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

Answer 2

[Cris LaPierre]

This error message means your code is taking too long to execute. This is usually caused by accidentally creating an infinite loop.

As a side note this appears to be an assignment. Are you aware and ok with posting this here knowing that it can't be deleted?

The gray lines in your screenshot are locked lines, meaning they are lines your instructor has written for you. You can't (and likely shouldn't) change those. That means you are left with what you have written for psi(i,j), omega(1,:), and omega_old(1,j). I'm assuming your equations are correct but just contain a syntax error somewhere.

A quick inspection leads me to believe your for loops should be calculating omega, and not omega_old. It also seems odd to be hardcoding the row to 1 inside nested for loops. Perhaps you should be indexing the same as you did for psi?

[Mohamed]

i am aware and am ok with posting this knowing that it cant be deleted.

is it possible that you could show me how to code it ?

i would be very thankful if you do.

[Cris LaPierre]

The infinite loop is because you are using the wrong variable name inside your for loop. Fix that, and the error message you are getting will go away.

[Mohamed]

Could you please specify which line it is and the correct way to write it ?

I will be very thankful for your help

[Cris LaPierre]

Please reread my original answer.

[Mohamed]

Could you please help me rewrite the specific part of the code ?

I will be extremely thankful for your help please.

[Cris LaPierre]

I have given you the information you need to be able to do this yourself. Please make an attempt and let us know what happened.

[Mohamed]

Hi

this is what i have ended up with:

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(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);

but i get this:

could you please help me find out where i went wrong ?

[Cris LaPierre]

Consider sharing the problem description, too.

[Mohamed]

I've added the descriptin to the main question

here is the question :

[Cris LaPierre]

That wasn't as helpful as I was hoping.

Are you sure you are using the correct equations for psi and omega? For help with fluids, I suggest turning to your instructor. Once you have the correct equations, we can certainly help you with implementing them in MATLAB.