Numerical comparisons of finite element stabilized methods for a 2D vortex dynamics simulation at high Reynolds number

Ahmed, Naveed; Rubino, Samuele

doi:10.1016/j.cma.2019.02.013

Cited by 24 publications

(9 citation statements)

References 47 publications

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“…To allow coarsening of the ONERA-D mesh in the free stream by mesh adaptation, we used a streamline-upwind Petrov–Galerkin method associated with a grad–div stabilization for solving the baseflow equations (Franca, Frey & Hughes 1992; Ahmed & Rubino 2019).…”

Section: Methodsmentioning

confidence: 99%

Attachment-line, cross-flow and Tollmien–Schlichting instabilities on swept ONERA-D and Joukowski airfoils

Kitzinger

Leclercq²,

Marquet³

et al. 2023

J. Fluid Mech.

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Linear stability analyses are performed to investigate the boundary layer instabilities developing in an incompressible flow around the whole leading-edge of swept ONERA-D and Joukowski airfoils of infinite span. The stability analyses conducted in our study are global in the chordwise direction and local in the spanwise direction. A neutral curve is drawn at a given leading-edge Reynolds number $Re_R$ and several overlapping regions, called ‘lobes’, are identified on a physical basis. A detailed study of the marginal modes reveals the presence of attachment-line and cross-flow instabilities, as well as modes whose features do not fall within the standards of a specific type. Connected cross-flow/Tollmien–Schlichting modes, that show a dominant spatial structure reminiscent of Tollmien–Schlichting waves but whose destabilization is linked to a cross-flow mechanism, have been identified. The comparison of several neutral curves at different $Re_R$ values reveals the greater stabilizing effect of the increase of $Re_R$ on the cross-flow instability compared with the attachment-line instability. The influence of the airfoil shape is also studied by comparing the neutral curves of the ONERA-D with the neutral curves of the Joukowski airfoil. These curves reveal similar characteristics with the presence of distinct lobes and their comparison at constant sweep angle shows that, under the conditions studied, the ONERA-D airfoil is more stable than the Joukowski airfoil, even for cross-flow instabilities. The absolutely or convectively unstable nature of the flow in the spanwise direction is also tackled and our results suggest that the flow is only convectively unstable.

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Section: Methodsmentioning

confidence: 99%

Attachment-line, cross-flow and Tollmien–Schlichting instabilities on swept ONERA-D and Joukowski airfoils

Kitzinger

Leclercq²,

Marquet³

et al. 2023

J. Fluid Mech.

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“…In [70], the stabilized formulations for the fully-implicit log-morphology equation is adopted and applied to the centrifugal ventricular assist device: it is shown that the VMS stabilized formulation has better convergence behaviour and superior stabilization properties compared to the SUPG one. On the other hand, in [69] the numerical tests carried out revealed that both SUPG and VMS-LES methods exhibit comparable accuracy and they conclude that for their case the SUPG stabilization method is accurate enough. However, in our experience, we found that, as the mesh is refined, comparable results are achieved with SUPG and VMS-LES methods: the role of the turbulence model hence vanishes as the mesh becomes finer, which is coherent with the standard definition of a LES model.…”

Section: Mesh Convergence and Comparison Of Supg And Vms-lesmentioning

confidence: 96%

Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical model

Zingaro,

Dede',

Menghini

et al. 2021

Preprint

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In this paper, we investigate the hemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational Multiscale (VMS) method is adopted to obtain a stable formulation of the Navier-Stokes equations discretized by means of the Finite Element method and to account for turbulence modeling based on Large Eddy Simulation (LES). The aim of this paper is twofold: on one hand to improve the general understanding of blood flow in the human LA in normal conditions; on the other, to analyse the effects of the turbulence VMS-LES method on a situation of blood flow which is neither laminar, nor fully turbulent, but rather transitional as in LA. Our results suggest that if relatively coarse meshes are adopted, the additional stabilization terms introduced by the VMS-LES method allow to better predict transitional effects and cycle-to-cycle blood flow variations than the standard SUPG stabilization method.

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“…As in [19], for the time discretization, a semi-implicit Backward Differentiation Formula of order two (BDF2) has been applied (see [2] for further details), with time step ∆t = 2 • 10 −3 s. Time integration is performed until a final time T = 7 s. In the time period [0, 5] s, after an initial spin-up, the flow is expected to develop to full extent, including a subsequent relaxation time. Afterwards, it reaches a periodic-in-time (statistically-or quasi-steady) state.…”

Section: Numerical Experimentsmentioning

confidence: 99%

On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods

García-Archilla¹,

Novo²,

Rubino³

2022

Preprint

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We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a full order method (FOM)) and a different discretization of the nonlinear term is applied in the POD method. We prove that an additional error term appears in this case, compared with the case in which the same discretization of the nonlinear term is applied for both the FOM and the POD methods. However, the added term has the same size as the error coming from the FOM so that the rate of convergence of the POD method is barely affected. We analyze the case in which we add grad-div stabilization to both the FOM and the POD methods because it allows to get error bounds with constants independent of inverse powers of the viscosity. We also study the case in which no stabilization is added. Some numerical experiments support the theoretical analysis.

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Numerical comparisons of finite element stabilized methods for a 2D vortex dynamics simulation at high Reynolds number

Cited by 24 publications

References 47 publications

Attachment-line, cross-flow and Tollmien–Schlichting instabilities on swept ONERA-D and Joukowski airfoils

Attachment-line, cross-flow and Tollmien–Schlichting instabilities on swept ONERA-D and Joukowski airfoils

Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical model

On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods

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