Lee, D.; McDaniel, S. T. Ocean acoustic propagation by finite difference methods. (English) Zbl 0637.76080 Comput. Math. Appl. 14, 305-423 (1987). A complete issue of the journal is devoted to one article on the calculation of acoustic waves in the ocean. It consists of a brief theoretical description of the governing equations, their expansion in numerical difference schemes, and computer listings of proven programs using the schemes. The theoretical description concentrates on the application of the parabolic approximation to the Helmholtz equation in cylindrical polar coordinates. The recent review by R. C. Spindel [Annu. Rev. Fluid Mech. 17, 217-237 (1985)] should have been cited, not least because it contains many references to investigations on sound transmission in the ocean, such as those in the new field of inverse techniques. The theory of the finite difference scheme developed for wave propagation problems is described fully, including sections on stability, initial and boundary conditions, and stepsize. Methods other than finite differences, such as a Fourier method, are mentioned briefly. A number of representative test examples are given so that users can gain experience with the computer code. A full listing of the computer codes is provided in FORTRAN IV, with no FORTRAN 77 improvements evident. This article provides an excellent foundation for independent numerical investigation into ocean acoustic problems for which the sound speed profile is known. Reviewer: P.Bryant Cited in 1 ReviewCited in 16 Documents MSC: 76Q05 Hydro- and aero-acoustics 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics 86A05 Hydrology, hydrography, oceanography Keywords:acoustic waves; numerical difference schemes; Helmholtz equation in cylindrical polar coordinates; sound transmission; inverse techniques; finite difference scheme; boundary conditions; Fourier method; FORTRAN IV PDFBibTeX XMLCite \textit{D. Lee} and \textit{S. T. McDaniel}, Comput. Math. Appl. 14, 305--423 (1987; Zbl 0637.76080) Full Text: DOI