Acoustic waves: a finite difference film

1983 ◽  
Vol 20 (3) ◽  
pp. 506-508
Author(s):  
George McMechan ◽  
Bill Price

A finite difference solution of the acoustic wave equation is an ideal basis for making movies since the computations naturally provide a series of frames at successive, discrete time increments. Each time frame contains a picture of the wave field present at that time. An example is illustrated in a short (~2.8 Min) 16 mm film that shows the dynamic response of a two-dimensional model to a point source. The model consists of a layer of varying thickness that overlies a half space. The film shows the point source expanding into a circular wavefront that is reflected, refracted, and diffracted by the model.

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 177 ◽  
Author(s):  
Dojin Kim

In this paper, we consider a two-dimensional acoustic wave equation in an unbounded domain and introduce a modified model of the classical un-split perfectly matched layer (PML). We apply a regularization technique to a lower order regularity term employed in the auxiliary variable in the classical PML model. In addition, we propose a staggered finite difference method for discretizing the regularized system. The regularized system and numerical solution are analyzed in terms of the well-posedness and stability with the standard Galerkin method and von Neumann stability analysis, respectively. In particular, the existence and uniqueness of the solution for the regularized system are proved and the Courant-Friedrichs-Lewy (CFL) condition of the staggered finite difference method is determined. To support the theoretical results, we demonstrate a non-reflection property of acoustic waves in the layers.


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