Exploratory Study on the Application of an Existing Finite-Element Navier-Stokes Code to Compute Potential Flows

摘要

The ease with which an existing time-dependent code for the incompressible Navier-Stokes (or Stokes) equations in primitive variables can be 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 approximations employed for the dependent variables. It is shown how a Navier-Stokes finite element code can be 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. It is concluded from this experience to date that better potential flow solutions will be obtained from the simpler and less expensive variational method (LF) than from the mixed method and that elements which perform well for viscous flows can be very poor for inviscid flows. (ERA citation 07:054752)