NUMERICAL SIMULATION OF LOW-FREQUENCY AEROACOUSTICS OVER IRREGULAR TERRAIN USING A FINITE ELEMENT DISCRETIZATION OF THE PARABOLIC EQUATION

Environmental noise raises serious concerns in modern industrial societies. As a result, the study of sound propagation in the atmosphere over irregular terrain is a subject of current interest in aeroacoustics. We use the standard parabolic approximation of the Helmholtz equation to simulate the far-field, low-frequency sound propagation in a refracting atmosphere, over terrains with mild range-varying topography. At an artificial upper boundary of the computational domain, described in range and height coordinates, a nonlocal boundary condition is used to model the effect of a homogeneous, semi-infinite atmosphere. We define a curvilinear coordinate system fitting the irregular topography. We discretize the transformed initial-boundary value problem with a finite element technique in height and a conservative Crank–Nicolson scheme for marching in range. The underlying transformation of coordinates allows the effective coupling with the nonlocal boundary condition. The resulting discretization method is accurate and efficient for the numerical prediction of noise levels in the atmosphere.