solution for steady flow at Re = 10. in coursera i took mathematics for engineers.for that i need to solve an assignment. For this code i cant get correct stream & vorticity

flow_around_cylinder_steady

psi = 101x101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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omega = 101x101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Unrecognized function or variable 'plot_Re10'.

Error in solution>flow_around_cylinder_steady (line 49)
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,:)=0 % Free stream boundary condition (psi = 0 at the top edge)
    
    %%%%% 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_old(i, j) + ...
                    r_psi * 0.5 * (psi_old(i+1, j) + psi_old(i-1, j) + ...
                    psi_old(i, j+1) + psi_old(i, j-1) - h^2 * omega(i, j));
            end
        end
        error_psi=max(abs(psi(:)-psi_old(:)));
        omega(1,:)=0 % Boundary condition at theta = 0
        for i=2:n-1
            for j=2:m-1
                omega(i,j)=... % (1 - r_omega) * omega_old(i, j) + ...
                    r_omega * ( (omega_old(i+1, j) + omega_old(i-1, j) + ...
                    omega_old(i, j+1) + omega_old(i, j-1) - ...
                    (4 - (2/h^2)) * omega_old(i, j)) / (4 - (2/h^2)) );
            end
        end
        error_omega=max(abs(omega(:)-omega_old(:)));
        error=max(error_psi, error_omega);
    end
    plot_Re10(psi);
end

Please refer to page 59 (64/69) of the PDF document for the 'plot_Re10' custom plotting function.

https://www.math.hkust.edu.hk/~machas/flow-around-a-cylinder.pdf

[SANTHOSH]

still i cant get solution

[SANTHOSH]

@Sam Chak i could'nt be able to get solution from thay pdf. please give me details about equation sam, i am really thankfull to you

[Sam Chak]

Hi @SANTHOSH,

I understand that you are a high-end Application User, focusing on applying the given template code with your specific engineering math problem, rather than writing the full code.

However, the error message {Unrecognized function or variable 'plot_Re10'} tells you that the MATLAB code provided in your question is incomplete, as the no-input flow_around_cylinder_steady function (which should be a script) needs to call the plotting function named plot_Re10().

To assist you further, please provide the entire MATLAB code, including the plotting function. You can do this by clicking the indentation icon and copying/pasting the formatted code into the provided grey field.

This will allow CFD experts or @LeoAiE to review the complete code and provide a more thorough response to your question.

[Sam Chak]

Some users have posted this problem in 2022, but no satisfactory answer has been accepted.

The URLs provided

• https://www.mathworks.com/matlabcentral/answers/1815915-can-anyone-please-help
• https://www.mathworks.com/matlabcentral/answers/1820840-can-anyone-please-help-me-with-this

contain the context for the original query. The full code is expected to generate the reported result.

[Sam Chak]

Hi @SANTHOSH

Have you had the opportunity to post the MATLAB code for plot_Re10 yet?

[SANTHOSH]

no i have not

[SANTHOSH]

can anyone pls help me on this. i got the plot, but still i couldnt be able to submit. here is the complete code which i have used. @LeoAiE @Sam Chak @Bhavesh Gyanchandan. i culdnt be able to submit it. it shows "Variable psi has an incorrect value and Variable omega has an incorrect value". i have attached my screen thank you in advance

[psi, omega] = flow_around_cylinder_steady;

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
%psi
%plot_Re10(psi);
figure(1)
contourf(xi,theta,psi.')
colorbar
figure(2)
contourf(xi,theta,omega.')
colorbar
end

[LeoAiE]

Hi,

I suggest you post the exact question from the assigment or read the question carefully they might be asking for spcific things. Or if you sure you have everything covered in your solution please contact their tech support and explain tthe issue.

[SANTHOSH]

@LeoAiE 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

[SANTHOSH]

@LeoAiE @Sam Chak 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

[Torsten]

And where do you take care of the inscribed cylinder in your code ? I only see a rectangular region in which you compute "psi" and "omega".

[SANTHOSH]

@Torsten. so how to overcome this, could you please help to sort out this

Answer 1

[LeoAiE]

Hi there!

This is not exact solution you looking for but more to help you think about the issue you are facing!

[psi, omega] = flow_around_cylinder_steady

Warning: Contour not rendered for constant ZData

psi = 101x101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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omega = 101x101

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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function [psi, omega] = flow_around_cylinder_steady
    Re = 10;

    % Define the grid
    n = 101; 
    m = 101; 
    N = n - 1; 
    M = m - 1; 
    h = 2 * pi / M; 
    xi = linspace(0, 1, N+1); 
    theta = linspace(0, 2*pi, M+1); 

    % Initialize the flow fields
    psi = zeros(n, m);
    omega = zeros(n, m);
    
    % Boundary conditions for psi (streamfunction)
    psi(n, :) = 0; % Top boundary (free stream)
    psi(1, :) = 0; % Bottom boundary (cylinder surface)
    psi(:, 1) = psi(:, 2); % Left boundary (symmetry)
    psi(:, end) = psi(:, end-1); % Right boundary (symmetry)
    
    % Boundary conditions for omega (vorticity)
    omega(1, :) = -2 * psi(2, :) / h^2; % No-slip condition at cylinder surface
    omega(:, 1) = omega(:, 2); % Left boundary (symmetry)
    omega(:, end) = omega(:, end-1); % Right boundary (symmetry)
    
    % Set relax params, tol, extra variables
    r_psi = 1.8; 
    r_omega = 0.9; 
    delta = 1.e-08; 
    error = 2 * delta; 

    % Main SOR Loop
    while (error > delta)
        psi_old = psi; 
        omega_old = omega;
        
        % Update psi
        for i = 2:n-1
            for j = 2:m-1
                psi(i, j) = (1 - r_psi) * psi_old(i, j) + ...
                    r_psi * 0.25 * (psi_old(i+1, j) + psi_old(i-1, j) + ...
                    psi_old(i, j+1) + psi_old(i, j-1) - h^2 * omega(i, j));
            end
        end
        error_psi = max(abs(psi(:) - psi_old(:)));
        
        % Update omega
        for i = 2:n-1
            for j = 2:m-1
                omega(i, j) = (1 - r_omega) * omega_old(i, j) + ...
                    r_omega * 0.25 * (omega_old(i+1, j) + omega_old(i-1, j) + ...
                    omega_old(i, j+1) + omega_old(i, j-1) - ...
                    (4 - h^2) * omega_old(i, j)) / (4 - h^2);
            end
        end
        error_omega = max(abs(omega(:) - omega_old(:)));
        error = max(error_psi, error_omega);
    end
    
    plot_Re10(psi);
end

%% Code snippet for plotting 'psi'
function plot_Re10(psi)
    % This function plots the streamfunction psi
    figure;
    contourf(psi', 20); % Transpose psi to get correct orientation
    colorbar;
    title('Streamfunction \psi for Re = 10');
    xlabel('x');
    ylabel('y');
end

Answer 2

[Sam Chak]

Hi @SANTHOSH

The code for plot_Re10() function is based on the video lecture of Prof. Jeffrey Chasnov.

https://www.youtube.com/watch?v=oTyLgQX7sRU

[psi, omega] = flow_around_cylinder_steady;

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
    %psi
    plot_Re10(psi);
    % figure(1)
    % contourf(xi,theta,psi.')
    % colorbar
    % figure(2)
    % contourf(xi,theta,omega.')
    % colorbar
end

%% Code by Prof. Jeffrey Chasnov
function plot_Re10(psi)
    % Reynolds number (design parameter)
    Re      = 10;
    
    % setup the 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);
    
    ... (Code is very long. Please refer to Prof. Jeffrey Chasnov's video lecture)
end

[SANTHOSH]

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+1); y=linspace(0,ymax,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);
%%%%% 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 balck 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');

[SANTHOSH]

i followed the thing by prof.jeff, in output it shows not enough input arguments. can anyone pl pls give me code to solve tis question, i am stucked here for past one month, really i dont know ho to solve this, so anyone pls give me correct code for this @Sam Chak @LeoAiE

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+1); y=linspace(0,ymax,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);
%%%%% 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 balck 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');

[SANTHOSH]

i kindly requesting here to help me to solve this problem, eventhough i got the correct plot, i couldnt be able to submit it, here is the attachment of my screenshot of submission page,,,anyone pls pls pls kindly 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.

Please see the attachment here

[Sam Chak]

Hi @SANTHOSH

The "auto" grader probably cannot process the image-based submission.

I believe you need to submit the matrix values for the variables 'psi' and 'omega'.

function [psi, omega] = flow_around_cylinder_steady

[SANTHOSH]

hi @Sam Chak thank you so much for your time and consideration.

but how can i submit it in matrix form

[Sam Chak]

Hi @SANTHOSH

This is probably a technical issue of the grader. Perhaps, inform your Professor about issue so that he can liaise with the Coursera technical team.

Answer 3

[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.