Description:
Finite element simulation of an incompressible flow past a circular cylinder for a Reynolds number Re = 100. The characteristic vortex shedding past the cylinder appears as the long-term solution. The figure below depicts the distribution of the vorticity at the periodic shedding range obtained by starting at rest. This periodic solution leads to a limit cycle in phase space, which corresponds to the global attractor of the 2D Navier-Stokes equations. The plot below is a delay plot of the computed lift coefficient on the cylinder, depicting this limit cycle. The time-stepping algorithm is shown to possess an algorithmic attractor as the continuum flow. Numerical simulations starting from different initial conditions lead to the same long-term solution.
References:
J.C. Simo and F. Armero [1994] ``Unconditional Stability and Long-Term Behavior of Transient Algorithms for the Incompressible Navier-Stokes and Euler Equations," Computer Methods in Applied Mechanics and Engineering, 111, 111-154.
F. Armero and J.C. Simo [1995] ``Long-Term Dissipativity of Time-Stepping Algorithms for an Abstract Evolution Equation with Applications to the Incompressible MHD and Navier-Stokes Equations," Computer Methods in Applied Mechanics and Engineering, in press.
armero@CE.Berkeley.EDU