Numerical Results For Wavefront Tracking
Abstract
A finitedifference, twostep 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 frontray coordinates is used to transform the PDEs into nondimensional form. The finitedifference 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 squareroot 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.
 Publication:

Wave propagation and scattering in varied media
 Pub Date:
 July 1988
 DOI:
 10.1117/12.945822
 Bibcode:
 1988SPIE..927...60Z
 Keywords:

 Finite Difference Theory;
 Plane Waves;
 Water Waves;
 Wave Diffraction;
 Wave Fronts;
 Jacobi Matrix Method;
 Mach Number;
 One Dimensional Flow;
 Partial Differential Equations;
 Tracking (Position);
 Two Dimensional Flow;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer