Reduced Order Models for Flow Problems

Optimization, control and design problems in aero and hydro dynamics require several evaluations of systems described by partial differential equations (PDEs) and characterized by complex geometrical features. Each realization usually entails some expensive steps:

  • the generation of a volumetric mesh starting from CAD based surfaces;
  • a high fidelity flow simulation;
  • the evaluation of the objective function which drives the optimization and possibly a geometrical transformation (of the CAD structure and/or the computational mesh) in case of optimal design problems;

Such an optimization process may require thousands of system evaluations, yielding a very strong computational effort. We developed a Reduced Basis method based on Isogeometric Analysis (RB-IGA) for the real-time and reliable solution of flow problems defined over complex geometries. By combining these two techniques, which have become very well-spread tools of scientific computing during the last decade, we implemented a new, integrated framework which alleviates the computational burden typical of optimization, control and design problems in aero and hydro dynamics.