Passive time-domain numerical models of viscothermal wave propagation in acoustic tubes of variable cross section

Numerical modeling of wave propagation in acoustic tubes is a subject of longstanding interest, particularly for enclosures of varying cross section, and especially when viscothermal losses due to boundary layer effects are taken into consideration. Though steady-state, or frequency domain methods, are a common avenue of approach, recursive time domain methods are an alternative, allowing for the generation of wideband responses, and offer a point of departure for more general modeling of nonlinear wave propagation. The design of time-domain methods is complicated by numerical stability considerations, and to this end, a passive representation is a useful design principle leading to simple stable and explicit numerical schemes, particularly in the case of viscothermal loss modeling. Such schemes and the accompanying energy and stability analysis are presented here. Numerical examples are presented for a variety of duct profiles, illustrating strict energy dissipation, and for comparison of computed input impedances against frequency-domain results.