Computational Fluid Dynamics at RuG

Direct Numerical Simulation versus Dynamical System

Low dimensional dynamical system

From DNS results at Re=22000 a proper orthogonal decomposition has been made. The resulting functions have been used as basisfunctions in a Galerkin approximation of the Navier-Stokes equations. Thus a cheap low-dimensional dynamical system has been obtained with which a bifurcation analysis during laminar-turbulent transition can be made.

The first movie below shows DNS results at Re=10000 showing two-periodic behaviour. The second movie shows the behaviour of the `cheap imitation' through the dynamical system. It is suggested to watch the two movies simultaneously, and to the notice the common features.

DNS of 2-periodic Driven Cavity flow at Re=10,000. (269 kB)
(W. Cazemier)

Dynamical system simulation of 2-periodic Driven Cavity flow at Re=11,300. (620 kB)
(W. Cazemier)

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Department of Mathematics
University of Groningen