  The interpolation on Grassmann manifolds in the framework of parametric
evolution partial differential equations is presented. Interpolation points on
the Grassmann manifold are the subspaces spanned by the POD bases of the
available solutions corresponding to the chosen parameter values. The
well-known Neville-Aitken's algorithm is extended to Grassmann manifold, where
interpolation is performed in a recursive way via the geodesic barycenter of
two points. The performances of the proposed method are illustrated through
three independent CFD applications, namely: the Von Karman vortex shedding
street, the lid-driven cavity with inflow and the flow induced by a rotating
solid. The obtained numerical simulations are pertinent both in terms of the
accuracy of results and the time computation.
