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Lawal November 7, 2004 02:37

Blasius equation.
 
Can anyone kindly tell me how to use Finite-diffence method to solve Blasius's equation of laminar boundary layer (2f''' + ff'' = 0). I have consulted many text-books but the numerical method is not used to solve the equation. I needed any online text or idea to quickly fix this.

Thanks, Lawal

Junseok Kim November 7, 2004 04:21

Re: Blasius equation.
 
Your equation looks wired to me, usually, Blasius's equation has f' term. By the way, what is your boundary conditions?


Junseok Kim November 7, 2004 04:24

Re: Blasius equation.
 

Junseok Kim November 7, 2004 04:30

Re: Blasius equation.
 
Sorry for the confusion,

2f''' + ff'' = 0

You can set

z = -0.5 f y y = f'' x = f'

and use, for example, Runge-Kutta method for the time or space marching.


Tom November 8, 2004 05:42

Re: Blasius equation.
 
The standard way to solve this equation is to use central differences to obtain a nonlinear set of equations which you can solve using Newton iteration.

An alternative is to use a Runge-Kutta and the "shooting" method,

Tom.

Jarmo Monttinen November 8, 2004 13:34

Re: Blasius equation.
 
See White "Viscous Flow" for a rather complete description and a code (Runge-Kutta)

-- Jarmo

Edwin Boadu November 14, 2004 13:08

Blasius equation.
 
I would be grateful if you could help solve this Blasius equation using shooting method for me f"' + ff" = 0, f(0) = 0, f'(0) = 0, f"(0) =0.4696 Thank You

Jarmo Monttinen November 15, 2004 15:45

Re: Blasius equation.
 
White's book has both the code needed and the R-K subroutine. I have done this long time ago myself, don't have the book or my own notes handy, and don't have enough time to start working on this now.

If you can find White's book, and still have some questions or run into problems, I may be able to provide some help at that point.

-- Jarmo


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