Overcoming slowly decaying Kolmogorov n-width by transport maps:
application to model order reduction of fluid dynamics and fluid--structure
interaction problems
In this work we focus on reduced order modelling for problems for which the
resulting reduced basis spaces show a slow decay of the Kolmogorov n-width,
or, in practical calculations, its computational surrogate given by the
magnitude of the eigenvalues returned by a proper orthogonal decomposition on
the solution manifold. In particular, we employ an additional preprocessing
during the offline phase of the reduced basis method, in order to obtain
smaller reduced basis spaces. Such preprocessing is based on the composition of
the snapshots with a transport map, that is a family of smooth and invertible
mappings that map the physical domain of the problem into itself. Two test
cases are considered: a fluid moving in a domain with deforming walls, and a
fluid past a rotating cylinder. Comparison between the results of the novel
offline stage and the standard one is presented.Comment: 26 pages, 11 figure