Finite-difference simulations of transient radiation from a finite-length pipe

The far-field radiation originating from a finite-length pipe is well studied, especially for steady-state conditions. However, because all physical systems do not begin in steady state, these radiation characteristics are only valid after the transient portion of the solution has decayed. Understanding transient radiation characteristics may be important (particularly for systems transmitting very short-duration signals), as they can differ quite significantly. A numerical complication to this problem involves dealing with a sharp corner in the domain of interest. While many numerical studies have attempted to couple solutions from the domains inside and outside a pipe, the analysis presented in this work treats the computational domain as a single region by expressing the entire physical domain as a map from a simple rectangular domain in generalized curvilinear coordinates. This method will be introduced in detail and general results of transient radiation will be presented for an infinitely baffled, finite-length pipe using the finite-difference method expressed in generalized curvilinear coordinates. Comparison will be made to previous results [P. Stepanishen and R. A. Tougas, J. Acoust. Soc. Am. 93, 3074-3084 (1993)] that used a semi-analytic approach with certain assumptions.