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Axi-symmetric co-ordinates

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Old   July 15, 1999, 05:44
Default Axi-symmetric co-ordinates
  #1
Kevan Moodley
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What are axi-symmetric co-ordinates? How would the solution be affected if they are/are not used.?

Could someone please give me some clarity on this issue.
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Old   July 15, 1999, 10:14
Default Re: Axi-symmetric co-ordinates
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Patrick Godon
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axi-symmetric coordinates are coordinate which have a symmetry around an axis of rotation. These are also known as cylindrical coordinate: r, phi and z. Any textbook of Physics, Mathematics, etc.. at an elementary level will give you details about cylindrical coordinates.

e.g. Courant, Differential and Integral calculus, vol.II (Interscience publisher), in the chapter on transformations of coordinate systems.

Or in the appendix of some technical book for engineering, e.g. Thompson, Compressible Fluid Dynamics, (McGraw Hill), in Apendix E. etc..

So that's is not too difficult to find.

If the solution is axisymmetric then it means that in fact if you rotate the problem around the z axis, the solution is the same. Therefore there is no need to solve for phi. So one write the eqs. in cylindrical coordinates and assume that the solution does not depends on phi (all the phi derivatives are dropped) and then one only need to solve a 2D problem (r and z) instead of a 3D problem (r z and phi).

If the problem is axisymmetric but the solution however depends on phi, then you really need to solve in 3D. Then the choice of coordinates is to help to deal with things such as boundary conditions (for example how are you going to solve for the flow inside a rotating cylinder if your computational domain is a square box?), accuracy of the solution (if you solve in the rotating frame of reference, then the angular velocity is more accurate), etc..

Some of the solution might be expressed more easily in term of cylindrical coordinates (e.g. modes of instability, etc..).

If you could give more details of your problem then it might be easier to assess how the solution would be affected by not using axisymmetric coordinates.

Cheers, Patrick
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Old   February 12, 2010, 11:20
Unhappy Coordinate System Components (v, w, x) ?
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Mdz
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I have been using the version of ansys 12.1, and the coordinate system appears with these component (v, w, x) , I have not found the form to change it a (x, y, z), since I can do it?
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