Trefry, M.G., and Townley, L.R. (1998), Laplace flow near an ellipsoidal conductor, Computers in Physics, 12(5), 503-511.

An existing solution for the steady three-dimensional temperature distribution around an ellipsoid embedded in a uniform, isotropic medium is used to study the characteristics of Laplace flow near a variety of objects. Symbolic integration techniques are used to derive new closed form algebraic expressions for flow potential near general ellipsoids. These expressions are used to derive simple algebraic results for various degenerate and limiting cases. Flow paths are calculated using numerical particle tracking techniques, defining capture and release zones for the embedded objects. The application and relevance of these results to the flow of groundwater near shallow lakes is discussed, and possibilities for future work are noted.

You are welcome to use and adapt our Mathematica notebook file, with appropriate acknowledgement.


Copyright © 2005 by Lloyd Townley
Last revised: 6 May 2005