@article{38651,
  keywords = {transition, dynamics, instability, coherent structures, proper orthogonal decomposition, bifurcation, navier-stokes equations, continuation, eigenfunction expansions, Galerkin method, sensitivity   analysis},
  author = {Bangia and Batcho and Kevrekidis and Karniadakis},
  title = {Unsteady two-dimensional flows in complex geometries: Comparative bifurcation studies with global eigenfunction expansions},
  abstract = { We present a bifurcation study of the incompressible Navier-Stokes equations in a model complex geometry: a spatially periodic array of cylinders in a channel. The dynamics of the how include a Hopf bifurcation from steady to oscillatory flow at an approximate Reynolds number R of 350 and the appearance of a second frequency at approximately R similar or equal to 890. The multiple frequency dynamics include a substantial increase in spatial and temporal scales with Reynolds number as compared with the simple limit cycle oscillation present close to R = 350. Numerical bifurcation studies of the dynamics are performed using three forms of global eigenfunction expansions. The first basis set is derived through principal factor analysis (Karhunen-Loeve expansion) of snapshots from accurate direct spectral element numerical solutions of the Navier-Stokes equations. The second set is obtained from the eigenfunctions of the Stokes operator for this geometry. Finally eigenfunctions are derived from a singular Stokes operator, i.e., the Stokes operator modified to include a Variable coefficient which vanishes at the domain boundaries. Truncated systems of (similar to 100) ODEs are obtained through projection of the Navier-Stokes equations onto the basis sets, and a comparative study of the resulting dynamical models is performed. },
  year = {1997},
  journal = {Siam Journal on Scientific ComputingSiam Journal on Scientific Computing},
  volume = {18},
  pages = {775-805},
  month = {05/1997},
  isbn = {1064-8275},
  language = {English},
}