Numerical studies of finite element variational multiscale methods for turbulent flow simulations

John, Volker; Kindl, Adela

doi:10.1016/j.cma.2009.01.010

Cited by 57 publications

(66 citation statements)

References 44 publications

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“…The mapping w h ∈ X h → z h ∈ X h admits a fixed point by Brouwer's Fixed Point Theorem which is the solution of model (98). This follows from the stability estimates (that are stated here just for the solution of (98)):…”

Section: Application To the Simulation Of Turbulent Flowsmentioning

confidence: 99%

“…There are several realizations of bubble VMS methods which differ in some details, e.g., see [62,68,69,98,112,113,31]. Here, exemplary the derivation of one of these realizations is presented.…”

Section: Derivationmentioning

confidence: 99%

“…In [68,69,62,98] each mesh cell was triangulated with a local grid and an approximation of the small resolved velocity with Q 1 finite elements was computed. In contrast, bubbles with a fixed polynomial degree were used in [112,113,31].…”

Section: Experience In Numerical Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

Ahmed

Rebollo

John

et al. 2015

Arch Computat Methods Eng

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Various realizations of variational multiscale (VMS) methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the incompressible Navier-Stokes equations and the scale separation is defined by projections. However, apart from these common basic features, the various VMS methods look quite different. In this review, the derivation of the different VMS methods is presented in some detail and their relation among each other and also to other discretizations is discussed. Another emphasis consists in giving an overview about known results from the numerical analysis of the VMS methods. A few results are presented in detail to highlight the used mathematical tools. Furthermore, the literature presenting numerical studies with the VMS methods is surveyed and the obtained results are summarized.

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Section: Application To the Simulation Of Turbulent Flowsmentioning

confidence: 99%

Section: Derivationmentioning

confidence: 99%

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A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

Ahmed

Rebollo

John

et al. 2015

Arch Computat Methods Eng

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“…In practice this term is often omitted, and until recently it was not clear if it is needed for technical reasons of the analysis or played an important role in computations. The role of the grad-div stabilization was again emphasized in the recent studies of the (stabilized) finite element methods for incompressible flow problems, see [21,38,43,50], also in conjunction with the rotation form of nonlinearities in the Navier-Stokes equations [33,34,42] and variational multiscale turbulence modelling [27]. Its relation to the variational multiscale approach is revealed in [15,22,44].…”

Section: The Finite Element Schemementioning

confidence: 99%

Enabling numerical accuracy of Navier-Stokes-αthrough deconvolution and enhanced stability

et al. 2010

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Abstract.We propose and analyze a finite element method for approximating solutions to the NavierStokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α suffer from two major sources of error if their solutions are considered approximations to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error on the velocity error that arises from the (necessary) use of the rotational form nonlinearity. The proposed scheme "fixes" these two numerical issues through the combined use of a modified grad-div stabilization that acts in both the momentum and filter equations, and an adapted approximate deconvolution technique designed to work with the altered filter. We prove the scheme is stable, optimally convergent, and the effect of the pressure error on the velocity error is significantly reduced. Several numerical experiments are given that demonstrate the effectiveness of the method.Mathematics Subject Classification. 65M12, 65M60, 76D05.

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“…This provides a good compromise between accuracy and computational complexity, while keeping the numerical diffusion levels below the sub-grid terms (cf. [25]). Indeed, on the one side, it produces less numerical diffusion with respect to a simple semi-implicit Euler scheme, and thus it does not tend to artificially increment the turbulent diffusion.…”

Section: Turbulent Channel Flow (3d)mentioning

confidence: 99%

Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

et al. 2018

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In this work, we study the performance of some local projection-based solvers in the Large Eddy Simulation (LES) of laminar and turbulent flows governed by the incompressible Navier-Stokes Equations (NSE). On one side, we focus on a high-order term-by-term stabilization Finite Element (FE) method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard Local Projection Stabilization (LPS) methods is replaced by an interpolation-stabilized structure. The interest of LPS methods is that they ensure a self-adapting high accuracy in laminar regions of turbulent flows, which turns to be of overall optimal high accuracy if the flow is fully laminar. On the other side, we propose a new Reduced Basis (RB) Variational Multi-Scale (VMS)-Smargorinsky turbulence model, based upon an empirical interpolation of the sub-grid eddy viscosity term. This method yields dramatical improvements of the computing time for benchmark flows. An overview about known results from the numerical analysis of the proposed methods is given, by highlighting the used mathematical tools. In the numerical study, we have considered two well known problems with applications in industry: the (3D) turbulent flow in a channel and the (2D/3D) recirculating flow in a lid-driven cavity.

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Numerical studies of finite element variational multiscale methods for turbulent flow simulations

Cited by 57 publications

References 44 publications

A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

Enabling numerical accuracy of Navier-Stokes-αthrough deconvolution and enhanced stability

Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

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