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Numerical algorithms

  • 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)
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag (1998)
  • R. Peyret, Spectral Methods for Incompressible Flows, Springer-Verlag (2002)
  • D. Viswanath, Recurrent motions within plane Couette turbulence, J. Fluid Mech. 580 (2007), arXiv:/physics/0604062
  • M. Frigo and S.G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE 93 (2) (2005)
  • 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.txt · Last modified: 2010/02/02 07:55 (external edit)