Abstract
A numerical approach for the treatment of irregular ocean bottoms within the framework of the standard parabolic equation is proposed. The present technique is based on the immersed interface method originally developed by LeVeque and Li [(1994). SIAM J. Numer. Anal. 31(4), 1019-1044]. The method conserves energy to high order accuracy and naturally handles generic range-dependent bathymetries, without requiring any additional specific numerical procedure. An illustration of its capabilities is provided by solving the well-known wedge problem.
Highlights
Propagation models based on different types of parabolic equations have been extensively used during the last 4 decades in underwater acoustics
The present technique is based on the immersed interface method originally developed by LeVeque and Li [(1994)
The parabolic equation is solved on a regular Cartesian grid, in which the bathymetry is “immersed.” Away from the bottom interface, standard centered finite difference schemes are employed to compute the derivatives along the vertical axis and the Crank-Nicolson method is used for the integration in range
Summary
Propagation models based on different types of parabolic equations have been extensively used during the last 4 decades in underwater acoustics. Current methods which allow one to properly handle range-dependent bottoms essentially include stair-step approximations within energy-conserving parabolic models (Collins and Westwood, 1991); domain rotations (Collins, 1990); and mapping techniques (Metzler et al, 2014). The proposed approach conserves energy to high order accuracy and allows handling generic range-dependent ocean bottoms. It can be viewed as a generalization of the IFD (Implicit Finite Difference) method developed by Lee and McDaniel (1988). The letter is organized as follows: after a brief review of the standard parabolic model (Sec. 2), the new method is presented (Sec. 3); an example of application is described (Sec. 4); concluding remarks are drawn
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