plotting streamlines from velocity components

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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

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Michael Wales 2018-5-1

@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 2018-5-1

编辑：Wick 2018-5-1

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.

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Answer 1

Wick 2018-5-1

编辑：Wick 2018-5-1

在 MATLAB Online 中打开

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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