Localized Reduced Basis Approach for Bifurcation Problems

PARTNERS: Florida State University, USA, University of Houston, USA, PUC Rio de Janeiro, Brazil

This project investigates the automatic generation of localized reduced order models for problems in computational fluid dynamics (CFD) undergoing bifurcations.
The numerical simulations consider the incompressible Navier-Stokes equations and use the spectral element method and finite element method for the discretization.
At a bifurcation point the solutions to a CFD problem exhibit qualitative changes, as e.g., an unsteady jump or multiple solution branches occur. We investigate sampling and clustering approaches to these phenomena.
The goal is to generate reduced order models, which are taking this structure into account, by automatically assigning localized basis functions to each branch for instance.
This allows much smaller reduced order models, than having a single global reduced order model.
The assignment of local basis functions can currently makes use of the detection of bifurcation points and centroidal Voronoi tesselations in the space of snapshots.

PEOPLE INVOLVED: Prof. Gianluigi Rozza (SISSA), Prof. Max Gunzburger (Florida State University, USA), Prof. Annalisa Quaini (University of Houston, USA), Prof. Alessandro Alla (PUC Rio de Janeiro, Brazil), Dr. Martin Hess (SISSA)