Visualize CFD data in a 2D mesh

I have a N-by-M 2D mesh with already assigned values of the quantity for each one of the N*M cells (i = 1, 2, 3, ..., N*M).

I have the nodes coordinates but I can't find a way to "plot" each quantity as a color in the respective i cell.

I have tried to use 'pcolor' and 'surf' but the vectors x and y that define the mesh coordinates are always 1 unit too big...

Do you know how I could solve this problem?

Thank you!

[Walter Roberson]

You talk about N*M cells. Is the implication that you have (N+1) y coordinates and (M+1) x coordinates? Or that you have an (N+1) by (M+1) array of x coordinates and another the same size of y coordinates?

You have coordinates of corners, including the corners at the end of the cell, but your mesh calculation is calculating on faces ?

[António Rebelo]

Yes, I have (N+1) different y coordinates and (M+1) different x coordinates. The value of is calculated at the center of each cell.

Fortunately I managed to fix the problem by using the function imagesc.

It does exactly what I want by using the values of and the two vectors that contain the x and y coordinates of the cell midpoints.

Thank you a lot for the help!

[Walter Roberson]

image and imagesc() ignores the coordinate vectors, except for the first and last coordinate in the vector. You cannot use imagesc() for the case where the nodes are not equally spaced.

Also note that the coordinates you pass to image() or imagesc() are treated as the coordinates of the center of the pixel. If you want to use the coordinates as the coordinates of the edge then you need to make an adjustment to the coordinates

Answer 1

[Fabio Freschi]

I assume you have the connectivity of your cells, if not you can create it with delaunay. Then use the low level funciton patch. Note that patch works also with four-node elements.

% dummy data
x = linspace(-1,1,30);
y = linspace(0,3,100);
[X,Y] = meshgrid(x,y);

% points coordinates
P = [X(:) Y(:)];
% create triangulation
T = delaunay(P);

% scalar function
phi = P(:,1).^2+P(:,2).^2;

% plot
figure
patch('Faces',T,'Vertices',P,'FaceVertexCData',phi,...
    'EdgeColor','none','FaceColor','interp');

[António Rebelo]

Thank you. It looks like a really good option, I'll definitly use that.

[Fabio Freschi]

Note that here the function ϕ is node-based

[Fabio Freschi]

In case it solvews your problem, please accept my answer

[António Rebelo]

I will try it today. Once it is done, I'll accept it. Thank you

[António Rebelo]

@Fabio Freschi In this case the mesh is made up by rectangles (not all the same size). 'delaunay' does not work,right? How do I assemble the connectivity matrix for rectangular cells?

[Fabio Freschi]

In theory, you can use triangles as weel, but it would be easier to have the connectivity of rectangles. In some way you should have the connectivity available, in any case you can create it on the fly

% dummy data
npx = 30;
npy = 100;
x = linspace(-1,1,npx);
y = linspace(0,3,npy);
[X,Y] = meshgrid(x,y);

% points coordinates
P = [X(:) Y(:)];

% create connectivity
nod = reshape(1:npx*npy,npy,npx).';
nElm = (npx-1)*(npy-1);

T = zeros(nElm,4);
T(:,1) = reshape(nod(1:npx-1,1:npy-1),nElm,1);
T(:,2) = reshape(nod(2:npx,1:npy-1),nElm,1);
T(:,3) = reshape(nod(2:npx,2:npy),nElm,1);
T(:,4) = reshape(nod(1:npx-1,2:npy),nElm,1);

% barycenters
B = (P(T(:,1),:)+P(T(:,2),:)+P(T(:,3),:)+P(T(:,4),:))/4;

% scalar function evaluated at barycenters
phi = B(:,1).^2+B(:,2).^2;

% plot
figure
patch('Faces',T,'Vertices',P,'FaceVertexCData',phi,...
    'EdgeColor','k','FaceColor','flat');