Numerical Results For Wavefront Tracking

Gholam-Ali Zakeri

doi:10.1117/12.945822

14 July 1988 Numerical Results For Wavefront Tracking

Gholam-Ali Zakeri

Proceedings Volume 0927, Wave Propagation and Scattering in Varied Media; (1988) https://doi.org/10.1117/12.945822
Event: 1988 Technical Symposium on Optics, Electro-Optics, and Sensors, 1988, Orlando, FL, United States

Abstract

A finite-difference, two-step scheme with a convex parameter is investigated. The scheme is applied to a system of partial differential equations containing a source term describing the propagation of a small amplitude wave. For an initially exponentially decaying pulse or a triangular pulse, a network of front-ray coordinates is used to transform the PDEs into non-dimensional form. The finite-difference scheme for these PDEs is written and the stability condition for the scheme and the stability of the boundary condition are discussed. Since these PDEs can be used to describe water waves at large distances, we investigate the diffraction of a plane wave around a smooth convex wall and a convex wall with a sharp corner. The numerical results using the above scheme are compared with those given by Lighthill and Whitham. It is shown that the change in the Mach number along the wall is asymptotically proportional to square-root of the media nonlinearity parameter and the initial Mach number. This change also depends on the limiting value of the angle of the wall at large distances. The propagation of an initially curved front is also investigated and it is shown that the center of hump moves faster for a smaller parameter value of the media nonlinearity, than with a larger value of the parameter. These comparisons are done for atmosphere, distilled water and water with 35% salinity.

Citation Download Citation

Gholam-Ali Zakeri "Numerical Results For Wavefront Tracking", Proc. SPIE 0927, Wave Propagation and Scattering in Varied Media, (14 July 1988); https://doi.org/10.1117/12.945822

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