This award will support Professor Bernard Grossman in a research collaboration with Professor Michele Napolitano of the University of Bari, Italy. The aim of the collaboration is to develop numerical procedures for multi-dimensional compressible flows, with very high levels of accuracy in smooth regions of the flow and capable of modelling complex shock patterns and other discontinuities. More specifically, numerical procedures will be developed using a highly accurate upwind scheme in regions of smooth flow and a very robust flux-vector/ difference-splitting method in regions containing and immediately surrounding shocks and other discrepancies. Approximate factorization and line/plane relaxation implicit schemes will be used to solve the discrete equation sets and a multigrid strategy may be necessary to accelerate convergence to a steady state. The joint work will combine the expertise of the U.S. side in flux-vector/difference-splitting methods with that of the Italian side on numerical methods using the so-called lambda formulation, which relies on a nonconservation form of the governing equations. The new methodology will be applied to solve external as well as internal compressible flows containing complex shock configurations and requiring exceptionally high levels of accuracy, such as flows with chemical reactions or flows inside highly-curved turbomachinery passages as in advanced aircraft and propulsion systems.
