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Fortin, A.; Fortin, M.; Gervais, J. J.

A numerical simulation of the transition to turbulence in a two- dimensional flow. (English) Zbl 0611.76071

J. Comput. Phys. 70, 295-316 (1987).
A numerical simulation of the transition to turbulence is performed using a finite element method. The unsteady Navier-Stokes equations are discretized using a standard Galerkin approximation and a loading strategy for increasing the Reynolds number. The numerical results are then analysed at different Reynolds numbers showing a transition from a steady-state solution to a weakly chaotic solution. Phase space diagrams are presented showing the presence of strange attractors. The dimension and Lyapunov’s exponents of these attractors are computed and compared with existing results in the literature.

Cited in 9 Documents

MSC:

76F99 Turbulence
76M99 Basic methods in fluid mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

numerical simulation; transition to turbulence; finite element method; unsteady Navier-Stokes equations; standard Galerkin approximation; steady-state solution; weakly chaotic solution; Phase space diagrams; strange attractors; Lyapunov’s exponents
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References:

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