A FINITE ELEMENT METHOD FOR THE PARABOLIC EQUATION IN AEROACOUSTICS COUPLED WITH A NONLOCAL BOUNDARY CONDITION FOR AN INHOMOGENEOUS ATMOSPHERE

The standard parabolic equation is used to simulate the far-field, low-frequency sound propagation over ground with mild range-varying topography. The atmosphere has a lower layer with a general, variable index of refraction. An unbounded upper layer with a squared refractive index varying linearly with height is considered and modeled by the nonlocal boundary condition of Dawson, Brooke and Thomson.1 A finite element/transformation of coordinates method is used to transform the initial-boundary value problem to one with a rectangular computational domain and then discretize it. The solution is marched in range by the Crank–Nicolson scheme. A discrete form of the nonlocal boundary condition, which is left unaffected by the transformation of coordinates, is employed in the finite element method. The fidelity of the overall method is shown in the numerical simulations performed for various cases of sound propagation in an inhomogeneous atmosphere over a ground with irregular topography.

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