# plot streamlines

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 December 18, 1999, 09:09 plot streamlines #1 JJ Guest   Posts: n/a I have got the velocities data from CFD program developing by ourself and want to plot the streamlines. Could anybody tell me how to plot the streamlines ?

 December 18, 1999, 12:00 Re: plot streamlines #2 John C. Chien Guest   Posts: n/a (1). To draw a fluid particle path (or trajectory)(x(s),y(s),z(s)) from the velocity field (u,v,w), you first start from a known velocity location (x1,y1,z1,u1,v1,w1) and calculate the second point location(x2,y2,z2), based on the velocity vector(u1,v1,w1) and the specified distance (ds). (like driving a car with steering wheel fixed at the initial position.) (2). At the second point(x2,y2,z2), you can repeat the process. It is likely that the velocity at the second point(U2,v2,w2) is not available. In this case, you will have to use interpolation to calculate the unknown velocity vector. (3). That's all. It is very simple and straight forward. (naturally, in order to get accurate particle path, you will need fine mesh solution for the velocity field as well as small integration step size. Other wise the car will hit the curve on the side of the road.)

 December 20, 1999, 12:21 Re: plot streamlines #3 ThoLi Guest   Posts: n/a (1) John's suggestion plots particle trajectories, not streamlines (2) but the result is almost the same, if you use the current velocity (constant in time) (3) because streamlines are everywhere parallel to the (current) velocity => John's suggestion is ok (4) streamlines are contours of the streamfunction: if you have a good program for contour lines, try the following: (5) compute the streamfunction psi by solving: rot rot psi = rot v (rot ist the rotation; see a book about vector analysis) (6) for FE-programs the above equation looks like (rot psi, rot phi) = (v, rot phi) for all phi (7) boundary conditions for psi: (7a) psi = constant on walls and other boundaries with v normal to wall = 0 (7b) d(psi) = v*normal on other boundaries (8) compute and plot contour lines of psi (9) for plane geometry, rot rot degenerates to the laplace-operator; for rotational symmetric geometry, look into an text book for vector analysis (calculus) ThoLi