Can anyone please help ?

im trying to compute the steady solutions for the stream function and scalar vorticity for a 2d flow around an infinite cylinder at RE = 10

here is the question:

Here is the code:

function [psi, omega] = flow_around_cylinder_steady
Re=10; 
%%%%% define the grid %%%%%
n=101; m=101; % number of grid points
N=n-1; M=m-1; % number of grid intervals
h=pi/M; % grid spacing based on theta variable
xi=(0:N)*h; theta=(0:M)*h; % xi and theta variables on the grid
%%%%% Initialize the flow fields %%%%%
psi=zeros(n,m);
omega=zeros(n,m);
psi(n,:)=exp(xi(n)) * sin(theta(:));
%%%%% Set relax params, tol, extra variables %%%%%
r_psi=1.8
r_omega=0.9
delta=1.e-08; % error tolerance
error=2*delta; % initialize error variable
%%%%% Add any additional variable definitions here %%%%%
...
...
%%%%% Main SOR Loop %%%%%
while (error > delta)
    psi_old = psi; omega_old = omega;
    for i=2:n-1
        for j=2:m-1
            psi(i,j)=exp(xi(i)) * sin(theta(j));
        end
    end
    error_psi=max(abs(psi(:)-psi_old(:)));
    omega(1,:)= (psi(3,j) - 8*psi(2,j)) * 1/(2*h^2); 
    for i=2:n-1
        for j=2:m-1
            omega_old(1,j)= (psi(3,j) - 8*psi(2,j)) * 1/(2*h^2); 
        end
    end
    error_omega=max(abs(omega(:)-omega_old(:)));
    error=max(error_psi, error_omega);
end
plot_Re10(psi);

The code to call the function is:

[psi, omega] = flow_around_cylinder_steady;

But i get this:

The server timed out while running your solution. Potential reasons include inefficient code, an infinite loop, and excessive output. Try to improve your solution.

is there any way to improve it ?

[Dyuman Joshi]

Your code is running the same loop again and overwriting the values.

For every iteration of the while loop, psi is the same. So the values are same and error will always be greater than delta, and your loop will run infinitely.

for i=2:n-1
    for j=2:m-1
        psi(i,j)=exp(xi(i)) * sin(theta(j));
    end
end

Check the formula again.

[Mohamed]

is there a better way to rewrite this :

psi(i,j)=exp(xi(i)) * sin(theta(j));

so that the loop will not run indefinetly ?

i can't change the gray areas.

[Samson]

Hi Mohamed,

I have exactly the same issue, and reviewed the class. and I don't see where is went wrong

did you solve it ?

[Samson]

omega_old seems to be one of the issue.. and my SOR doesnt seem to work /:

Answer 1

[Bhavesh Gyanchandani]

Here is the assignment code which i wrote

It is correct

function [psi, omega] = flow_around_cylinder_steady
Re=10; 
%%%%% define the grid %%%%%
n=101; m=101; % number of grid points
N=n-1; M=m-1; % number of grid intervals
h=pi/M; % grid spacing based on theta variable
xi=(0:N)*h; theta=(0:M)*h; % xi and theta variables on the grid
%%%%% Initialize the flow fields %%%%%
psi=zeros(n,m);
omega=zeros(n,m);
psi(n,:)=exp(xi(n))*sin(theta(:)); % Write the free stream bc here
%%%%% Set relax params, tol, extra variables %%%%%
r_psi=1.8; % Set the relaxation parameter here, psi equation
r_omega=0.9; % Set the relaxation parameter here, omega equation
delta=1.e-08; % error tolerance
error=2*delta; % initialize error variable
%%%%% Add any additional variable definitions here %%%%%
...
...
%%%%% Main SOR Loop %%%%%
while (error > delta)
    psi_old = psi; omega_old = omega;
    for i=2:n-1
        for j=2:m-1
            psi(i,j)=(1-r_psi)*psi(i,j)+(r_psi/4)*(psi(i+1,j)+psi(i-1,j)+psi(i,j+1)+psi(i,j-1)+h*h*exp(2*xi(i))*omega(i,j));% Write psi equation here
        end
    end
    error_psi=max(abs(psi(:)-psi_old(:)));
    omega(1,:)=(psi(3,:) - 8*psi(2,:))/(2*h^2); % Write the boundary condition here
    for i=2:n-1
        for j=2:m-1
            omega(i,j)=(1-r_omega)*omega(i,j)+(r_omega/4)*(omega(i+1,j)+omega(i-1,j)+omega(i,j+1)+omega(i,j-1)+(Re/8)*((psi(i+1,j)-psi(i-1,j))*(omega(i,j+1)-omega(i,j-1))-(psi(i,j+1)-psi(i,j-1))*(omega(i+1,j)-omega(i-1,j)))); % Write omega equation here
        end
    end
    error_omega=max(abs(omega(:)-omega_old(:)));
    error=max(error_psi, error_omega);
end
plot_Re10(psi);

[Pravar Agnihotri]

Were you able to do re = 60 one?

[屹林]

Can you tell me the unsteady flow at Re=60? I have been troubled by this problem for 3 weeks and I would be very grateful

[SANTHOSH]

but after run the function i couldnt be able to submit. it shows that " Variable psi has an incorrect value and Variable omega has an incorrect value"

[SANTHOSH]

@Bhavesh Gyanchandani. i got good plot. but after submitting it shows "Variable psi has an incorrect value and Variable omega has an incorrect value". can you pls help me to overcome this issue