stream lines for discrete data set of velocities

I had a set of discrete points whose velocities are known and postions and velocities will change with time , I want to use the streamline function, but in that , the condition is that the data sets should be monotonic . Is there any way to obtain stream lines for discrete particle locations which changes with time .

Answer 1

[Bjorn Gustavsson]

Your question is a bit too vague. Or rather, the input-data you have is a bit vaguely described. The answer depends on how you'll specify that input...

If you have a reasonably low number of particles and their trajectories (something like ) you could simply go for a looped version of plot3, maybe something like:

clf
hold on
E_kin = squeeze(sum(v(:,1,:).^2,3));
g = (E_kin-min(E_kin))/(max(E_kin)-min(E_kin));
r = (r(:,1,1)-min(r(:,1,1)))/(max(r(:,1,1))-min(r(:,1,1)));
b = (r(:,1,2)-min(r(:,1,2)))/(max(r(:,1,2))-min(r(:,1,2)));
for i1 = num_particles:-1:1
    ph(i1) = plot3(r(i1,:,1),r(i1,:,2),r(i1,:,3));  
    set(ph(i1),'color',[r(i1),g(i1),b(i1)])
end

That would plot the trajectories of all your particles in 3-D with the trajectories coloured according to their

initial x-y position (red and blue), and initial kinetic energy (green).

On the other hand that seems like such an obvious solution, so you might such a large number of particles that this doesnt work. For that perhaps you can use local averaged velocities, but that would involve a lot of looping:

for each time-step for each sub-volume, find all all particles inside, calculate their average velocity, when done with all subvolumes, you should be able to use streamline3, then on to next time-step

HTH

[bharathi Dasari]

I had 75 spherical particles in a square whose positions will be changing with respect to time ,at every time step i'm having velocity data for every particle.i was trying to assign velocities to cells by dividing the square in to smaller grids ,for this i was not able to draw streamlines and velocity contour

[Bjorn Gustavsson]

OK, this specifies the problem a good bit!

Still a question: Can you identify the particles (from 1 to 75) throughout your experiment?

If so the streamlines should just be the particle trajectories, right?

Since you haven't done that, I'll have to assume that's not the case, and that you instead have indistinguishable particles for which you know the position and velocities at each time-step. For that I'd first simlpy plot the velocities as arrows from the particle positions. There are two arrow-drawing contributions on the file exchange that are good to use (for my useage I typically use either with some random binary probabillity each time): arrow3 and arrow, using those for your 75 velocity-positions is the "most true representation" of what information you have. If you want streamlines, I'd try to use griddata/TriScatteredInterp/scatteredInterpolant to reinterpolate your winds from the irregular particle positions to a regular grid:

[xi,yi] = meshgrid(x_min:dx:x_max,y_min:dy:y_max);
vx_at_t = griddata(x_particles_at_t,y_particles_at_t,v_x_at_t,xi,yi);
vy_at_t = griddata(x_particles_at_t,y_particles_at_t,v_y_ay_t,xi,yi);

and then called streamlines with xi, yi, vx_at_t and vy_at_t as input (with suitable inputs for streamline-starts as well).

HTH

[bharathi Dasari]

Thanks..

[bharathi Dasari]

Bjron,

when i'm trying to use the syntax it was showing nan for some grid points in vx_at_t and vy_at_t.

[Bjorn Gustavsson]

If your nans on the edges of the grid this might be because of a "simple" reason: the griddata (and the triscatteredinterp-functions (TriScatteredinterp, scatteredinterp, etc)) typically returns interpolated values inside the convex hull of the points you have data at - outside of that region (area in 2-D, volume in 3-D) it would be an extrapolation. You can test different interpolation-methods and some of the functions allow you to explicitly chose extrapolation methods.

How to handle extrapolation in the general case I dont know.

As far as I understand these methods should not return nan inside the convex hull - unless you have a nan in the input-data.

HTH

[bharathi Dasari]

I don't have any data saying as nan ,my velocity values are small