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Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences

  • 2021
  • OriginalPaper
  • Chapter
Published in:
Authors
Maria Strazzullo
Zakia Zainib
Francesco Ballarin
Gianluigi Rozza
Published in
Numerical Mathematics and Advanced Applications ENUMATH 2019
Publisher
Springer International Publishing

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Abstract

This chapter delves into the use of reduced order methods (ROMs) to tackle parametrized optimal flow control problems (OFCPs) constrained by partial differential equations (PDEs). These problems are computationally intensive, especially when involving time dependency and non-linearity. The chapter introduces a framework that recasts these problems into a low-dimensional, yet reliable, framework. It applies this methodology to two significant cases: a riverbed in environmental sciences and a bypass graft in cardiovascular applications. The test case in environmental sciences is governed by time-dependent Stokes equations, essential for simulating evolving natural phenomena. In cardiovascular mechanics, the framework aims to quantify outflow conditions automatically while matching physiological data. The work is structured to provide a comprehensive understanding of the problem formulation, methodology, numerical results, and conclusions. The chapter also briefly describes the problem and solution strategy for time-dependent non-linear boundary OFCPs, highlighting the use of Galerkin Finite Elements and Proper Orthogonal Decomposition (POD)–Galerkin methods.
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previous chapter A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens
next chapter Mathematical Assessment of the Role of Three Factors Entangled in the Development of Glaucoma by Means of the Ocular Mathematical Virtual Simulator
Title
Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences
Authors
Maria Strazzullo
Zakia Zainib
Francesco Ballarin
Gianluigi Rozza
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_83
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