Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers

Guermond, Jean‐Luc; Marra, Antonino Maria; Quartapelle, L.

doi:10.1016/j.cma.2005.08.016

Cited by 56 publications

(33 citation statements)

References 18 publications

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“…It is well known that Galerkin techniques are not well suited for the solution of hyperbolic problems (see for instance [9]). The list of techniques aiming at addressing this issue is endless; among these methods one can cite Galerkin-Least Squares [23], Discontinuous-Galerkin [23,30], subgrid viscosity [14], method of characteristics [8], edge stabilization [5], entropy viscosity [16] and many others. We assume that the sequence of approximate densities {ρ k h } k=0,...,K ⊂ W h is obtained by one of these stabilization techniques.…”

Section: Description Of the First-order Schemementioning

confidence: 99%

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

Guermond¹,

Salgado²

2011

SIAM J. Numer. Anal.

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Abstract. In this paper we analyze the convergence properties of a new fractional time-stepping technique for the solution of the variable density incompressible Navier-Stokes equations. The main feature of this method is that, contrary to other existing algorithms, the pressure is determined by just solving one Poisson equation per time step. The method is formally second-order accurate in time. Stability and error estimates are proven.

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Section: Description Of the First-order Schemementioning

confidence: 99%

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

Guermond¹,

Salgado²

2011

SIAM J. Numer. Anal.

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“…Continuous, piecewise bilinears and biquadratics have been studied there in a two-level context. Stabilisation of both phenomena, dominating convection and violation of the discrete Babuška-Brezzi condition, are investigated in [7][8][9]23] for the incompressible Navier-Stokes equation. For the flow around a NACA 0012 airfoil, numerical results are given for Reynolds numbers up to 10 6 in [23].…”

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confidence: 99%

“…Stabilisation of both phenomena, dominating convection and violation of the discrete Babuška-Brezzi condition, are investigated in [7][8][9]23] for the incompressible Navier-Stokes equation. For the flow around a NACA 0012 airfoil, numerical results are given for Reynolds numbers up to 10 6 in [23]. Convincing are also the result of a benchmark problem of the flow around a cylinder in 2D [9] and 3D [8].…”

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confidence: 99%

“…In the following we refer to numerical results obtained by schemes belonging to the considered class of stabilisation methods. The application of subgrid modelling (gradients of fluctuations) to scalar transport equations of convection-diffusion type has been numerically studied in [15,[19][20][21][22][23] in the two-level context for continous piecewise linear and quadratic elements.…”

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confidence: 99%

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A unified convergence analysis for local projection stabilisations applied to the Oseen problem

Matthies¹,

Skrzypacz²,

Tobiska³

2007

ESAIM: M2AN

170

183

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Abstract. The discretisation of the Oseen problem by finite element methods may suffer in general from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated. Second, spurious oscillations occur due to the dominating convection. One way to overcome both difficulties is the use of local projection techniques. Studying the local projection method in an abstract setting, we show that the fulfilment of a local inf-sup condition between approximation and projection spaces allows to construct an interpolation with additional orthogonality properties. Based on this special interpolation, optimal a-priori error estimates are shown with error constants independent of the Reynolds number. Applying the general theory, we extend the results of Braack and Burman for the standard two-level version of the local projection stabilisation to discretisations of arbitrary order on simplices, quadrilaterals, and hexahedra. Moreover, our general theory allows to derive a novel class of local projection stabilisation by enrichment of the approximation spaces. This class of stabilised schemes uses approximation and projection spaces defined on the same mesh and leads to much more compact stencils than in the two-level approach. Finally, on simplices, the spectral equivalence of the stabilising terms of the local projection method and the subgrid modelling introduced by Guermond is shown. This clarifies the relation of the local projection stabilisation to the variational multiscale approach.Mathematics Subject Classification. 65N12, 65N30, 76D05.

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“…It is frequently advocated in the literature that linear stabilization must be supplemented with a shock capturing technique to handle properly shocks and large gradients [23,25,10,6,19]. We want to investigate the effects of combining the edge stabilization with the entropy viscosity described in the Appendix.…”

Section: Edge Stabilization Plus Entropy Viscositymentioning

confidence: 99%

Weighting the Edge Stabilization

Ern¹,

Guermond²

2013

SIAM J. Numer. Anal.

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Abstract. A modification of the edge stabilization technique is proposed to improve the behavior of the method when solving conservation equations with non-smooth data and/or non-smooth solutions. The key ingredient is tempering the edge stabilization in regions of large gradients through appropriate weights. The new method is shown to preserve the convergence properties of the original method on smooth solutions and numerical tests indicate that it performs better on non-smooth solutions.

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Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers

Cited by 56 publications

References 18 publications

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

A unified convergence analysis for local projection stabilisations applied to the Oseen problem

Weighting the Edge Stabilization

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