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Blasius numerical solution?

  1. Apr 18, 2004 #1

    Clausius2

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    I have been doing a simulation of Blasius equation:

    F'''+FF''/2=0 with F(eta) where eta is a similarity variable
    eta=(y-1)/(x^(1/2))

    F'(0)=1 u(y=1,x<<1)=1
    F(0)=0 v(y=1,x<<1)=0
    F'(infinite)=0 u(y=infinite, x<<1)=0

    You can observe that the BC's are different of the flow over flat plate. This is obtained for a mixing thickness in the near field of a two-dimensional jet, near the orifice of exhaust (are you agree?).

    in this page:
    http://www.rit.edu/~pnveme/Matlab_Course/Matlab_App_ODE.html
    where shooting method is employed in Matlab, it is said numerical methods (Runge Kutta, or the internal Matlab function ODE45) have normalized value F'(infinity)=1.

    I have programmed it in Matlab but now I don't know how consider the value 0 at infinity instead of 1.
    Could you help me?.
    Thanks.
     
  2. jcsd
  3. Apr 19, 2004 #2
    particular solution

    Hi, Clausius2;
    It seems to me, I was wrong in my private message to you about the almightiness of SMM. The only solution that classic SMM can give us is:
    F(eta)=6/(eta+C),
    where C is an arbitrary constant.
    See you in your old thread,
    Max.
     
  4. Apr 19, 2004 #3

    Clausius2

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    I have used the superposition principle:

    F(0)=0 F(0)=0 F(0)=0
    F'(0)=1 F'(0)=1 F'(0)=0
    F'(inf)=0 F'(inf)=2 F'(inf)=2
    = -


    :biggrin: Hey, it seems it works!, and I did't need your help. :cool:

    But now, guys, you have to tell me if superposition principle is valid for this equation. Is it linear?. Hands up if you are agree!
     
  5. Dec 6, 2011 #4
    hello...... I am in a real bind here. i tried runnning numerous scripts but they dont work... the programme should include runge kutta
    ps: Need help pronto!!!!
    i would truely appreciate it
     
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