A Study of the Short Wave Components in Computational Acoustics

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

doi:10.1007/978-1-4613-8342-0_6

Cited by 57 publications

(88 citation statements)

References 2 publications

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“…As in Refs. [3,4,6,7] we consider uniform grids, such that ∆x i = ∆x, and β i j = j − i. Moreover, for internal points, filters are symmetric, and M = N. In that case g i, j becomes independent of the position i of the internal point.…”

Section: Construction Of High-order Conservative Boundary Filtersmentioning

confidence: 99%

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Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

Wu¹,

Meyers²

2011

Computers & Fluids

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In computational aero-acoustics, large-eddy simulations (LES) or direct numerical simulations (DNS) are often employed for flow computations in the source region. As part of the numerical implementation or required modeling, explicit spatial filters are frequently employed. For instance, in LES spatial filters are employed in the formulation of various subgrid-scale (SGS) models such as the dynamic model or the variational multi-scale (VMS) Smagorinsky model; both in LES or DNS, spatial high-pass filters are often used to remove undesired grid-to-grid oscillations.Though these type of spatial filters adhere to local accuracy requirements, in practice, they often destroy global conservation properties in the presence of non-periodic boundaries conditions. This leads to the incorrect prediction of the flow properties near the hard boundaries, such as walls. In the current work, we present globally conservative high-order accurate filters, which combine traditional filters at the internal points with one-sided conservative filters near the wall boundary. We test these filters to remove grid-to-grid oscillations both in a channel-flow case and in 2D cavity flow. We find that the use of a non-conservative filter leads to erroneous predictions of the skin friction in channel flows up to 30%. In the cavity-flow simulations, the use of non-conservative filters to remove grid-to-grid oscillations leads to important shifts in the Strouhal number of the dominant mode, and a change of the flow pattern inside the cavity. In all cases, the use of conservative high-order filter formulations to remove grid-to-grid oscillations lead to very satisfactory results. Finally, in our channel-flow test case, we also illustrate the importance of using conservative filters for the formulation of the VMS Smagorinsky model.

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Section: Construction Of High-order Conservative Boundary Filtersmentioning

confidence: 99%

“…For the construction of internal filters, the filter coefficients are determined by imposing a number of constraints on the filter transfer function [3,4,6]. Firstly, normalization (12) leads to G(0) = 1.…”

Section: Construction Of High-order Conservative Boundary Filtersmentioning

confidence: 99%

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

Wu¹,

Meyers²

2011

Computers & Fluids

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“…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%

“…Typically these methods utilize symmetric ÿnite-di erence stencils that result in zero inherent numerical dissipation. While this is desirable for resolved scales, it is well known that unresolved scales when using high-order methods can eventually corrupt a solution and/or lead to instability if not properly controlled [32]. These error modes stem from a variety of sources including approximate boundary treatments, mesh stretching, and con icting initial and boundary conditions.…”

Section: Spatial Discretizationmentioning

confidence: 99%

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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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