Proper Orthogonal Decomposition in Optimal Control of Fluids PDF Download

Author: S. S. Ravindran
Publisher:
ISBN:
Category : Fluid dynamics
Languages : en
Pages : 34

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Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781723748813
Category : Science
Languages : en
Pages : 32

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Book Description
In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.Ravindran, S. S.Langley Research CenterNAVIER-STOKES EQUATION; TURBULENT FLOW; OPTIMAL CONTROL; UNSTEADY FLOW; ACTIVE CONTROL; FLUID FLOW; GALERKIN METHOD; PARTIAL DIFFERENTIAL EQUATIONS; ORTHOGONAL FUNCTIONS; DYNAMICAL SYSTEMS; EIGENVALUES; SIMULATION; MODELS

Author: E. Arian
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 26

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Book Description
The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations, e.g., fluid flows. It can also be used to develop reduced order control models. Fundamental is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model. We present an approach where suitable reduced order models are derived successively and give global convergence results.

Author: Wilhelmus H. Schilders
Publisher: Springer Science & Business Media
ISBN: 3540788417
Category : Mathematics
Languages : en
Pages : 471

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Book Description
The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

Author: Peter Benner
Publisher: Springer Science & Business Media
ISBN: 3540279091
Category : Technology & Engineering
Languages : en
Pages : 397

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In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

Author: K.-H. Hoffmann
Publisher: Birkhäuser
ISBN: 3034881487
Category : Mathematics
Languages : en
Pages : 290

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Book Description
Interest in the area of control of systems defined by partial differential Equations has increased strongly in recent years. A major reason has been the requirement of these systems for sensible continuum mechanical modelling and optimization or control techniques which account for typical physical phenomena. Particular examples of problems on which substantial progress has been made are the control and stabilization of mechatronic structures, the control of growth of thin films and crystals, the control of Laser and semi-conductor devices, and shape optimization problems for turbomachine blades, shells, smart materials and microdiffractive optics. This volume contains original articles by world reknowned experts in the fields of optimal control of partial differential equations, shape optimization, numerical methods for partial differential equations and fluid dynamics, all of whom have contributed to the analysis and solution of many of the problems discussed. The collection provides a state-of-the-art overview of the most challenging and exciting recent developments in the field. It is geared towards postgraduate students and researchers dealing with the theoretical and practical aspects of a wide variety of high technology problems in applied mathematics, fluid control, optimal design, and computer modelling.

Author: Marianna Braza
Publisher: Springer
ISBN: 3319273868
Category : Technology & Engineering
Languages : en
Pages : 358

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This book addresses flow separation within the context of fluid-structure interaction phenomena. Here, new findings from two research communities focusing on fluids and structures are brought together, emphasizing the importance of a unified multidisciplinary approach. The book covers the theory, experimental findings, numerical simulations, and modeling in fluid dynamics and structural mechanics for both incompressible and compressible separated unsteady flows. There is a focus on the morphing of lifting structures in order to increase their aerodynamic and/or hydrodynamic performances, to control separation and to reduce noise, as well as to inspire the design of novel structures. The different chapters are based on contributions presented at the ERCOFTAC Symposium on Unsteady Separation in Fluid-Structure Interaction held in Mykonos, Greece, 17-21 June, 2013 and include extended discussions and new highlights. The book is intended for students, researchers and practitioners in the broad field of computational fluid dynamics and computational structural mechanics. It aims at supporting them while dealing with practical issues, such as developing control strategies for unsteady separation and applying smart materials and biomimetic approaches for design and control.

Author: Philip Holmes
Publisher: Cambridge University Press
ISBN: 1107008255
Category : Mathematics
Languages : en
Pages : 403

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Book Description
Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.

Author: Zhendong Luo
Publisher: Academic Press
ISBN: 0128167998
Category : Mathematics
Languages : en
Pages : 278

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Book Description
Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems. Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Author: Maurizio Falcone
Publisher: Springer
ISBN: 3030019594
Category : Science
Languages : en
Pages : 275

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Book Description
This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.