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start-up flow poiseuille w/finite difference

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Old   October 12, 2010, 14:23
Default start-up flow poiseuille w/finite difference
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I'd appreciate if someone with matlab knowledge could help me.
I'm trying to solve the above mentioned pde in matlab.

I have the following code:

h = 1;
dr = 0.01; dt = 0.01;
nmax = 4000; epsilon = 0.0001;
r = [0:dr:h];
t = [0:dt:h];
n1 = fix(h/Dr)+1;
m1 = fix(h/Dt)+1;
% Initialize solution matrices
velocity = zeros(n1,m1)
velocityN =velocity
% Iterative process for the solution
for k = 1:nmax
% boundary conditions:
velocityN(:,n1) = zeros(n1,1);

% Calculate velocityN in interior points
for i = 2:n1-1
for j = 1:m1
velocityN(i,j+1)= (beta*(1-(1/(2*i)))*velocity(i-1,j)+(1-2*beta)*velocity(i,j)+beta*(1+1/(2*i))*velocity(i+1,j));
% Check convergence
nfail = 0;
for i = 1:n1
for j = 1:m1
if abs(velocityN(i,j)-velocity(i,j))>epsilon
nfail = nfail+1;

if nfail > 0
velocity = velocityN;
fprintf('No convergence after %i iterations.',k);
[X,Y] = meshgrid(r,t);

however, for r=0 I have dv/dr=0 as the second boundary condition.

How do I incorporate this into the program.
dV/dr should be:

Same with the initial condition say a constant 10 atm/cm is applied at t=0


Last edited by piper10; October 12, 2010 at 14:40.
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