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I am looking for a simple method to compute potential flow (then non-viscous) around an obstacle. The method I am looking for must NOT use coordinate transformation, panel methods, finite element methods; it should work just on a standard cartesian grid and it should preferably use the finite differences method. There is no need for it to be efficient or fast, it should only be SIMPLE. It is only for demonstration purposes. Thank you.

I looked at the Shortley-Weller algorithm, but I didn't understand what should I do exactly... can it be used to impose Neumann conditions on the obstacle boundary (even an asymmetric arbitrary boundary)? If yes, how can it be done?

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    $\begingroup$ Ironically, there is an algorithm in CFD called SIMPLE. $\endgroup$ – Geoff Oxberry Jun 4 '13 at 5:41
  • $\begingroup$ The question scicomp.stackexchange.com/q/7508/1804 is your follow-up question, right? If the current answers do not help you, you should edit your question to include more details: Which equation are you trying to solve (you can use LaTeX here)? What does the domain look like (i.e., what does 'asymmetric' mean)? $\endgroup$ – Christian Clason Jun 4 '13 at 15:41
  • $\begingroup$ It looks like you've got two separate accounts, which means you cannot edit your original post or leave comments. The StackExchange staff can merge them together for you. $\endgroup$ – Christian Clason Jun 11 '13 at 16:43
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I think the easiest way would be to use a Shortley-Weller finite difference scheme. In particular if you know a simple representation of your obstacle (e.g., a circle), it should be easy to identify the nodes near and at the boundary. You then only need to modify the stencils near the boundaries and use normal finite differences in the interior.

For a detailed description, you can for instance refer to Hackbusch's book on Elliptic Differential Equations (Chapter 4.8)

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I recommend the book

Numerical Simulation in Fluid Dynamics: A Practical Introduction Volume 3 of Monographs on Mathematical Modeling and Computation Authors: Michael Griebel, Thomas Dornsheifer, Tilman Neunhoeffer

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