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Finding the inverse of a mapping of a disk onto an airfoil

SALIOU TELLY
Posted 9 years ago
POSTED BY: SALIOU TELLY
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I wonder if you can interpolate the derivatives, instead of derivating the interpolation.
POSTED BY: Gianluca Gorni

If a numerical inverse is enough for you, you can compute the direct transformation in the points in a grid, reverse the order and then use something like ListInterpolation.
POSTED BY: Gianluca Gorni
SALIOU TELLY
SALIOU TELLY
Posted 9 years ago

Thanks Gianluca for the suggestion!

I was trying to first take the route of finding an expression for the inverse, but I may have to look at the numerical inverse or just formulate a transformation from scratch to map interior points of an airfoil onto interior points of a circle.

The issue with the numerical inverse is that I plan to next find the deformation gradient matrix and its Jacobian from this map, which involves finding derivatives with respect to variables. That task would be "easier" if I could find an explicit expression ....

Thanks again,

Saliou
POSTED BY: SALIOU TELLY
SALIOU TELLY
SALIOU TELLY
Posted 9 years ago

Daniel,

Thanks for the suggestion.

Attached is the simplified notebook that I am using....

Regards,

Saliou Telly

Attachments:
POSTED BY: SALIOU TELLY
POSTED BY: Daniel Lichtblau
SALIOU TELLY
SALIOU TELLY
Posted 9 years ago

Thanks Daniel!

I am actually interested in the inverse of the last map in the notebook ((xd, yd) ---> (xa, ya)), which maps the circular annulus to the airfoil annulus. So I would like to find an expression for the inverse map ((xa, ya) ---> (xd, yd)).

What you have solved is the inverse mapping of a circular disk to a circular annulus, which was just a step that I use to generate a circular annulus before mapping it to an airfoil annulus.

I will try your approach to see if it helps in finding the inverse map of interest.....

Thanks again,

Saliou
POSTED BY: SALIOU TELLY
POSTED BY: Daniel Lichtblau
POSTED BY: Kay Herbert
SALIOU TELLY
SALIOU TELLY
Posted 9 years ago
POSTED BY: SALIOU TELLY
POSTED BY: Kay Herbert
SALIOU TELLY
SALIOU TELLY
Posted 9 years ago
POSTED BY: SALIOU TELLY
SALIOU TELLY
SALIOU TELLY
Posted 9 years ago
POSTED BY: SALIOU TELLY

It would be more easy to test this if Mathematica code were provided.
POSTED BY: Daniel Lichtblau
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