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

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.

#EDIT: Confirming that the equations used above were incorrect

[SANTHOSH]

this is the full code which i have used for the question: Compute the steady solutions for the stream function and scalar vorticity for a two-dimensional flow around an infinite cylinder at Re = 10. Plot the stream function.

Still i got same issue eventhough i got the perfect plot. can anyone pls pls tell me why i ouldnt be able to submit, why it shows that "Variable psi has an incorrect value, Variable omega has an incorrect value". hereby i have attached the plot which i got today

@Sam Chak @Cris LaPierre @Mohamed @Samson @LeoAiE

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);
function plot_Re10(psi)
    Re = 10; 
    %%%%% xi-theta grid %%%%%
    n = size(psi, 1); 
    m = size(psi, 2);
    N = n - 1; 
    M = m - 1;
    h = pi / M; % grid spacing 
    xi = (0:N) * h; 
    theta = (0:M) * h; 
    [XI, THETA] = meshgrid(xi, theta);

    %%%%% x-y grid %%%%%
    nx = 640; 
    ny = 480 / 2; % number of pixels in x and half of y
    xmin = -1.5; 
    xmax = 2.5; 
    ymax = (xmax - xmin) * ny / nx; 
    ymin = -ymax;
    x = linspace(xmin, xmax, nx);  % Adjusted size to be nx instead of nx+1
    y = linspace(0, ymax, ny);     % Adjusted size to be ny instead of ny+1
    [X, Y] = meshgrid(x, y);

    %%%%% construct interpolation points %%%%%
    xi_i = 0.5 * log(X.^2 + Y.^2);
    theta_i = wrapTo2Pi(atan2(Y, X));

    %%%%% interpolate %%%%%
    psi_xy = interp2(XI, THETA, psi', xi_i, theta_i, 'linear', 0);

    %%%%% set psi to zero inside cylinder %%%%%
    psi_xy(xi_i < 0) = 0;

    %%%%% scale contour levels %%%%%
    %%%%% negative values have same range as positive values %%%%%
    psi_min = min(psi_xy(:));
    psi_max = max(psi_xy(:));
    psi_xy(psi_xy < 0) = psi_xy(psi_xy < 0) / abs(psi_min);
    psi_xy(psi_xy > 0) = psi_xy(psi_xy > 0) / abs(psi_max);

    %%%%% set colormap for contours %%%%%
    levels = linspace(-1, 1, 1000);
    cmap = flipud(jet(length(levels)));
    colormap(cmap);

    %%%%% plot color contours %%%%%
    imagesc(x, y, psi_xy); 
    hold on;
    imagesc(x, -y, -psi_xy); % negative values of y

    %%%%% plot contour lines %%%%%
    v = [-0.9:0.2:-0.1, 0, 0.0005, 0.001, 0.002:0.004:0.01, 0.02:0.04:0.9];
    contour(X, Y, psi_xy, v, 'LineColor', 'k');
    contour(X, -Y, -psi_xy, -v, 'LineColor', 'k');

    %%%%% draw black circle for cylinder %%%%%
    t = linspace(0, 2*pi, 1000);
    a = cos(t); 
    b = sin(t);
    fill(a, b, [0 0 0]);

    %%%%% neaten plot %%%%%
    set(gca, 'YDIR', 'normal');
    axis([xmin xmax ymin ymax]); 
    set(gcf, 'color', 'w'); 
    axis off; 
    axis equal;
    text(xmin + 0.75*(xmax - xmin), ymin + 0.08*(ymax - ymin),...
        ['Re=', num2str(Re, '%3.0f')], 'FontSize', 22, 'color', 'k');

[Cris LaPierre]

Assuming this exercise is coming from Week 2 of Mathematics for Engineers: The Capstone Course, I can't duplicate the error. I'd suggest trying to submit your solution again.

[SANTHOSH]

@Cris LaPierre @Sam Chak @Walter Roberson

Coursera Credentials

[SL: snipped user name and password. You shouldn't post them publicly.]

Assignment link page: https://learningtool.mathworks.com/launch

Hi all members here, i have been trying this assignment for more than 2 months, still i cant submit, even though i called instructor, he told me to check the codes, i ghave been trying codes for infinity times. so anyone pls help me to sort out this, even though i got hr correct plot i couldnt be able to submit. thats why here i am uploading my login credentials. pls someone help me for this, its been more than two months as of now....its my kind request. hereby i have attached thje code for function and code to call the function. once i have run the function in the above mentioned link, i got the correct plot, but still i couldnt be able to submit, and the instructor aslo told me that he cant help me. finally this is my only hope, so pls guys help me to sort this out

Question: Compute the steady solutions for the stream function and scalar vorticity for a two-dimensional flow around an infinite cylinder at Re = 10. Plot the stream function

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; % 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)=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);

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);

[Walter Roberson]

The

...
...

parts are suspicious.

The behaviour is well defined:

...
...
%%%%% Main SOR Loop %%%%%

is to be executed as-if the code had been

  %%%%% Main SOR Loop %%%%%

but it is so uncommon to continue into a comment statement that I have to wonder whether the behaviour is deliberate.

[Sam Chak]

Hi @SANTHOSH

This issue is most likely related to the MATLAB Grader. What did the Course Administrator advise you to do? Are you expected to submit the image in a specific pixel resolution and format (i.e., JPG, PNG) so that the Grader can evaluate the RGB values of each pixel?

[Cris LaPierre]

You have pasted 2 versions of the function. Be sure you are only submitting one. As for which, I already let you know the code you shared previously worked.

[SANTHOSH]

@Sam Chak @Cris LaPierre My course instructor told me that its ur side that has to be done correctly. i have uploaded two version because one is function and another one is code to call function, thats what that page look alike. ....is there anyother way to sort out this issue...

[Cris LaPierre]

In your most recent post, you shared two functions named flow_around_cylinder_steady. The first one appears to be the one Mohamed shared at the top of this thread, and the second is the one you shared previously. The code to call your function is just [psi, omega] = flow_around_cylinder_steady

This is not an issue with Grader, only with how you have been entering your solution into Grader. I'd suggest going line by line comparing your solution to the template in the problem. Make sure you copy/paste everything you added to the template code back into the appropriate line in Grader before submitting.

[Cris LaPierre]

@SANTHOSH, I see you asking for help on this in multiple posts on Answers. Again, based on my observations, the issue is what I point out above - you have not actually entered the solution correctly into the assessment. Please follow the steps above, submit, and, if your answer is still incorrect, take a screenshot of the screen showing your code and the assessment results and share that here.

[SANTHOSH]

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, :) = 1; % Free stream boundary condition

r_psi = 1.0; % Relaxation parameter for psi equation

r_omega = 1.0; % Relaxation parameter for omega equation

delta = 1.e-08; % Error tolerance

error = 2*delta; % Initialize error variable

%%%%% Additional variable definitions %%%%%

x = xi*cos(theta);

y = xi*sin(theta);

%%%%% Main SOR Loop %%%%%

while (error > delta)

psi_old = psi; omega_old = omega;

% Update psi

for i = 2:n-1

for j = 2:m-1

if (x(i, j)^2 + y(i, j)^2 < 1)

psi(i, j) = 0; % No-slip boundary condition on cylinder

else

psi(i, j) = (1 - r_psi)*psi_old(i, j) + r_psi/4*(psi_old(i+1, j) + psi_old(i-1, j) + psi_old(i, j+1) + psi_old(i, j-1));

end

end

end

error_psi = max(abs(psi(:) - psi_old(:)));

% Update omega

omega(1, :) = 0; % Set vorticity to zero at the outer boundary

for i = 2:n-1

for j = 2:m-1

if (x(i, j)^2 + y(i, j)^2 < 1)

omega(i, j) = 0; % No vorticity inside the cylinder

else

omega(i, j) = (1 - r_omega)*omega_old(i, j) + r_omega/4*(omega_old(i+1, j) + omega_old(i-1, j) + omega_old(i, j+1) + omega_old(i, j-1)) - (psi(i, j+1) - psi(i, j-1))/(2*h);

end

end

end

error_omega = max(abs(omega(:) - omega_old(:)));

error = max(error_psi, error_omega);

end

plot_Re10(psi);

end

[Cris LaPierre]

Please share a screenshot from Coursera so we can see how you are entering this.