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Chaos in the lid-driven square cavity

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  • Garcia, Salvador

Abstract

As the Reynolds number Re⟶∞ the primary eddy switches from clockwise- to counterclockwise-rotating, a switching repeatedly reversing as the time t⟶∞. The primary eddy is the eddy leading the dynamics. Marking the genesis of chaos, the switching first is observed at Re=307,000 at the upper side of the total kinetic energy range. But then, it is observed at Re=310,000 at the lower side of the total kinetic energy range and unexpectedly relies upon the occurrence of a unique lowest spike in the total kinetic energy range. However, this reliance is not observed at Re=307,000, even when the lowest spike is more pronounced herein, but continues occurring systematically beyond Re=310,000. At extreme Reynolds numbers Re=O(1eps)=O(1015), where eps is the machine epsilon in double precision, as the time t⟶∞, an interesting dynamics still endures where the switching repeatedly reverses or where it stays put, the primary eddy rotating solely counterclockwise.

Suggested Citation

  • Garcia, Salvador, 2017. "Chaos in the lid-driven square cavity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 98-112.
    • Handle: RePEc:eee:matcom:v:142:y:2017:i:c:p:98-112
    DOI: 10.1016/j.matcom.2017.04.010
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    References listed on IDEAS

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    1. Garcia, Salvador, 2000. "Incremental unknowns for solving the incompressible Navier–Stokes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(5), pages 445-489.
    2. Garcia, Salvador, 2011. "Aperiodic, chaotic lid-driven square cavity flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1741-1769.
    3. Gorban, A.N. & Packwood, D.J., 2014. "Enhancement of the stability of lattice Boltzmann methods by dissipation control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 285-299.
    4. Song, Lunji & Wu, Yujiang, 2009. "Incremental unknowns method based on the θ-scheme for time-dependent convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2001-2012.
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