CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Blasius Equation Discretization:

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   April 16, 2011, 12:59
Default Blasius Equation Discretization:
  #1
New Member
 
Join Date: Apr 2011
Posts: 2
Rep Power: 0
john_t is on a distinguished road
Ive been trying the discretization of Blasius equation: f'''+1/2 ff''=0 using the center scheme (finite difference) but im not able to do it correctly. Any help or suggestions? Thanks
john_t is offline   Reply With Quote

Old   April 17, 2011, 06:18
Default
  #2
New Member
 
Nikolay Vinnichenko
Join Date: Nov 2010
Posts: 14
Rep Power: 15
nickvinn is on a distinguished road
I solved it with such discretizations:
f''''=(f(i+1)-3f(i)+3f(i-1)-f(i-2))/h^3 (take central differences for second derivatives in (i-1) and i, totally centered at (i-1/2)),
f''=(f(i-2)-2f(i-1)+f(i))/h^2 (centered at (i-1)),
f=f(i-1),
resulting in equation:
f(i+1)=3f(i)-3f(i-1)+f(i-2)-f(i-1)(f(i-2)-2f(i-1)+f(i))h/2
This variant is a little bit biased, but the performance is OK.At least when you have to solve it only before main computations in order to obtain initial laminar boundary layer solution.
nickvinn is offline   Reply With Quote

Old   April 17, 2011, 16:39
Default
  #3
New Member
 
Join Date: Apr 2011
Posts: 2
Rep Power: 0
john_t is on a distinguished road
Quote:
Originally Posted by nickvinn View Post
I solved it with such discretizations:
f''''=(f(i+1)-3f(i)+3f(i-1)-f(i-2))/h^3 (take central differences for second derivatives in (i-1) and i, totally centered at (i-1/2)),
f''=(f(i-2)-2f(i-1)+f(i))/h^2 (centered at (i-1)),
f=f(i-1),
resulting in equation:
f(i+1)=3f(i)-3f(i-1)+f(i-2)-f(i-1)(f(i-2)-2f(i-1)+f(i))h/2
This variant is a little bit biased, but the performance is OK.At least when you have to solve it only before main computations in order to obtain initial laminar boundary layer solution.
can this be solved using C++ or Fortran ??
Any idea about Tri Diagonal matrix discretization ??
john_t is offline   Reply With Quote

Old   April 18, 2011, 03:22
Default
  #4
New Member
 
Nikolay Vinnichenko
Join Date: Nov 2010
Posts: 14
Rep Power: 15
nickvinn is on a distinguished road
Well, I wrote my code in Fortran. It is quite simple.
There is no tridiagonal matrix here. The discretization is explicit: if you know values in 3 neighbouring points e.g. f(0), f(h) and f(2h), then you obtain f(3h) according to above formula. Then you get f(4h), etc. Of course, you need to know values in 3 points at the left border to start the process. You have the boundary conditions f(0)=f'(0)=0. So, f(0)=f(h)=0. Since this is the 3-rd order equation, you need one more initial condition for Cauchy problem. So, you can set some value for the second derivative f''(0) and thus obtain f(2h). Then, you get the solution for all points and find out if the boundary condition at the right boundary f'(infinity)=1 is OK. Of course, it is not, and you adjust the value of f''(0), and try once more. This is called the shooting method, you can find it in any elementary computational methods textbook.
nickvinn is offline   Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
mass flow in is not equal to mass flow out saii CFX 12 March 19, 2018 06:21
Calculation of the Governing Equations Mihail CFX 7 September 7, 2014 07:27
Blasius equation help :( johnt447 Main CFD Forum 0 March 18, 2011 18:57
Constant velocity of the material Sas CFX 15 July 13, 2010 09:56
Space and time discretization of Euler equation Hooman Main CFD Forum 2 June 6, 2010 09:30


All times are GMT -4. The time now is 12:40.