Where Can I Find the Complete Derivation of the Vortex Panel Method?

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Discussion Overview

The discussion revolves around the quest for a complete derivation of the vortex panel method, particularly focusing on the transition from fundamental equations to their usable form involving influence coefficients. Participants seek resources such as books or webpages that provide detailed mathematical explanations and derivations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant, Chris, requests resources for the complete derivation of the vortex panel method, noting difficulty in understanding the integration process to obtain influence coefficients.
  • Another participant mentions having found a book, "Low speed aerodynamics: from wing theory to panel methods" by Katz & Plotkin, which covers various panel methods, including the linear vortex panel method, although it approaches the topic differently.
  • There is a repeated request for clarification on how the equations related to the vortex panel method are derived, indicating a need for detailed mathematical exposition.
  • A participant expresses interest in using XFOIL for simulations but seeks numerical details regarding the vortex panel method combined with boundary layer analysis.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the availability of resources or the specific derivation details, indicating that multiple views and needs remain unaddressed.

Contextual Notes

The discussion highlights a lack of accessible resources and detailed derivations, with participants expressing varying levels of familiarity with the mathematical aspects of the vortex panel method.

Who May Find This Useful

This discussion may be useful for students and professionals interested in fluid dynamics, specifically those looking for derivations and resources related to vortex panel methods and numerical simulation techniques.

ChrisHarvey
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Hi,

Can anybody tell me where I can find the complete derivation of the vortex panel method (book / webpage)? It's easy enough to see where the fundamental equation comes from, but completing the integration etc. to get it in the form of influence coefficients is beyond me. I have the solution, but no maths or explanation to go with it and I haven't found anything on the net.

Thanks,
Chris
 
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In case you're wondering exactly what equations I'm talking about, I've attached them to this post. Problem.GIF shows the fundamental equations. Solution.GIF shows the equations in the more usuable form, the derivation of which I can't find.
 

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    Problem.GIF
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  • Solution.GIF
    Solution.GIF
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If anyone's interested, or somebody later digs up this topic, I've found a book that covers many different panel methods and techniques including the linear vortex panel method I mentionned above (different approach though to solving): "Low speed aerodynamics: from wing theory to panel methods" (Katz & Plotkin). It was very hard to get hold of, but was worth the effort.
 
ChrisHarvey said:
In case you're wondering exactly what equations I'm talking about, I've attached them to this post. Problem.GIF shows the fundamental equations. Solution.GIF shows the equations in the more usuable form, the derivation of which I can't find.

how these equations are derived? anyone who can put these here?
 
Hi All ,

Currently , i m using xfoil for sinmulation but i need the numerics of xfoil - viscous; vortex panel method with boundary layer analysis. Can anyone share with me

cxfoil
 

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