Panel Methods -- Introduction

Since the equations solved by panel methods are linear, we can multiply a known solution by a scalar and add these results together to form more general solutions. This can be made to work in both subsonic and supersonic cases.

Panel methods may be based on one or more fundamental solutions to the Prandtl-Glauert equation or Laplace's equation. These commonly include source, vortex, and doublet flows, discussed in the section on potential theory.

The basic idea is to add up known solutions...
... such as a uniform flow...
...and a point source....
... to produce a streamline pattern that matches the flow of interest.

Here we add a freestream, a source, and a sink (negative source strength) to produce the flow over an oval (called a Rankine Oval).

We could superimpose many sources and sinks to get nearly any flow pattern we desired:

Panel methods are based on this idea. Sources (or doublets or vortices) of some strength are located in the flow such that their combined solutions satisfy the boundary conditions of the problem. The boundary conditions are typically that the combined flow does not go through the surface, and that far from the body, the flow approaches the freestream solution.