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Old   May 28, 2010, 02:32
Question Finite Difference in MATLAB Help
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Abe
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Hi all,

I am working on a class project, which requires me to model blasius equation and pohlhausen eqaution (I posted regarding this a while back). I am finally getting back to it again. So for the blasius equation, I got it to work with the shooting method, and now working on the pohlhausen equation with finite difference and need help with it. To be honest, I took numerical methods 5-6 years ago, and vaguely remember it. I have looked online, and none help in matlab programming. I know I have to use for loop, but lost. Also, I don't know how would I implement the infinity boundary condition. Here's the POL eq:

dT/(dETA)^2+(Pr/2)f(dt/dETA)=0 with B.C. T(0) = 0, T(inf) = 1

Here's my finite difference form:

(T(i-1)-2T(i)+T(i+1))/(deltaETA)^2 + (Pr/2)(f)(T(i+1)-T(i-1))/(2*deltaETA) = 0

Then I collected the like terms:

T(i-1)[(1/(deltaETA)^2 - (Pr/2)(f)(1/(2*deltaETA))] + T(i)[-2] + T(i+1)[(1/(deltaETA)^2 - (Pr/4)(f)(1/(4*deltaETA))] = 0

Now, I have no idea to implement this into MATLAB

In the above equation, f is obtained from the Blasius solution, and here's my code for it.

clc
clear all

ti = 0.0;
tf = 8.0;
tintval = [ti tf]
delta = 0.1;

guess1 = 0.0;
guess2 = 0.0;
guess3 = 0.33206;

bcinit = [guess1 guess2 guess3];

[ETA,f]=ode45('BlasiusFunc',tintval,bcinit);
[ETA,f]

plot(ETA,f(:,2),'-k')
grid on

xlabel('ETA')
ylabel('Dimensionless velocity - u/U_i_n_f')
title('Blasius Equation - Laminar Flow Over A Flat Plate')

ETAFIT = [0:delta:8];
fFIT = interp1(ETA,f,ETAFIT,'spline'); % display in regular interval

[ETAFIT,fFIT]

CODE END

At the end of the code, I am using the interp1 function to make the [ETA f] at regular interval so use it in POL equation, but I end up getting this error:

??? Error using ==> horzcat
CAT arguments dimensions are not consistent.

Error in ==>Blasius at 39
[ETAFIT,fFIT]

I think it has to do something with the size of the matrix because ETA has 1 column, while f has 3 columns.

Can someone please help?

Thank you
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