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  Direct numerical simulations (DNS)


    We have extended the influence-matrix method (Kleiser and Schumann, 1980) for direct numerical simulations to account for the generalized boundary conditions (Robin type). The paper detailing the new method has been published by the Journal of Computational Physics. See the Publications section for details.

    The main contributions outlined in the JCP paper:
  • Generalized velocity boundary conditions for the streamwise and spanwise directions (Robin type)
  • Wall normal direction velocity could also be arbitrary (no penetration, blowing/suction, etc.)
  • It does not matter if steady or unsteady B.C.
  • "Tau" correction algorithm to achieve high accuracy (up to machine precision)
    The contributions which are not outlined in the JCP paper (limited by the length):
  • Parallel computation (OpenMP). We have done simulations using upto 1024 cores in NCSA supercomputers.
  • Boussinesq approximation for buoyancy. We used this code for simulations of density/turbidity current.
    I would like to thank Dr. John Gibson from University of New Hampshire for discussions and suggestions. The new method was implemented in his pseudo-spectral code, Channelflow.

    You can download my version of the code here: channelflow_Uc.tgz.

    The new method greatly extends the applicability of the influence-matrix method. The original method is only good for wall bounded channel flows. Here are some examples demonstrating the new method.              
  • Open channel flow (Re*=60.4, Ret=171): B.Cs: Bottom: no slip Top: shear-free
3D
2D


Mean velocity profile
R.M.S.




Divergence of the velocity field


   

    Density current in wall-bounded and open channels (Gr=1.5E6)
    Reference: Liu and Jiang (2013), see Publications.

Open Channel

Wall-bounded Channel


Open Channel (spanwise averaged)

Wall-bounded Channel (spanwise averaged)



Open Channel (spanwise averaged, velocity vector)

Wall-bounded Channel (spanwise averaged, velocity vector)