Conformal Mapping in MATHCAD PRIME

[gianfry]

Good evening.

I would like to implement a MATHCAD PRIME worksheet to map a solution on a circle to another domain. This technique is well known as conformal transformation. However, I tried to solve it numerically without success. I use this to predict the potential flow pressures around a body in 2D. Does anyone knows if this problem has already beel solved and indicating in which thread? I tried with the search function on the website, but no results. Thanks in advance for the support. 

[Werner_E · Accepted solution]

Which kind of conformal map function do you have in mind? f(z):=1/z or inversion (f(z)=1/conjugate z).

Here is a quick hack. The mapping is done point by point, not analytically.

You may chose your own mapping function.

Hope it helps.

Prime10 file attached

[gianfry]

Good night Werner.

Thanks for the mapping solution. Unfortunately the domain I need to map into a unit circle is not described with a function, but by points. I am talking about a wing section.

I think that if I provide a vector of value your algorithm should work. Am I correct in my understanding?

[gianfry]

[Werner_E]

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@gianfry wrote:

Good night Werner.

Thanks for the mapping solution. Unfortunately the domain I need to map into a unit circle is not described with a function, but by points. I am talking about a wing section.

I think that if I provide a vector of value your algorithm should work. Am I correct in my understanding?

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As long as the mapping is done by a function this should work.

Actually my approach only works with a matrix of point coordinates - n x 2 matrix, first column x-coordinates, second column y-coordinates. The result of my function is a similar matrix with the coordinated of the mapped points.

I used an explicit function (the sinus) and the parametric equation of an epicycloid just for demonstration. It was necessary to sample x- and y-values anyway so that my function could do its job. So if thats the data structure you have right from the start it should be OK.

[gianfry]

Good evening, Werner.

Following your spreadsheet I finally was able to get the transformation I was looking for. Of course it is based on a function. Now I am working on the implementation of a mapping for a general shape into a unit circle, when the mapping function is not known. I found a paper from Theodorsen, dealing with such a type of problems, but before doing that I am working on plotting stremlines of a potential flow around this type of profile. The solution is well known...I need to figure it out numerically.

Thanks again.

Regards,

Gianfranco