Potential flows and transformation groups

Abstract

In this work we will consider the steady and two-dimensional potential flow of an incompressible fluid past a body without friction. Contrary to common experience, we will show that it is possible to calculate the Lie point symmetries that will leave the boundary value problem invariant. We are able to do this by solving the determining equation for the Lie point symmetries subject to a side condition. The side condition is a consequence of the boundary condition that occurs in the boundary value problem. We will show that solutions of the boundary value problem that were obtained previously using the method of conformal transformations are also group invariant solutions of the boundary value problem. We will also show that every group invariant solution of the boundary value problem can be used to generate new group invariant solutions of the same boundary value problem.