A numerical method for inverse design based on the inverse Euler equations

We present a numerical method for the inverse shape design of internal flows based on the inverse Euler equations (Keller JJ, Physics of Fluids 1999; 11 and Zeitschrift fur Angewandte Mathematik und Physik 1998; 49). We describe an efficient numerical method based on a finite difference discretization and on a Newton-Krylov solver. After showing that the three-dimensional (3D) inverse Euler equations hold only for complex lamellar flows, we extend the basic axis-symmetric flow model to handle viscous effects by means of a distributed loss model and to handle quasi-3D effects by deriving a quasi-3D formulation of the inverse Euler equations from the passage averaged 3D Euler equations. The coupling of the 2D inverse Euler equations with an integral boundary layer method is presented too.