Using Euler lets to Give a Boundary Integral Formulation in Euler Flow and Discussion on Applications

摘要

Boundary element models in inviscid (Euler) flow dynamics for a manoeuvring body are difficult to formulate even for the steady case; Although the potential satisfies the Laplace equation, it has a jump discontinuity in two-dimensional flow relating to the point vortex solution (from the 2 pi jump in the polar angle), and a singular discontinuity region in three-dimensional flow relating to the trailing vortex wake. So, instead models are usually constructed bottom up from distributions of these fundamental solutions giving point vortex thin body methods in two-dimensional flow, and panel methods and vortex lattice methods in three-dimensional flow amongst others. Instead, the idea here is to present initially a boundary integral formulation in Euler flow that can then produce a true top down boundary element formulation. This is done for the steady two-dimensional case by matching the Euler flow to a far-field Oseen flow to determine the appropriate description for the Green's function Euler lets. It is then shown how this reduces to the standard point vortex representations. Finally, two applications are outlined that can be used to test this approach, that of steady flow past a semi-infinite flat plate and steady flow past circular cylinder.