Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics

Tam, Christopher K. W.; Webb, Jay C.

doi:10.1006/jcph.1993.1142

Cited by 1,974 publications

(1,257 citation statements)

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“…The LEE in generalized coordinates are solved using a finite-difference solver, in which spatial derivatives are approximated with a seven-point, fourth-order dispersion relation preserving (DRP) scheme [23]. A four-stage optimized explicit Runge-Kutta scheme [24] is used to advance the time solution.…”

Section: Methodsmentioning

confidence: 99%

Instability waves and low-frequency noise radiation in the subsonic chevron jet

Ran

Wan

et al. 2017

Acta Mech. Sin.

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Spatial instability waves associated with lowfrequency noise radiation at shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at downstream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.

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Section: Methodsmentioning

confidence: 99%

Instability waves and low-frequency noise radiation in the subsonic chevron jet

Ran

Wan

et al. 2017

Acta Mech. Sin.

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“…For aeroacoustics computations fourth order finite volume schemes have been designed and have successfully been exploited (e.g., see [23,46]), but their application is restricted by the requirement of carefully generated structured grids. Thus a higher order DG scheme appears to be a reliable alternative to existing approaches, as the obtained results demonstrate that the DG method is a strong candidate for computational aero-acoustics problems.…”

Section: Propagation Of a Spherical Acoustic Wavementioning

confidence: 99%

Application of a Higher Order Discontinuous Galerkin

Wolkov

Hirsch

Petrovskaya

2011

Math. Model. Nat. Phenom.

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Abstract. We discuss the issues of implementation of a higher order discontinuous Galerkin (DG) scheme for aerodynamics computations. In recent years a DG method has intensively been studied at Central Aerohydrodynamic Institute (TsAGI) where a computational code has been designed for numerical solution of the 3-D Euler and Navier-Stokes equations. Our discussion is mainly based on the results of the DG study conducted in TsAGI in collaboration with the NUMECA International. The capacity of a DG scheme to tackle challenging computational problems is demonstrated and its potential advantages over FV schemes widely used in modern computational aerodynamics are highlighted.

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“…low dissipation and dispersion) to accurately resolve convective ow-features over a wide range of space/time scales and amplitudes. To meet this need, most prior approaches have utilized high-order accurate ÿnite di erence methods such as the compact schemes in Reference [30] and the dispersion relation preserving methods in Reference [31]. Typically these methods utilize symmetric ÿnite-di erence stencils that result in zero inherent numerical dissipation.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…We conclude this section with a comparison of the original formulation (15)- (17) and reformulation (31), (32). In reformulation (31), (32) the optimization variable is h = g t .…”

Section: Problem Reformulationmentioning

confidence: 99%

Optimal control of unsteady compressible viscous flows

Collis

Ghayour

Heinkenschloss

et al. 2002

Numerical Methods in Fluids

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SUMMARYThe control of complex, unsteady ows is a pacing technology for advances in uid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical ow control systems. However, most of the prior work in this area has focused on incompressible ow which precludes many of the important physical ow phenomena that must be controlled in practice including the coupling of uid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier-Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter-rotating viscous vortices above an inÿnite wall which, due to the self-induced velocity ÿeld, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall-normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the in uence of control regularization for each case.

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Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics

Cited by 1,974 publications

References 0 publications

Instability waves and low-frequency noise radiation in the subsonic chevron jet

Instability waves and low-frequency noise radiation in the subsonic chevron jet

Application of a Higher Order Discontinuous Galerkin

Optimal control of unsteady compressible viscous flows

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