Overcoming slowly decaying Kolmogorov n-width by transport maps: application to model reduction of fluid dynamics and fluid–structure interaction problems

In this talk we will focus on reduced order modelling (ROMs) 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. We will introduce an additional preprocessing step during the offline phase of the reduced basis method, in order to obtain smaller reduced basis spaces. Two test cases will be considered: a fluid moving in a domain with deforming walls, and a fluid past a rotating cylinder.

This is a joint work with Professor Y. Maday at LJLL, Paris VI.

Monica Nonino is a PhD student at SISSA (Trieste).