A space marching scheme for underwater acoustic wave propagation in fluid-elastic media

We present in this paper partial differential equations which govern three- dimensional acoustic wave propagation in fluid-elastic media. Working equat ions are parabolized so as to allow the analysis to be conducted in a plane -by-plane fashion. This simplification, while permitting only outgoing wave propagation, facilitates the analysis and cuts down on computing time and disk storage. To couple working equations in fluid and elastic layers, we i mpose physically relevant conditions on the interface. On the horizontal in terface we demand continuity of the normal displacement and normal stress. In addition, physical reasoning requires that shear stresses vanish on the interface for the present analysis, which is formulated under the inviscid flow assumption. We approximate spatial derivatives with respect to theta a nd z using the second-order accurate centered scheme. The resulting ordinar y differential equation is solved using the implicit scheme to render also second-order prediction accuracy in r. With a numerical scheme, it is highl y desirable to be able to check its prediction against suitable test proble ms, preferably ones for which an axact solution is available. In this three -dimensional study, test problems were chosen to demonstrate the applicabil ity of the code to the individual fluid and elastic laser. We have also ver ified that the code is applicable to analysis of wave propagation in water and elastic layers, across which there is an interface.