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

Ahmed, Naveed; Rebollo, Tomás Chacón; John, Volker; Rubino, Samuele

doi:10.1007/s11831-015-9161-0

Cited by 81 publications

(74 citation statements)

References 130 publications

(316 reference statements)

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“…[19]). This recently proposed projection-based VMS turbulence model (called VMS-S model, see [1,18,19,21,49]) has thus a dual nature, as it results in a combination of (high-order term-by-term) stabilization and (projection) VMS-LES modeling. The analysis of the multi-scale Smagorinsky term may be found in [1,18,19,21,49].…”

Section: A Local Projection Stabilization Modelmentioning

confidence: 99%

“…Since LPS methods may be cast in the Variational Multi-Scale (VMS) framework (cf. [10]), the present paper also constitutes a step forward to the survey and classification of VMS methods (see [1] for a recent detailed review of VMS methods for the simulation of turbulent incompressible flows). The connection to VMS methods was a motivation to perform the studies presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a Full Space–Time Discretization of the Navier–Stokes Equations by a Local Projection Stabilization Method

et al. 2016

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A finite element error analysis of a local projection stabilization (LPS) method for the time-dependent Navier-Stokes equations is presented. The focus is on the high-order term-by-term stabilization 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 LPS methods is replaced by an interpolation-stabilized structure. The main contribution is on proving, theoretically and numerically, the optimal convergence order of the arising fully discrete scheme. In addition, the asymptotic energy balance is obtained for slightly smooth flows. Numerical studies support the analytical results and illustrate the potential of the method for the simulation of turbulent flows. Smooth unsteady flows are simulated with optimal order of accuracy.

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Section: A Local Projection Stabilization Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a Full Space–Time Discretization of the Navier–Stokes Equations by a Local Projection Stabilization Method

et al. 2016

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“…[9,28]. Actually, LPS schemes can be viewed as simplifications of residual-based VMS methods [2], since they are not fully consistent (only specific dissipative interactions are retained), but are of optimal order with respect to the FE interpolation. For a detailed description of different variants of LPS schemes, we refer to [44,54,71].…”

Section: Space Approximation: a Finite Element Local Projection Stabimentioning

confidence: 99%

“…[17], which does not involve the full residual, and presents a simpler and less expensive structure for practical implementations. This method is a particular type of Local Projection Stabilization (LPS) scheme that may be cast in the VMS framework [2], and constitutes a low-cost, accurate solver (of optimal order) for incompressible flows, despite being only weakly consistent. It presents the same structure of the Streamline Derivative-based (SD-based) LPS model [13,54], but it differs from it because at the same time it uses continuous buffer functions, it does not need enriched FE spaces, it does not need element-wise projections satisfying suitable orthogonality properties, and it does not need different nested meshes.…”

Section: Introductionmentioning

confidence: 99%

Efficient and scalable discretization of the Navier–Stokes equations with LPS modeling

Haferssas

Jolivet

Rubino

2018

Computer Methods in Applied Mechanics and Engineering

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In this work, we address the solution of the Navier-Stokes equations (NSE) by a Finite Element (FE) Local Projection Stabilization (LPS) method. The focus is on a LPS 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 LPS methods is replaced by an interpolation-stabilized structure, which only acts on the high frequency components of the flow. As a main contribution, we propose and test an efficient discretization of the model via a stable velocity-pressure segregation, using semi-implicit Backward Differentiation Formulas (BDF) in time. On the one hand, numerical studies illustrate that the solver accurately reproduces first and second-order statistics of benchmark turbulent flows for relatively coarse meshes. On the other hand, they show that the solver works in an efficient (i.e., robust and fast) way, especially when interfaced with scalable domain decomposition methods. Such scalability results are obtained on up to 16,384 cores with a near-ideal speedup.

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“…[5,6]), which is to our knowledge unavailable for most turbulence models in the current literature (cf. [13]). …”

Section: Numerical Analysismentioning

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

Cited by 81 publications

References 130 publications

Analysis of a Full Space–Time Discretization of the Navier–Stokes Equations by a Local Projection Stabilization Method

Analysis of a Full Space–Time Discretization of the Navier–Stokes Equations by a Local Projection Stabilization Method

Efficient and scalable discretization of the Navier–Stokes equations with LPS modeling

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

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