Moubachir / Zolesio Moving Shape Analysis and Control

Applications to Fluid Structure Interactions
1. Auflage 2010
ISBN: 978-1-4200-0324-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 312 Seiten

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

Problems involving the evolution of two- and three-dimensional domains arise in many areas of science and engineering. Emphasizing an Eulerian approach, Moving Shape Analysis and Control: Applications to Fluid Structure Interactions presents valuable tools for the mathematical analysis of evolving domains. The book illustrates the efficiency of the tools presented through different examples connected to the analysis of noncylindrical partial differential equations (PDEs), such as Navier–Stokes equations for incompressible fluids in moving domains. The authors first provide all of the details of existence and uniqueness of the flow in both strong and weak cases. After establishing several important principles and methods, they devote several chapters to demonstrating Eulerian evolution and derivation tools for the control of systems involving fluids and solids. The book concludes with the boundary control of fluid–structure interaction systems, followed by helpful appendices that review some of the advanced mathematics used throughout the text. This authoritative resource supplies the computational tools needed to optimize PDEs and investigate the control of complex systems involving a moving boundary.

Zielgruppe

Engineers, applied mathematicians, students, and researchers, especially those with a focus on fluid mechanics.

Autoren/Hrsg.

Moubachir, Marwan

Zolesio, Jean-Paul

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Introduction
Classical and Moving Shape Analysis
Fluid–Structure Interaction Problems
Plan of the Book
Detailed Overview of the Book
An Introductory Example: The Inverse Stefan Problem
The Mechanical and Mathematical Settings
The Inverse Problem Setting
The Eulerian Derivative and the Transverse Field
The Eulerian Material Derivative of the State
The Eulerian Partial Derivative of the State
The Adjoint State and the Adjoint Transverse Field
Weak Evolution of Sets and Tube Derivatives
Introduction
Weak Convection of Characteristic Functions
Tube Evolution in the Context of Optimization Problems
Tube Derivative Concepts
A First Example: Optimal Trajectory Problem
Shape Differential Equation and Level Set Formulation
Introduction
Classical Shape Differential Equation Setting
The Shape Control Problem
The Asymptotic Behavior
Shape Differential Equation for the Laplace Equation
Shape Differential Equation in Rd+1
The Level Set Formulation
Dynamical Shape Control of the Navier–Stokes Equations
Introduction
Problem Statement
Elements of Noncylindrical Shape Calculus
Elements of Tangential Calculus
State Derivative Strategy
Min-Max and Function Space Parameterization
Min-Max and Function Space Embedding
Conclusion
Tube Derivative in a Lagrangian Setting
Introduction
Evolution Maps
Navier–Stokes Equations in Moving Domain
Sensitivity Analysis for a Simple Fluid–Solid Interaction System
Introduction
Mathematical Settings
Well-Posedness of the Coupled System
Inverse Problem Settings
KKT Optimality Conditions
Conclusion
Sensitivity Analysis for a General Fluid–Structure Interaction System
Introduction
Mechanical Problem and Main Result
KKT Optimality Conditions
Appendix A: Functional Spaces and Regularity of Domains
Appendix B: Distribution Spaces
Appendix C: The Fourier Transform
Appendix D: Sobolev Spaces
References
Index