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Numerical algorithms

  1. L. Kleiser and U. Schuman, Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows, in Proc. 3rd GAMM Conf. Numerical Methods in Fluid Mechanics, ed. E. Hirsch (1980)
  2. C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag (1998)
  3. R. Peyret, Spectral Methods for Incompressible Flows, Springer-Verlag (2002)
  4. D. Viswanath, Recurrent motions within plane Couette turbulence, J. Fluid Mech. 580 (2007), arXiv:/physics/0604062
  5. M. Frigo and S.G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE 93 (2) (2005)
  6. P.R. Spalart, R.D. Moser, M.M. Rogers. Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions, J. Comp. Phys. 96, 297–324 (1990)

Dynamics of turbulence

  • M. Nagata, Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity, J. Fluid Mech. 217 (1990). Calculation of a lower/upper branch pair of equilibrium solutions to plane Couette flow.
  • J. M. Hamilton, J. Kim and F. Waleffe, Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech. 287 (1995). Identification and numerical study of organized dynamics in low-Reynolds plane Couette flow in small aspect ratio cells.
  • F. Waleffe, Homotopy of exact coherent structures in plane shear flows, Phys. Fluids 15 (2003). Exact numerical solutions to plane Couette flow with a variety of boundary conditions. Nagata-Waleffe lower branch and upper branch solutions served as the starting point of our investigation.
  • G. Kawahara and S. Kida, Periodic motion embedded in Plane Couette turbulence: regeneration cycle and burst, J. Fluid Mech. 449, 291 (2001). The first determination of unstable time-periodic solutions in a fully-resolved Navier-Stokes flow.
  • D. Viswanath, Recurrent motions within plane Couette turbulence J. Fluid Mech. 580 (2007) [arXiv:/physics/0604062]. A novel combination of the Newton-hookstep trust-region minimization algorithm with the GMRES algorithm for iterative solution of high-dimensional linear algebra problems. First computation of relative periodic orbits of plane Couette flow, using a CFD algorithm to evaluate Navier-Stokes dynamics and close recurrences for initial guesses.
  • J. F. Gibson, J. Halcrow and P. Cvitanović, Visualizing the geometry of state space in plane Couette flow, J. Fluid Mech. 611 (2008), [arXiv:0705.3957]. A technical exposition of the material presented in this tutorial. PDF
  • J. Halcow, J.F. Gibson, P. Cvitanović, and D. Viswanath, Heteroclinic connections in plane Couette flow, J. Fluid Mech. (2009) to appear. Calculation of four heteroclinic connections between unstable equilibria of plane Couette flow. PDF
  • J. Halcrow, J.F. Gibson and P. Cvitanović, Equilibrium and traveling waves solutions of low-Reynolds plane Couette flow, Submitted to JFM PDF
  • T. M. Schneider, J.F. Gibson, M. Lagha, F. De Lillo, B. Eckhardt Laminar-turbulent boundary in plane Couette flow Phys. Rev. E (2008) 78, 037301 PDF
  • J. Wang, J.F. Gibson, and F. Waleffe Lower branch coherent states: transition and control Phys. Rev. Lett. (2007) 98, 20 PDF
references.1247062725.txt.gz · Last modified: 2009/07/08 07:18 by gibson