DIFFICULTIES IN SENSITIVITY CALCULATIONS FOR FLOWS WITH DISCONTINUITIES

The use of flow sensitivities has become an integral part, of flow opt imization-based aerodynamic design and is useful for the efficient cal culation of perturbed flows. However, there are still many issues to b e resolved, especially for flows having discontinuities. Flow sensitiv ities for several numerical methods are calculated using finite differ ence quotients, automatic differentiation, and the sensitivity equatio n method, The flow sensitivities are calculated for the Riemann proble m of gas dynamics. An attempt is made to expose, explain, and understa nd difficulties that arise in the calculation of flow sensitivities in flows with discontinuities.