Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models

Abstract

A methodology to design broadband time-domain impedance boundary conditions (TDIBCs) from the analysis of acoustical models is presented. The derived TDIBCs are recast exclusively as first-order differential equations, well-suited for high-order numerical simulations. Broadband approximations are yielded from an elementary linear least squares optimization that is, for most models, independent of the absorbing material geometry. This methodology relies on a mathematical technique referred to as the oscillatory-diffusive (or poles and cuts) representation, and is applied to a wide range of acoustical models, drawn from duct acoustics and outdoor sound propagation, which covers perforates, semi-infinite ground layers, as well as cavities filled with a porous medium. It is shown that each of these impedance models leads to a different TDIBC. Comparison with existing numerical models, such as multi-pole or extended Helmholtz resonator, provides insights into their suitability. Additionally, the broadly-applicable fractional polynomial impedance models are analyzed using fractional calculus.

Bayesian inference for the ultrasonic characterization of rigid porous materials using reflected waves by the first interface

“…These terms inα(t) andβ(t) represent the dispersive kernel, expressing the dispersive nature of the viscous and thermal effects in the pores at high frequencies. For a more in-depth analysis of fractional derivatives in acoustical modeling, the reader is referred to [25] and the references therein. Combining Eqs.…”

Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions

“…The motivation behind the definition of this kernel is physical as it models passive systems that arise in e.g. electromagnetics [21], viscoelasticity [17,41], and acoustics [28,37,48]. By assumption, the right-hand side of (4) is a sum of positive-real kernels that each admit a dissipative realization.…”

“…This section, as well as Sections 4 and 5, deals with IBCs that have an infinitedimensional realization, which arise naturally in physical modeling [48]. Let us first consider the time-delayed impedancê…”

Delayed-time domain impedance boundary conditions (D-TDIBC)

“…(10) directly. In computationally intensive frameworks such as DNS/LES of turbulent flows, a more efficient compact-in-time method is required for the evaluation of A in n (t), as shown in recent papers on this topic [1][2][3][4]14,[22][23][24][25][26].…”