Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

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

This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance: time-delayed, standard diffusive (which includes the Riemann-Liouville fractional integral) and extended diffusive (which includes the Caputo fractional derivative). The method of proof consists in formulating an abstract Cauchy problem on an extended state space using a dissipative realization of the impedance operator, be it finite or infinite-dimensional. The asymptotic stability of the corresponding strongly continuous semigroup is then obtained by verifying the sufficient spectral conditions derived by Arendt and Batty (Trans. Amer. Math. Soc., 306 (1988)) as well as Lyubich and V\~u (Studia Math., 88 (1988))

Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

Adaptive mesh refinement computation of acoustic radiation from an engine intake

A block-structured adaptive mesh refinement (AMR) method was applied to the computational problem of acoustic radiation from an aeroengine intake. The aim is to improve the computational and storage efficiency in aeroengine noise prediction through reduction of computational cells. A parallel implementation of the adaptive mesh refinement algorithm was achieved using message passing interface. It combined a range of 2nd- and 4th-order spatial stencils, a 4th-order low-dissipation and low-dispersion Runge–Kutta scheme for time integration and several different interpolation methods. Both the parallel AMR algorithms and numerical issues were introduced briefly in this work. To solve the problem of acoustic radiation from an aeroengine intake, the code was extended to support body-fitted grid structures. The problem of acoustic radiation was solved with linearised Euler equations. The AMR results were compared with the previous results computed on a uniformly fine mesh to demonstrate the accuracy and the efficiency of the current AMR strategy. As the computational load of the whole adaptively refined mesh has to be balanced between nodes on-line, the parallel performance of the existing code deteriorates along with the increase of processors due to the expensive inter-nodes memory communication costs. The potential solution was suggested in the end

High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling

Copyright @ 2014 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over inline image for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease