Time dependent subscales in the stabilized finite element approximation of incompressible flow problems

Codina, Ramon; Principe, Javier; Guasch, Oriol; Badia, Santiago

doi:10.1016/j.cma.2007.01.002

Cited by 235 publications

(356 citation statements)

References 35 publications

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“…The decomposition of = ℎ + �, = + � refers to space splitting 0 = ℎ,0 ⊕ � ℎ . The velocity time derivation can be split as = ℎ + � where the second term is saved because it is chosen to deal with dynamical subscales [15]. Enforcing the sub scales to be L 2 orthogonal to the finite element or, in other words, � 0 is taken as subspace of h V ⊥ this solution leads to the separate energy bounds for the two different scales.…”

Section: Orthogonal Sgs Methods With Dynamical Subscalesmentioning

confidence: 99%

Numerical prediction of aerodynamic noise generated from missile for low Mach number flows

Jazarević

Rašuo

2017

Teh. vjesn.

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Original scientific paper Paper describes numerical prediction of aerodynamic noise generated from the missile. Simulation of turbulent flow is done solving incompressible Navier-Stokes equation, where turbulence is modelled with the orthogonal subgrid scale (OSGS) method with dynamical subscales. Because of comparison, the same simulation is done using the LES (Large Eddy simulation). It is shown how simulation of turbulent flow affects the prediction of acoustic sources calculated using Lighthill's analogy. Translation from time to frequency domain is done through DFT (Direct Fourier Transform), which gives smaller usage of memory. Acoustic sources are used in inhomogeneous Helmholtz equation to simulate pressure wave propagation in the domain. It is shown that OSGS with dynamical subscales gives better representation of the spectrum. Overall, better prediction of energy transfer across large and small eddies will give better allocation and presentation of acoustics sources. These sources will change wave propagation of the pressure in acoustic field. Keywords: aeroacoustics; direct Fourier transform; inhomogeneous Helmholtz equation; Litghill's analogy; noise; orthogonal SGS method with dynamical subscales Numeričko predviđanje aerodinamične buke koja se generira na projektilu pri malim Mahovim brojevimaIzvorni znanstveni članak Rad predstavlja numeričko predviđanje aerodinamične buke koja se generira s projektila. Simulacija turbulentnog strujanja je urađena rješavanjem NavierStoksove jednadžbe za nestlačiv fluid, gde je turbulencija modelirana metodom orthogonalne podgrupne ljestvice (OSGS) s dinamičkim podljestvicama. Zbog usporedbe, ista simulacija je urađena i s metodom LES (Large Eddy Simulation). Pokazano je kako simulacija turbulentnog strujanja utječe na predviđanje akustičnih izvora koji su izračunati Lighthill analogijom. Translacija s vremenskog područja ka frekventnom području je urađena s DFT (Direct Fourier Transform), što dovodi do manje uporabe memorije. Akustični izvori su korišteni u nehomogenoj Helmholtz jednadžbi da bi se simuliralo širenje tlaka u područje. Pokazano je da ova metoda dovodi do bolje prezentacije spektra. Općenito, bolje predviđanje energetskog transfera između malih i velikih vrtloga dati će mogućnost bolje i snažnije prezentacije akustičnog izvora. Ovakvi izvori će promjeniti širenje vala u akustičnom polju.

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Section: Orthogonal Sgs Methods With Dynamical Subscalesmentioning

confidence: 99%

Numerical prediction of aerodynamic noise generated from missile for low Mach number flows

Jazarević

Rašuo

2017

Teh. vjesn.

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“…The interesting feature about VMS is that it is capable of providing, at the same time, a numerical stabilization mechanism for the studied equations (in this case, the incompressible Navier-Stokes equations) and a turbulence model which takes into account the under-resolved scales (those which cannot be captured by the finite element mesh). This has been studied in several works [27,18,14,15,23] with successful results. The advantage of using this kind of approach is that there is no interference between the numerical stabilization and the turbulence models because both issues are taken care of by the numerical subgrid scales.…”

Section: Introductionmentioning

confidence: 99%

Variational Multiscale based dissipation models for the estimation of atmospheric seeing

Baiges

Codina

2015

Computers & Fluids

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In this work we present a numerical model for the estimation of atmospheric seeing in observation sites. The particularity of the method is that it is based on a Variational MultiScale turbulence model, its main feature being that the numerical mechanisms which are used to deal with stability issues (convection and the inf-sup condition for incompressible flows) do also take care of the modeling of turbulence. Based on this turbulence model, we develop the expressions for the viscous and thermal dissipations, num and χ num , which are later used for evaluating the constant of structure of the refraction index C 2 n following the classical model developed by Tatarski. Numerical examples show the behavior of the proposed numerical scheme when applied to turbulent flow practical cases, which include a convective boundary layer, the flow inside a transfer optics room, and a telescope enclosure.

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“…In particular, the subgrid scale stabilization methods (also known as variational multiscale stabilization methods) [31,32] are of special interest for the simulation of turbulent flows. This is so because, if well designed, they not only allow one to circumvent the above mentioned numerical problems, but also act as implicit large eddy simulation models [32,33,34,35,36]. The basic idea of subgrid scale methods is that of splitting the problem unknowns, u 0 and p 0 for (15), and the test functions, v 0 and q 0 , into large scale components, u 0 h and p 0 h , which can be resolved by the computational mesh, and small scale components,ũ 0 andp 0 , which cannot be captured and whose effects onto the large scales have to be modeled.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…The reader is referred to [35] for a detailed derivation of the above equations. These arise as a particular case of the most general situation in which subscales are tracked in time and all its non-linear contributions retained.…”

Section: Spatial Discretizationmentioning

confidence: 99%

Concurrent finite element simulation of quadrupolar and dipolar flow noise in low Mach number aeroacoustics

et al. 2016

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The computation of flow-induced noise at low Mach numbers usually relies on a two-step hybrid methodolgy. In the first step, an incompressible fuid dynamics simulation (CFD) is performed and an acoustic source term is derived from it. The latter becomes the inhomegenous term for an acoustic wave equation, which is solved in the second step, often resorting to boundary integral formulations. In the presence of rigid bodies, Curle's acoustic analogy is probably the most extended approach. It has been shown that Curle's boundary dipolar noise contribution does in fact correspond to the diffraction of the quadrupolar aerodynamic noise generated by the flow past the rigid body. In this work, advantage is taken from this fact to propose an alternative computational methodology to get the individual quadrupolar and dipolar contributions to the total acoustic pressure. For any linear acoustic wave operator, the unknown acoustic pressure can be split into its incident and diffracted components and be computed simultaneously to the incompressible flow field, in a single finite element computational run. This circumvents the problem found in Curle's analogy of needing the total pressure at the body's boundary, which includes the acoustic pressure fluctuations. The latter cannot be obtained from an incompressible CFD simulation. The proposed unified strategy could be beneficial for a large variety problems such as those involving noise generated from duct terminations, or those related with the simulation of fricatives in numerical voice production, among many others.

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Time dependent subscales in the stabilized finite element approximation of incompressible flow problems

Cited by 235 publications

References 35 publications

Numerical prediction of aerodynamic noise generated from missile for low Mach number flows

Numerical prediction of aerodynamic noise generated from missile for low Mach number flows

Variational Multiscale based dissipation models for the estimation of atmospheric seeing

Concurrent finite element simulation of quadrupolar and dipolar flow noise in low Mach number aeroacoustics

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