Blasius numerical solution?

[Clausius2]

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.

 

[Max0526]

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.

 

[Clausius2]

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
= -


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

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!

 

[stichini2000]

hello... I am in a real bind here. i tried runnning numerous scripts but they don't work... the programme should include runge kutta
ps: Need help pronto!
i would truly appreciate it

 

[blue_raver22]

I am familiar with the Blasius equation and its use in fluid dynamics simulations. The Blasius numerical solution is a common method for solving this equation, which is used to model boundary layer flow over a flat plate. The equation is a third-order nonlinear differential equation, which can be challenging to solve analytically. Therefore, numerical methods such as the shooting method and Runge Kutta are often used to find solutions.

In the content provided, the Blasius equation is being used to simulate flow in a two-dimensional jet near the orifice of an exhaust. It is noted that the boundary conditions are different from those for flow over a flat plate, with a mixing thickness in the near field being taken into account. The goal of the simulation is to find the value of F'(infinity), which represents the velocity at infinity.

The link provided shows the use of the shooting method in Matlab to solve the Blasius equation, and it is stated that the numerical methods used will result in a normalized value of F'(infinity)=1. However, in this case, the desired value is actually 0 instead of 1. This is likely due to the fact that the boundary conditions for this specific case are different from those used in the typical flat plate scenario.

To adjust the solution to give a value of 0 at infinity instead of 1, you may need to modify the boundary conditions or the numerical methods being used. It would be helpful to consult with other researchers or experts in this field to determine the best approach for your specific simulation. Additionally, you may want to explore other numerical methods or software that can handle non-standard boundary conditions. Overall, it is important to carefully consider the assumptions and limitations of any numerical solution and to validate the results with experimental data or other methods.