ACCURATE TREATMENT OF A GENERAL SLOPING INTERFACE IN A FINITE-ELEMENT 3D NARROW-ANGLE PE MODEL

Abstract

Parabolic equation models in 3D usually apply the "staircase" approximation to general range–varying interfaces between adjacent layers. This is the simplest technique available: it consists in neglecting range and azimuthal derivatives in the associated interface conditions. Our aim in this paper is to analyze the influence of the stair-step approximation technique, common to most 3D PE models, on a one-way sound wave propagation problem. We present a new finite-element 3D narrow-angle PE model which accurately treats the variable interface conditions. This is accomplished by using (i) an appropriate parabolized condition of the same aperture as the parabolic equation used, and (ii) a new change-of-variable technique which does not require any homotheticity condition of the layers as in previous works. Numerical simulations for the 3D wedge problem are presented. The convergence of the numerical solutions with respect to the azimuth is investigated. Unlike other 3D PE models working in cylindrical coordinates, the convergence tests have been carried out using a range-dependent number of points in azimuth. Numerical solutions obtained with the newly developed model are compared with a reference solution based on the image source and with a solution obtained with a 3D PE model that uses a stair-step technique.