POD-Galerkin reduced order methods for inverse and multi-physics problems in fluid dynamics

Monica Nonino,Zakia Zainib,Maria Strazzullo,Gianluigi Rozza,Francesco Ballarin

doi:10.14293/p2199-8442.1.sop-math.qwthxt.v1

Monica Nonino, Zakia Zainib + Show 3 more

Open Access

https://doi.org/10.14293/p2199-8442.1.sop-math.qwthxt.v1

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Abstract

In this work we will focus on recent advances in reduced order modelling for parametrized problems in computational fluid dynamics, with a special attention to the case of inverse problems, such as optimal flow control problems and data assimilation, and multi-physics applications. Among the former, we will discuss applications arising in environmental marine sciences and engineering, namely a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations describing North Atlantic Ocean dynamic. Similar methodologies will also be employed in problems related to the modeling of the cardiovascular system. Among the latter, we will present further recent developments on reduction of fluid-structure interaction problems, based on our earlier work. Reduced order approaches for parametric optimal flow control will also be applied in combination with domain decomposition in view of further applications in multi-physics. This work is in collaboration with Y. Maday (UPMC Université Paris 06, France), L. Jiménez-Juan (Sunnybrook Health Sciences Centre, Toronto, Canada), P. Triverio (University of Toronto, Canada), R. Mosetti (National Institute of Oceanography and Applied Geophysics, Trieste, Italy).

Highlights

Introduction and MotivationParametrized inverse problems, such as optimal flow control problems (OFCP(μ)), data assimilation, and multi-physics applications, play an ubiquitous role in several fields of application, yet are usually very demanding from a computational standpoint
Problem: simulate the displacement in the time interval [0, T ] of a thin structure Ωst at the top of a 2D rectangle filled with a fluid Ωft
Discretization: we adopt an ALE formulation, which results in a nonlinear system of equations to be solved with monolithic approach

Summary

Introduction

Introduction and MotivationParametrized inverse problems, such as optimal flow control problems (OFCP(μ)), data assimilation, and multi-physics applications, play an ubiquitous role in several fields of application, yet are usually very demanding from a computational standpoint. Problem: simulate the displacement in the time interval [0, T ] of a thin structure Ωst at the top of a 2D rectangle filled with a fluid Ωft . Discretization: we adopt an ALE formulation, which results in a nonlinear system of equations to be solved with monolithic approach. Figure: decay of the first singular values for the original and for the preprocessed displacements.

Results

Conclusion