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

Abstract

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.

Passive volumetric time domain simulation for room acoustics applications

“…No linear system solution is required for the update because there is no transmission of energy along the wall surface itself, which is reflected by the diagonal nature of the wall admittance matrix Y. It is rather direct to see, however, from the compact form of the semi-discrete system given in (36), that the extension to the case of non-locally reactive boundary conditions could entail a generalisation of Y to a full symmetric matrix, perhaps with a sparsity pattern reflecting communication between neighboring boundary faces. If Y remains positive real, now in a matrix sense, then the bounds on pole locations for the complete system would follow as before.…”

Dissipative time-domain one-dimensional model for viscothermal acoustic propagation in wind instruments

“…The classical horn equations describing plane wave propagation in an axisymmetric lossless pipe can be retrieved from an asymptotic analysis relying on Euler's equations in a pipe with varying section (Rienstra, 2005). Model (ZK) can be seen as a perturbation of these horn equations, and has been employed for dissipative pipes with varying section for instance in (Chaigne and Kergomard, 2016), (Bilbao and Harrison, 2016), (Tournemenne 6 Viscothermal time model for wind instruments and Chabassier, 2019) in the harmonic regime. Curvature of the wave fronts can occur in varying geometries and especially in the instrument bell, which can be modeled by an equation similar to (1) (Hélie et al, 2013).…”

“…Time-domain simulations of wind musical instruments require the choice of a balance between efficiency and accuracy. Real-time synthesis techniques, such as digital waveguide synthesis with lumped wall loss filter (Abel et al, 2003), (Mignot et al, 2010), modal decomposition (Silva et al, 2014), and Finite Difference -Time Domain (Bilbao and Harrison, 2016), favor their performance objective at the expense of model and discretization errors. By contrast, computer aided instrument prototyping requires a fine assessment of the physical phenomena occurring in the instrument, including dissipation and dispersion effects on propagative waves inside air filled pipes, caused by viscous and thermal boundary layers.…”

Physical Modeling, Algorithms, and Sound Synthesis: The NESS Project

“…The synthesis of brass instrument sounds has been approached using several methods-from the early AM synthesis of Risset (1965) to frequency modulation synthesis (Morrill 1977) and then later physical modeling work using digital waveguides (Cook 1991). Under the NESS project, a fully articulated brass instrument environment has been developed using FD methods (Bilbao and Harrison 2016), and the algorithm design resembles seminal speech synthesis work by Kelly and Lochbaum (1962). The user has complete control over the instrument design, including the specification of the bore profile, valve positions and lengths of valve sections, and lip parameters.…”

“…Wave simulations of room acoustics were first attempted in the 1990s using finite difference methods (Chiba et al 1993;Botteldooren 1994Botteldooren , 1995 as well as the digital waveguide-mesh paradigm applied in an equivalent finite-difference form (Savioja, Rinne, and Takala 1994). In the NESS project, the main developments were with respect to the modeling of complex geometries and frequencydependent boundaries (Bilbao et al 2016), air absorption effects and acceleration over parallel computing hardware (Webb and Bilbao 2011), and the use of non-Cartesian spatial grids (Hamilton and Bilbao 2013) for computational efficiency. Such wave-based simulations can typically be parallelized over the underlying spatial grid.…”