PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach

We present an SCRBE PDE App framework for accurate and interactive calculation and visualization of the parametric dependence of the pressure field and associated Quantities of Interest (QoI)—such as impedance and transmission loss—for an extensive family of acoustic duct models. The Static Condensation Reduced Basis Element (SCRBE) partial differential equation (PDE) numerical approach incorporates several principal ingredients: component-to-system model construction, underlying “truth” finite element PDE discretization, (Petrov)-Galerkin projection, static condensation at the component level, parametrized model-order reduction for both the inter-component (port) and intra-component (bubble) degrees of freedom, and offline-online computational decompositions; we emphasize in this paper reduced port spaces and QoI evaluation techniques, especially frequency sweeps, particularly germane to the acoustics context. A PDE App constitutes a Web User Interface (WUI) implementation of the online, or deployed, stage of the SCRBE approximation for a particular parametrized model: User model parameter inputs to the WUI are interpreted by a PDE App Server which then invokes a parallel cloud-based SCRBE Online Computation Server for calculation of the pressure and associated QoI; the Online Computation Server then downloads the spatial field and scalar outputs (as a function of frequency) to the PDE App Server for interrogation and visualization in the WUI by the User. We present several examples of acoustic-duct PDE Apps: the exponential horn, the expansion chamber, and the toroidal bend; in each case we verify accuracy, demonstrate capabilities, and assess computational performance.