Numerical solution for various inverse problems

This study considers the classical two-dimensional model of jet flow using an ideal, incompressible, weightless fluid. Solving a direct problem consists in determining the pressure (or velocity) distribution on an obstacle in a flow. The aim of this paper is to describe and illustrate a numerical method for constructing wetted walls to obtain arbitrary velocity distributions, i.e. solving the inverse problem. This method is applied to airfoil design and to the construction of an infinite wall impinged by a jet. The specified distributions may entail constraints that require an analysis of the existence of the solution.