Plenary Talk

Reduced order modelling in CFD: state of the art, perspectives and challenges

Gianluigi ROZZA

Gianluigi Rozza is professor in Numerical Analysis and Scientific computing at International School for Advanced Studies -SISSA, Trieste, Italy. Phd in Applied Mathematics at EPFL in 2005, MSc in Aerospace Engineering at Politecnico di Milano in 2002, post-doc at MIT. At SISSA he is the coordinator of SISSA mathematics area, lecturer in the master in High Performance Computing, in the master degree in Mathematics with the University of Trieste, and in the master degree in data science and scientific computing. He is SISSA Director's delegate for Valorisation, Innovation, Technology Transfer and Industrial Cooperation. His research is mostly focused in numerical analysis and scientific computing, developing reduced order methods. Author of more than 150 scientific publications (editor of seven books and author of three books). Co-advisor of 35 master thesis, co-director/director of 20 PhD theses since 2009. Principal Investigator of the European Research Council Consolidator Grant (H2020) AROMA-CFD and PoC ARGOS (HE), as well as for the project FARE-AROMA-CFD funded by Italian Government. Within SISSA mathLab he is responsible of several industrial projects with companies such as Danieli, Electrolux, Wartsila and Fincantieri. He is member of the Applied Mathematics Committee of European Mathematical Society.


The state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs) is provided. We focus on some perspectives in their current trends and developments, with a special interest in parametric problems arising in offline-online Computational Fluid Dynamics (CFD). Efficient parametrisations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances. Current ROM developments in CFD include: (i) a better use of stable high fidelity methods, to enhance the quality of the reduced model too, also in presence of bifurcations and loss of uniqueness of the solution itself, (ii) capability to incorporate turbulence models and to increase the Reynolds number; (iii) more efficient sampling techniques to reduce the number of the basis functions, retained as snapshots, as well as the dimension of online systems; (iv) the improvements of the certification of accuracy, established on residual based error bounds, and of the stability factors, as well as (v) the guarantee of the stability of the approximation with proper space enrichments. Last, but not least, the use of automatic learning. All the previous aspects are quite relevant -- and often challenging -- in CFD problems to focus on real time simulations for complex parametric industrial, environmental and biomedical flow problems, or even in a control flow setting with data assimilation and uncertainty quantification. Some model problems will be illustrated by focusing on few benchmark study cases, for example on simple fluid-structure interaction problems and on shape optimisation, as well as on some industrial and environmental problems of interest.