Nonlinear parabolic equation model for finite-amplitude sound propagation in an inhomogeneous medium over a nonflat, finite-impedance ground surface

A nonlinear parabolic equation (NPE) model for weakly nonlinear sound propagation in an inhomogeneous medium is described. The model being formulated in the time domain, complex impedances cannot be used to simulate ground surfaces. A second NPE model is thus derived to include the medium in the computational system. Based on a nonlinear extension of the Zwikker‐Kosten model for rigidly‐framed porous media, it allows to include Forchheimer's nonlinearities. Both models are then adapted to terrain‐following coordinates, and used together with an interface condition, allow to simulate finite‐amplitude sound propagation over a nonflat, finite‐impedance ground surface. Numerical examples show that the NPE model is in good agreement with the solutions of the frequency domain boundary element method. Applications of this model to the simulation of sound propagation from explosions in air are then discussed.