Analytical/numerical matching for efficient calculation of scattering from cylindrical shells with lengthwise constraints

Structural discontinuities in highly coupled fluid-structure systems are modeled by an approach called analytical/numerical matching (ANM). This method separates the low-resolution global influence of a discontinuity from the relatively high-resolution local effects. A continuous, smoothed replacement for a fundamental structural discontinuity is constructed so that the system is identically unchanged beyond a small smoothing region. Simultaneously, the precise local effect of smoothing the discontinuity is retained in analytical form. The smoothed problem is solved by numerical techniques, with rapid convergence and reduced computational cost. The original discontinuous character is restored using the analytical expression for the local difference between the smoothed and the original problems. ANM has been successfully applied to two-dimensional cases of acoustic scattering from a thin, infinitely long cylindrical shell, with multiple structural discontinuities. Local solutions for longitudinal line discontinuities with radial, tangential, and rotational constraints have been formulated using ANM. Line constrained scattering problems, as well as line driven problems, are investigated. The ability of analytical/numerical matching to replace a discontinuous physical problem by a well behaved continuous one for numerical evaluation, while ultimately retaining the original geometry and physical behavior, is illustrated.