Atmospheric parabolic equation with Galerkin discretization and boundary fitted grid for modeling infrasound propagation over topography

Abstract

Studies utilizing the parabolic equation (PE) to model infrasound propagation over topography have traditionally implemented them as 2D or Nx2D PE models. These methods, to one extent or another, trade-off accuracy for enhanced computational speed. Three-dimensional parabolic equation (3DPE) models are seldom seen in atmospheric acoustic propagation studies compared to their 2D and Nx2D counterparts, despite the fact that theta coupling and proper modeling of horizontal refraction and diffraction in a 3DPE model should enable greater accuracy. In this work a 3DPE in cylindrical coordinates is developed under the alternating direction implicit scheme, with a Galerkin discretization and boundary fitted grid, such that the PE is capable of handling arbitrary and irregular topography features. Finally, 2D, Nx2D, and 3D implementations of the aforementioned PE model are examined for cases of propagation over a simple hill in homogeneous, downward refracting, and upward refracting atmospheres. Insights are drawn with regards to the accuracy at a variety of positions and ranges, and the computational speeds of the various methods.