UCSC sent a team of 2 persons to Virginia Tech from January to February 2023 for a secondment to work on regularized ROM (Reg-ROM) for Navier-Stokes and Burgers’ equations. In particular, the team formulated a new Reg-ROM, i.e., the approximate deconvolution Leray ROM (ADL-ROM). Our numerical investigation is meant to show that the new ADL-ROM is more accurate than the Leray ROM, and both are significantly more accurate than the classical Galerkin ROM.
The team worked mainly on the numerical aspects of the proposed research by testing all the ROMs in different settings, e.g., different domains for the Navier-Stokes equations (flow behind a cylinder, backward facing step). Moreover, we analyzed the differences between the approximate and the exact deconvolution, and investigated the sensitivity of the results to model coefficients such as filtering radius.
The secondment has also had an impact on young researchers working in Prof. Iliescu’s group. In particular, the secondee worked closely with Ian Moore, an undergraduate student under the supervision of the host, to introduce him to the FEniCSx finite element library, and the RBniCSx reduced order modelling package, of which Dr. Ballarin is the lead developer and Ms, Sanfilippo uses daily for her PhD thesis.
Dr. Ballarin and Prof. Iliescu organized on February 2 the event “ARIA@VT Seminar on Regularized ROMs”. The event was attended by around 25 participants worldwide, and Dr. Ballarin, Ms. Sanfilippo and Prof. Iliescu delivered presentations on their research activites.