Commun. Comput. Phys., 12 (2012), pp. 1359-1391.


An Application of the Level Set Method to Underwater Acoustic Propagation

Sheri L. Martinelli 1*

1 Torpedo Systems Department, Naval Undersea Warfare Center, 1176 Howell Street, Newport, Rhode Island 02841, USA; and Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA.

Received 19 March 2011; Accepted (in revised version) 23 December 2011
Available online 8 May 2012
doi:10.4208/cicp.190311.231211a

Abstract

An algorithm for computing wavefronts, based on the high frequency approximation to the wave equation, is presented. This technique applies the level set method to underwater acoustic wavefront propagation in the time domain. The level set method allows for computation of the acoustic phase function using established numerical techniques to solve a first order transport equation to a desired order of accuracy. Traditional methods for solving the eikonal equation directly on a fixed grid limit one to only the first arrivals, so these approaches are not useful when multi-path propagation is present. Applying the level set model to the problem allows for the time domain computation of the phase function on a fixed grid, without having to restrict to first arrival times. The implementation presented has no restrictions on range dependence or direction of travel, and offers improved efficiency over solving the full wave equation which under the high frequency assumption requires a large number of grid points to resolve the highly oscillatory solutions. Boundary conditions are discussed, and an approach is suggested for producing good results in the presence of boundary reflections. An efficient method to compute the amplitude from the level set method solutions is also presented. Comparisons to analytical solutions are presented where available, and numerical results are validated by comparing results with exact solutions where available, a full wave equation solver, and with wavefronts extracted from ray tracing software.

AMS subject classifications: 65M06, 65M22, 65M25
PACS: 43.30.Gv, 43.30.Zk
Key words: Geometric acoustics, level set method, high-frequency acoustic propagation, WENO method.

*Corresponding author.
Email: sheri_martinelli@brown.edu (S. L. Martinelli)
 

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