plotting streamlines from velocity components

I am having trouble creating streamlines in MATLAB. I have: (1) x,y,z coordinates and (2) velocity components (Vx, Vy, Vz).

I have no trouble plotting the quiver (arrow) plot, but I cannot figure out the streamlines.

Any help would be greatly appreciated.

Thanks,

-Mike

[Wick]

Have you tried the 'streamline' command? The example in the help is decent. The trick is you've got to pick the (x, y, z) points to start from and it will "connect the dots" from there until the streams pass outside of the range of the data. It doesn't automatically create a new streamline for every data point.

[Michael Wales]

@Chad, my problem is that MATLAB wants U,V,W to be 3x3 matrices. My velocity components (Vx,Vx,Vz) are a single column each. I can combine them to get a 3x1 matrix, but not a 3x3 .

[Wick]

So your X and and Y are not plaid (as if created by meshgrid).

Are you fields continuous, differentiable, and functions? That is, for every (x,y,z) value, do you only have one (u,v,w)? If so, your best bet is to create a 3D plaid grid using ndgrid covering the (x,y,z) domain of interest. Then use some sort of interpolation to fill in the velocities for every point. The function 'scatteredInterpolant' is probably your friend here. The you can use commands like mesh, surf, slice, streamlines, and others that expect 2- or 3D rectangular data to work with.

Edit: I'm not sure my comment addressed your concern. Can you upload a .mat file with some values I can try to work with? I can then write you some code that will manipulate it properly.

Answer 1

[Wick]

Michael,

I've got some code below that plots slices and streamlines for your data but the data itself is odd. It looks like you've got an impeller blowing into a tank but the velocity vector that's coming out of it is normal to the impeller. However, that's what the quiver arrows show so the streamlines follow the arrows. So at least, you can now look at your streamlines as you work on the velocities (if necessary.

Good luck!

    clearvars
    load 'velocity components.mat'

    mag_V = sqrt(Vx.^2 + Vy.^2 + Vz.^2);

    % Filtering out zero velocity walls.
    index = mag_V > 0.1;

    xx = x(index);
    yy = y(index);
    zz = z(index);
    Vxx = Vx(index);
    Vyy = Vy(index);
    Vzz = Vz(index);

    FVx = scatteredInterpolant(xx,yy,zz,Vxx,'linear','none');
    FVy = scatteredInterpolant(xx,yy,zz,Vyy,'linear','none');
    FVz = scatteredInterpolant(xx,yy,zz,Vzz,'linear','none');

    % This is a very ugly grid for your problem but it works.
    % A cylindrical grid would probably be more resource efficient

    elements = 40; % how many subdivisions per dimensions.
    % Mind you, this is 3D. Total memory gets large fast

    [X3, Y3, Z3] = meshgrid(linspace(min(x),max(x),elements),...
        linspace(min(y),max(y),elements),...
        linspace(min(z),max(z),elements));
    V3x = FVx(X3,Y3,Z3);
    V3y = FVy(X3,Y3,Z3);
    V3z = FVz(X3,Y3,Z3);

    mag_V3 = sqrt(V3x.^2 + V3y.^2 + V3z.^2); % velocity vector magnitude

    starting_x = zeros(5,5); % starting points for streamlines
    [starting_y, starting_z] = meshgrid(linspace(-0.005,.005,5), ...
        linspace(-0.005,.005,5));

    figure(1)
    clf

    plot3(x,y,z,'.k','MarkerSize',4);
    hold on
    quiver3(x,y,z, Vx,Vy,Vz);

    h = slice(X3,Y3,Z3,mag_V3,[],0,-0.02:.02:0);
    set(h,'EdgeColor','w','FaceAlpha',0.75');

    h = streamline(X3,Y3,Z3,V3x,V3y,V3z,starting_x,starting_y,starting_z);
    set(h,'LineColor','r','LineWidth',4);

    axis equal
    grid on
    hold off

[Michael Wales]

@Chad...thank you very much, it works great.

Answer 2

[Michael Wales]

Here is my data and code for the quiver plot:

figure (202) plot3(x,y,z,'ok'); hold on;

quiver3(x,y,z, Vx,Vy,Vz);

- -

You are correct, I only have one (u,v,w) for every (x,y,z) value

Answer 3

[Syed Fazuruddin]

How to draw a wavy wall of a square in matlab