A pseudo-compressibility method for solving inverse problems based on the 3D incompressible Euler equations

A numerical technique to solve the three-dimensional inverse problems that arise in aerodynamic design is presented. The approach, which is well established for compressible flows, is extended to the incompressible case via artificial compressibility preconditioning. The modified system of equations is integrated with a characteristic-based Godunov method. The solution of the inverse problem is given as the steady state of an ideal transient during which the flow field assesses itself to the boundary conditions, which are prescribed as design data, by changing the boundary contour. The main aspects of the Eulerian-Lagrangian numerical procedure are illustrated and the results are validated by comparing with theoretical solutions and experimental results.