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.