Reduced Order Methods: State of the Art and Perspectives with Focus on Computational Fluid Dynamics


Wednesday, 5 July, 2017 - 15:00
Speaker: Gianluigi Rozza (SISSA)
Date and Venue: Wednesday, 5 July 2017, 15:00 - 17:00 SISSA main building, Lecture room A-128

Abstract. In this talk, 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 Computational Fluid Dynamics (CFD). Systems modelled by PDEs are depending by several complex parameters in need of being reduced, even before the computational phase in a pre-processing step in order to reduce parameter space. Efficient parametrizations (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: a better use of stable high fidelity methods, such as parametric spectral element method, enhancing the quality of the reduced model too; the use of finite volume discretisation with turbulent models; more efficient sampling techniques to reduce the number of the basis functions, retained as snapshots, and the dimension of online systems; the improvements of the certification of accuracy based on residual based error bounds and stability factors, as well as the the guarantee of the stability of the approximation with proper space enrichment. For nonlinear systems, also the investigations on of bifurcations of parametric solutions are crucial and they may be obtained thanks to a reduced eigenvalue analysis. All the previous aspects are very important in CFD problems to be able to focus in real time on complex parametric industrial and biomedical flow problems or even in a control flow setting, and to couple viscous flows -velocity, pressure, as well as thermal field - with a structural field or a porous medium, thus requiring also an efficient reduced parametric treatment of interfaces between different physics. Model flow problems will focus on few benchmark cases in a time-dependent framework, as well as on fluid-structure interaction problems. The research has been carried out at SISSA mathLab within the ERC AROMA-CFD project.