Intermittency and transition to chaos in the cubical lid-driven cavity flow

Transition from steady state to intermittent chaos in the cubical lid-driven flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov-Poincar\'e-Hopf bifurcation at a critical Reynolds number $Re_c$ = 1914. As for the 2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of the primary vortex core. A Reynolds-Orr analysis reveals that the unstable perturbation relies on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only one eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics during the intermittencies are surprisingly well characterized by one of the stable eigenpairs.Comment: Accepted for publication in Fluid Dynamics Researc

Systèmes conjugués et ingénierie moléculaire, de la molécule au composant

Date du colloque : 11/2010</p

Direct Numerical Simulation in a Lid-Driven Cubical Cavity at High Reynolds Number by a Chebyshev Spectral Method

Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 1.2 104 and 2.2 104. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier-Stokes equations in a cubical domain. The Projection-Diffusion method [Leriche and Labrosse (2000, SIAM J. Sci. Comput. 22(4), 1386-1410), Leriche et al. (2005, J. Sci. Comput., in press)] allows to decouple the velocity and pressure computation in very efficient way and the simple geometry allows to use the fast diagonalisation method for inverting the elliptic operators at a low computational cost. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presente

Molecular engineering of conjugated systems, from molecules to solar devices

Date du colloque : 03/2011</p

A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation

Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legendre spectral element method is used for the spatial discretization to solve the filtered Navier--Stokes equations. A novel variant of approximate deconvolution models blended with a mixed scale model using a dynamic evaluation of the subgrid-viscosity constant is proposed. This model is validated by comparing the large-eddy simulation with the direct numerical simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds number of 12'000. Subgrid modeling in the case of a flow with coexisting laminar, transitional and turbulent zones such as the lid-driven cubical cavity flow represents a challenging problem. Moreover, the coupling with the spectral element method having very low numerical dissipation and dispersion builds a well suited framework to analyze the efficiency of a subgrid model. First- and second-order statistics obtained using this new model are showing very good agreement with the direct numerical simulation. Filtering operations rely on an invertible filter applied in a modal basis and preserving the C0-continuity across elements. No clipping on dynamic parameters was needed to preserve numerical stability

Motivation d’étudiants en éducation physique au cégep à l’aide de l’approche « Sport Education » et points de vue d’enseignantes

Conférence présentée lors de la Journée de la recherche sur la motivation au collégial - 2e édition, organisée dans le cadre du 87e congrès de l'Acfas, Gatineau, le 27 mai 2019

Large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method

This paper presents the large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method (SEM) using the dynamic model. Two spectral filtering techniques suitable for these simulations have been implemented. Numerical results for Reynolds number $\text{Re}=12'000$ are showing very good agreement with other experimental and DNS results found in the literature

Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptoticall