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

Douasbin, Quentin; Scalo, Carlo; Selle, Laurent; Poinsot, Thiérry

doi:10.1016/j.jcp.2018.05.003

Cited by 25 publications

(25 citation statements)

References 40 publications

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“…It is worth noting that IBCs have other uses and denominations. In simulations of combustion chambers, IBCs are used to truncate a part of the chamber [32,33] or model injectors [32,34] for instance. In mathematical control, TDIBCs (also known as Dirichlet to Neumann maps) are commonly used to stabilize the wave equation since they modify the underlying semigroup generator and can yield asymptotic or even exponential stability.…”

Section: Modeling and Applications Of Impedance Boundary Conditionsmentioning

confidence: 99%

“…For instance, there does not seem to be a consensus on whether a TDIBC should be based on the impedance z [19,46,20,28,31], the admittance y [21,22], or the reflection coefficient β [47,30,32]. This topic has been mentioned by Gabard & Brambley [28] who warned that some instabilities reported in the literature may be due to an unsuitable implementation and showed the benefit of a characteristic-based implementation in their study, which is echoed in works that focus on large eddy simulations and direct numerical simulations [30,32,34,33].…”

Section: Time-domain Discretization Of Impedance Boundary Conditionsmentioning

confidence: 99%

“…6. The computation of β A v through (34) involves a transport equation whose N ψ -point discretization is characterized by its number of points per wavelength (33): here, N ψ = 4 is sufficient. The bottom left graph covers the non-passive scattering operator B = 3I, outside of the scope of the analysis presented in this paper.…”

Section: Numerical Flux Based On the Scattering Operatormentioning

confidence: 99%

See 2 more Smart Citations

Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations

Monteghetti

Matignon

Piot

2018

Journal of Computational Physics

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Time-domain impedance boundary conditions (TDIBCs) can be enforced using the impedance, the admittance, or the scattering operator. This article demonstrates the computational advantage of the last, even for nonlinear TDIBCs, with the linearized Euler equations. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow ducts.

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Section: Modeling and Applications Of Impedance Boundary Conditionsmentioning

confidence: 99%

Section: Time-domain Discretization Of Impedance Boundary Conditionsmentioning

confidence: 99%

Section: Numerical Flux Based On the Scattering Operatormentioning

confidence: 99%

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Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations

Monteghetti

Matignon

Piot

2018

Journal of Computational Physics

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“…Scalo et al (2015) used the reflection coefficient of the MSD wall together with a convolution integral [22], as recommended by Fung and Ju [36]. Their method was extendend in [44,42], also for use with the Navier-Stokes equations. An inconvenient is that the order of the time integration method decreases (even if it could possibly be fixed by using ADE).…”

Section: Mass Spring Damper Boundary Conditionmentioning

confidence: 99%

Numerical simulation of a turbulent channel flow with an acoustic liner

Sebastian

Marx

Fortuné

2019

Journal of Sound and Vibration

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Numerical simulations of a compressible turbulent channel flow with an acoustic impedance boundary condition are performed to assess how the flow is modified compared with a channel flow with rigid walls. When the liner resonance frequency is not too large and the resistance sufficiently small, turbulent statistics deviate from those obtained with rigid walls and surface waves are found traveling along the liner surface. For small resonance frequencies these waves are two-dimensional, they have a large wavelength compared to the turbulent structures and modulate these structures. As a result, they transport momentum toward the impedance wall, causing a drag increase. When the resonance frequency increases, the waves along the liner surface progressively lose their spanwise coherence while their streamwise wavelength decreases to get close to the flow typical length scales, which may also result in a drag increase when the resistance is sufficiently small. In the cases in which the surface waves are twodimensional, a connection is established between them and the unstable modes computed by using a linear stability analysis. Given the streamwise periodicity of the channel, a temporal stability analysis is performed rather than a spatial analysis, the latter being more frequently encountered in acoustic mode computations. This temporal analysis shows that the unstable mode in the vicinity of an acoustic liner arises from the A-branch of wall modes.

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“…Nonlinear wave processes are observed in a variety of engineering and physics applications such as acoustics [1,2], combustion noise [3,4], jet noise [5][6][7], thermoacoustics [8,9], surface waves [10], and plasmaphysics [11], requiring nonlinear evolution equations to describe the dynamics of perturbations. In the case of high amplitude planar acoustic wave propagation, two main nonlinear effects are present: acoustic streaming [2,12] and wave steepening [1,13].…”

Section: Introductionmentioning

confidence: 99%

Spectral energy cascade and decay in nonlinear acoustic waves

Gupta

Scalo

2018

Phys. Rev. E

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We present a numerical and theoretical investigation of nonlinear spectral energy cascade of decaying finite-amplitude planar acoustic waves in a single-component ideal gas at standard temperature and pressure (STP). We analyze various one-dimensional canonical flow configurations: a propagating traveling wave (TW), a standing wave (SW), and randomly initialized Acoustic Wave Turbulence (AWT). Due to nonlinear wave propagation, energy at the large scales cascades down to smaller scales dominated by viscous dissipation, analogous to hydrodynamic turbulence. We use shock-resolved mesh-adaptive direct numerical simulations (DNS) of the fully compressible onedimensional Navier-Stokes equations to simulate the spectral energy cascade in nonlinear acoustic waves. The simulation parameter space for the TW, SW, and AWT cases spans three orders of magnitude in initial wave pressure amplitude and dynamic viscosity, thus covering a wide range of both spectral energy cascade and the viscous dissipation rates. The shock waves formed as a result of energy cascade are weak (M < 1.4), and hence we neglect thermodynamic non-equilibrium effects such as molecular vibrational relaxation in the current study. We also derive a new set of nonlinear acoustics equations truncated to second order and the corresponding perturbation energy corollary yielding the expression for a new perturbation energy norm E (2) . Its spatial average, satisfies the definition of a Lyapunov function, correctly capturing the inviscid (or lossless) broadening of spectral energy in the initial stages of evolution -analogous to the evolution of kinetic energy during the hydrodynamic break down of three-dimensional coherent vorticity -resulting in the formation of smaller scales. Upon saturation of the spectral energy cascade i.e. fully broadened energy spectrum, the onset of viscous losses causes a monotonic decay of in time. In this regime, the DNS results yield ∼ t −2 for TW and SW, and ∼ t −2/3 for AWT initialized with white noise. Using the perturbation energy corollary, we derive analytical expressions for the energy, energy flux, and dissipation rate in the wavenumber space. These yield the definitions of characteristic length scales such as the integral length scale (characteristic initial energy containing scale) and the Kolmogorov length scale η (shock thickness scale), analogous to K41 theory of hydrodynamic turbulence (A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30 , 9 (1941)). Finally, we show that the fully developed energy spectrum of the nonlinear acoustic waves scales as E k k 2 −2/3 1/3 ∼ C f (kη), with C ≈ 0.075 constant for TW and SW but decaying in time for AWT. arXiv:1809.02202v1 [physics.flu-dyn]

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

Abstract: OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

Cited by 25 publications

References 40 publications

Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations

Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations

Numerical simulation of a turbulent channel flow with an acoustic liner

Spectral energy cascade and decay in nonlinear acoustic waves

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