A discontinuous enrichment method for three‐dimensional multiscale harmonic wave propagation problems in multi‐fluid and fluid–solid media

An evanescent wave occurs when a propagating incident wave impinges on an interface between two fluid, solid, or fluid–solid media at a subcritical angle. Mathematical properties of such a wave make it difficult to capture with standard finite element discretization schemes. For this reason, the discontinuous enrichment method (DEM) developed in (Comput. Methods Appl. Mech. Eng. 2001; 190:6455–6479; Comput. Methods Appl. Mech. Eng. 2003; 192:1389–1419; Comput. Methods Appl. Mech. Eng. 2003; 192:3195–3210; Int. J. Numer. Meth. Engng 2004; 61:1938–1956; Wave Motion 2004; 39(4):307–317; Int. J. Numer. Meth. Engng 2006; 66:2086–2114; Int. J. Numer. Meth. Engng 2006; 66:796–815) is extended here to the solution of a class of three‐dimensional evanescent wave problems in the frequency domain. To this effect, new DEM elements for three‐dimensional elastodynamic problems are first proposed. Then, these and other DEM elements previously developed for the efficient solution of the Helmholtz problem are further enriched with free‐space solutions of model evanescent wave problems, in order to achieve high accuracy at practical mesh resolution for fluid–fluid and fluid–solid applications. The performance of the extended DEM elements is reported to be better than that of its basic Helmholtz and Navier counterparts and superior to that achieved by the classical high‐order polynomial finite element method. Copyright © 2008 John Wiley & Sons, Ltd.

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