A boundary integral formulation for the kinetic field in aerodynamics. Part I: Mathematical analysis

This paper presents a new boundary integral formulation for the velocity field in Aerodynamics, which includes rotational flows with wakes, sources, sinks and vorticity blobs. The velocity field is represented via the Poincare identity in terms of its div, curl and normal and tangential trace on the boundary. If the first three quantities are supposed to be given, the determination of the velocity field reduces to solving a vector boundary integral equation for the latter. Existence, uniqueness and stability estimates for the (weak) solution of this integral equation are proved by a suitable variational method. This kinematical problem is thus well-posed. The formulation here deals explicity with 3D external flows, but a discussion is also included concerning the different qualitative behaviour of 3D and 2D flows. The latter will be explicitly considered in detail in Part II of the paper, together with the necessary coupling with the dynamical equations, and a few numerical applications.