Mathematical Problems in Engineering
Volume 1 (1995), Issue 1, Pages 11-25

A high-precision algorithm for axisymmetric flow

A. Gokhman1 and D. Gokhman2

1Fluid and Power Research Institute, San Francisco, California, USA
2Division of Mathematics, Computer Science, and Statistics, University of Texas at San Antonio, USA

Received 10 October 1994

Copyright © 1995 A. Gokhman and D. Gokhman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.