Seminar by Gianluigi Rozza

Speaker

Gianluigi Rozza (Scuola Internazionale Superiore di Studi Avanzati)

Title

Reduced Order Modelling in Computational Fluid Dynamics: state of the art, challenges and perspectives

Date

  • October 02, 2023 16:00 CEST+0200 (Europe/Rome)

  • October 02, 2023 10:00 EDT-0400 (US/Eastern)

  • October 02, 2023 09:00 CDT-0500 (US/Central)

  • October 02, 2023 07:00 PDT-0700 (US/Pacific)

Abstract

We provide the state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs), and 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. 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 simplefluid-structure interaction problems and on shape optimisation, applied to some industrial and environmental problems of interest.

Recording

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