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February 1st, 2016, 04:25 AM   #1
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Cool circle approximation

Hi guys,

I am trying to apply the Mangler's transformation (fluid dynamics) onto a sphere.
In order to do so, I need a single variable function r(x) to approximate a circle.

Do you know of any simple method? Accuracy is not an issue.

Regards,
shai

Last edited by skipjack; February 1st, 2016 at 04:31 AM.
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February 1st, 2016, 04:34 AM   #2
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No function has a circle as its graph if Cartesian coordinates are being used. Can you clarify what you mean?
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February 1st, 2016, 05:10 AM   #3
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The Mangler's transformation is used for boundary layer flow over an axisymmetric bodies of revolution and is used to simplify the Navier-Stokes equations. Since a sphere is a body of revolution, I want to use this method and the first step is to define how the radius of the body (a cross section of a sphere = circle) changes.. hope that is more clear.

Last edited by skipjack; February 1st, 2016 at 05:45 AM.
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February 1st, 2016, 06:03 AM   #4
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If the cross-section is perpendicular to the axis of revolution and the sphere has radius r, the cross-section's radius could be √(r² - x²), the graph of which is a semicircle.
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February 2nd, 2016, 05:04 AM   #5
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Thanks..
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