Time dependent boundary conditions for hyperbolic systems

Thompson, Kevin W.

doi:10.1016/0021-9991(87)90041-6

Cited by 1,167 publications

(579 citation statements)

References 6 publications

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“…The characteristic boundary conditions of Thompson (1987) are used for the outer boundary, while centreline conditions are derived following Mohseni & Colonius (2000). The same approach of Gudmundsson & Colonius (2011) was applied to obtain numerical solutions of the system of equations (4.3).…”

Section: Linear Parabolized Stability Equations (Pses)mentioning

confidence: 99%

Wavepackets in the velocity field of turbulent jets

et al. 2013

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We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers m ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers 0.3 St 0.9 and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

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Section: Linear Parabolized Stability Equations (Pses)mentioning

confidence: 99%

Wavepackets in the velocity field of turbulent jets

et al. 2013

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“…The computational domain extends up to 5H in the y-direction above the wall. The boundary conditions are non-reflective at the top boundary (Thompson 1990;Poinsot & Lele 1992), with a buffer zone implemented to avoid spurious reflections (Colonius, Lele & Moin 1993;Freund 1997). In preliminary studies, larger heights of the simulation domain were tested, up to 18H, as used in our previous work on the acoustic properties of porous coatings (Brès et al 2010).…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer

et al. 2013

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Numerical simulations of the linear and nonlinear two-dimensional Navier-Stokes equations, and linear stability theory are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings. The porous coatings consist of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. For the numerical simulations, temporally (rather than spatially) evolving boundary layers are considered and we provide evidence that this approximation is appropriate for slowly growing second-mode instabilities. We consider coatings operating in the typical regime where the pores are relatively deep and acoustic waves and second-mode instabilities are attenuated by viscous effects inside the pores, as well as regimes with phase cancellation or reinforcement associated with reflection of acoustic waves from the bottom of the pores. These conditions are defined as attenuative and cancellation/reinforcement regimes, respectively. The focus of the present study is on the cases which have not been systematically studied in the past, namely the reinforcement regime (which represents a worst-case scenario, i.e. minimal second-mode damping) and the cancellation regime (which corresponds to the configuration with the most potential improvement). For all but one of the cases considered, the linear simulations show good agreement with the results of linear instability theory that employs an approximate porous-wall boundary condition, and confirm that the porous coating stabilizing performance is directly related to their acoustic scattering performance. A particular case with relatively shallow pores and very high porosity showed the existence of a shorter-wavelength instability that was not initially predicted by theory. Our analysis shows that this new mode is associated with acoustic resonances in the pores and can be more unstable than the second mode. Modifications to the theoretical model are suggested to account for the new mode and to provide estimates of the porous coating parameters that avoid this detrimental instability. Finally, nonlinear simulations confirm the conclusions of the linear analysis; in particular, we did not observe any tripping of the boundary layer by small-scale disturbances associated with individual pores.

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“…Boundary conditions based on asymptotic solutions of the linearized Euler equations for radiation from a fixed (point) source have also been developed (see [30], and references therein), and these offer similar accuracy to the low-order Fourier/Laplace conditions. A popular and more robust alternative is the (nonlinear) one-dimensional characteristic-based boundary conditions developed by Thompson [31,32] and extended to viscous flows by Poinsot and Lele [23]. Though these can lead to large reflections of multidimensional disturbances, they can be improved when used in combination with the buffer region techniques described below.…”

Section: Introductionmentioning

confidence: 99%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.

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Time dependent boundary conditions for hyperbolic systems

Cited by 1,167 publications

References 6 publications

Wavepackets in the velocity field of turbulent jets

Wavepackets in the velocity field of turbulent jets

Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

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