Re: Numerical Algorithm for Blasius Equation
- To: mathgroup at smc.vnet.net
- Subject: [mg37680] Re: Numerical Algorithm for Blasius Equation
- From: bghiggins at ucdavis.edu (Brian Higgins)
- Date: Fri, 8 Nov 2002 02:15:42 -0500 (EST)
- References: <aqdkp9$10a$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Ganesh, You can solve Blasius' equation using a shooting method as
shown below. For those not familiar with fluid mechanics the BCs are
f[0]=0,f'[0]=0,f[Infinity]=1. In the shooting method I truncate the
domain to x=8; The third order ODE is converted into a system of 3
first order ODEs
system[p_] = {2*w'[x] == -f[x]*u'[x], f'[x] ==
u[x], u'[x] == w[x], f[0] == 0, u[0] == 0, w[0] == p};
myODEsoln[p_] := NDSolve[system[p], {f[x], u[x], w[x]},
{x, 0, 8}]
yend[p_] := u[x] /. myODEsoln[p] /. x -> 8
bc = FindRoot[First[yend[p]] == 1, {p, 1, 1.1}];
Plot[Evaluate[{f[x], u[x], w[x]} /. myODEsoln[p /. bc]],
{x, 0, 8}, AxesLabel -> {"x", "f,u,w"},
PlotStyle -> {RGBColor[0, 0, 1], RGBColor[1, 0, 0],
RGBColor[1, 0, 1]}];
Cheers,
Brian
Ganesh Chandra Bora <gcbora at ksu.edu> wrote in message news:<aqdkp9$10a$1 at smc.vnet.net>...
> Hi,
>
> I am Ganesh. I am trying to find a Numerical Algorithm to
> Solve Blasius Equation for Boundary layer: ff''+2f'''=0
> Can anyone please help me with a computer program to
> solve the equation.
>
> Thank you very much.
> Ganesh