Numerical Investigation on the Stability of Singular Driven Cavity Flow

Auteri, Franco; Parolini, Nicola; Quartapelle, L.

doi:10.1006/jcph.2002.7145

Cited by 139 publications

(139 citation statements)

References 28 publications

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“…Numerically, a steady solution seems to exist up to Re = 7,500 approximately. Bifurcations to periodic unsteady solutions, obtained by DNS simulations, are reported by many authors, e.g., [5,70]. So, for Re = 1,000 and 5,000, we assume that a stationary solution is reached if the velocity deviation between two consecutive time steps is lower than a chosen tolerance, fixed as:…”

Section: D Lid-driven Cavity Flowsupporting

confidence: 40%

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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Section: D Lid-driven Cavity Flowsupporting

confidence: 40%

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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“…λ ∈ C, leading to periodic solutions (Toro, 2006) or Bifurcations. In (Auteri et al, 2002) the bifurcation for a cavity flow was located between 8017,6 and 8018,8 (Re numbers) but since 1995 (Goyon, 1995) reported the existence of particular periodic flow located in the upper left corner of a square cavity. In order to find the flow periodicity for Re 10,000 and determine if the system had reached its asymptotic state the system energy was used as a measure.…”

Section: Periodicity In Cavity Flowsmentioning

confidence: 40%

Flow Evolution Mechanisms of Lid-Driven Cavities

Toro¹,

Pedraza²

2011

Hydrodynamics - Advanced Topics

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“…For example, in [2] it was found that the first point of bifurcation for the 2D driven cavity problem occurs around Re = 8.018. Therefore, for the case of small viscosity solving unsteady, rather then steady, Navier-Stokes equations can be more appropriate sometimes.…”

Section: Eigenvalues Estimatesmentioning

confidence: 45%

Pressure Schur Complement Preconditioners for the Discrete Oseen Problem

Olshanskii¹,

Vassilevski²

2007

SIAM J. Sci. Comput.

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Abstract. We consider several preconditioners for the pressure Schur complement of the discrete steady Oseen problem. Two of the preconditioners are well known from the literature and the other is new. Supplemented with an appropriate approximate solve for an auxiliary velocity subproblem, these approaches give rise to a family of the block preconditioners for the matrix of the discrete Oseen system. In the paper we critically review possible advantages and difficulties of using various Schur complement preconditioners. We recall existing eigenvalue bounds for the preconditioned Schur complement and prove such for the newly proposed preconditioner. These bounds hold both for LBB stable and stabilized finite elements. Results of numerical experiments for several model two-dimensional and three-dimensional problems are presented. In the experiments we use LBB stable finite element methods on uniform triangular and tetrahedral meshes. One particular conclusion is that in spite of essential improvement in comparison with "simple" scaled mass-matrix preconditioners in certain cases, none of the considered approaches provides satisfactory convergence rates in the case of small viscosity coefficients and a sufficiently complex (e.g., circulating) advection vector field.

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Numerical Investigation on the Stability of Singular Driven Cavity Flow

Cited by 139 publications

References 28 publications

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

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

Flow Evolution Mechanisms of Lid-Driven Cavities

Pressure Schur Complement Preconditioners for the Discrete Oseen Problem

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