Exploratory study on the application of an existing finite-element Navier-Stokes code to compute potential flows

The ease with which an existing time dependent code for the incompressible Navier-Stokes equations in primitive variables is used to compute potential flows and the utility of this approach via an example calculation are examined. As a numerical example, the potential flow over a cylinder is considered. The calculations are performed on a single mesh with various piecewise polynomial approximation employed for the dependent variables. A Navier-Stokes finite element code is used in a rather straightforward manner to obtain numerical solutions to potential flow problems. Whereas the Laplace's equation approach generates a solution for the velocity potential only, the mixed formulation obtains both the velocity and potential fields. Better potential flow solutions are obtained from the simpler and less expensive variational method (LF) than the mixed method and that elements which perform well for viscous flows can be very poor for inviscid flows.