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Vorticity equations

  1. Jul 7, 2010 #1

    I have a parallelepiped domain, divided in nodes. Each node has a velocity vector (3D). I want to evaluate the vorticity. Starting from the definition of vorticity (e.g. w_x=[tex]\partial[/tex]u_z/[tex]\partial[/tex]y-[tex]\partial[/tex]u_y/[tex]\partial[/tex]z) I calculated the vorticity in a fortran progem like: w_x=(u_z(x,y+1,z)-u_z(x,y,z))-(u_y(x,y,z+1)-u_y(x,y,z)) but it is not really doing what it is supposed to do. I read the following document: http://folk.uio.no/jks/matpiv/html/node31.html I'd like to have your opinion.

    Thank you for any advice

    p.s. u_i is the velocity in the i-th direction, (x,y,z) indicates the node

  2. jcsd
  3. Mar 9, 2011 #2
    They are applying finite differences.. and using the equation of vorticity, in order to do so... I don't know how you are solving it.. but you need to apply finite differences with a known boundary, etc. in order to solve it. for example (see the jpeg attached), the blue symbolizes the vortex.. you need to tell the computer what your mesh/geometry of interest is, how you want to divide it so you evaluate the differential equation via finite differences at it, and then how calculate it. This is what the article says.

    1) Determine the length, width, height, shape of the geometry
    2) determine where the vortex is in the geometry
    3) Set up the mesh via matlab/C++/whatever, to divide the geometry by delta x, delta y, or by small x's and y's that specify height, etc.
    4) is there anything else but the vortex going in the geometry? If not, then write the vortex equation via finite differences (as in the website) to describe behavior at that geometrical spatial point
    5) Finish Collect and store that information in a matrix, solve using matrix inversion or gauss siedel

    If you give me more information, if this is an undergrad. or grad. problem, then I can help out. Assuming it is undergrad. there many simplications you can make in order to make this problem easier and not use computational tools.


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