could be used to predict urban noise.

Within the scope of a study of external noise propagation from moving ground vehicles, a numerical method is developed to compute the acoustic field emitted by a moving source in the presence of scattering objects such as roads, buildings or noise-shields. This method is developed with the purpose of being used in a vehicle design process and therefore it must have a low computational cost, which requires a certain number of approximations. The case of a fixed point source is studied first then the effect of a movement of the source is taken into account through the introduction of a retarded time. The acoustic source is assumed to be represented by one or many harmonic monopoles of possibly different frequency moving with a constant speed in a quiescent flow field. Scattering from nearby perfectly reflecting objects is computed through a Kirchhoff–Helmholtz integral equation applying the Kirchhoff approximation. A ray-surface intersection algorithm to compute shadow areas is proposed. The method is validated against analytical solutions and experimental results for a fixed source, and against a higher-order finite difference time-domain method for the multiple scattering of a moving source. Results are good and show that this method can potentially be used to predict urban noise.