Applications to Fluid Structure Interaction
by Marwan Moubachir
Moving Shape Analysis and Control illustrates the efficiency of the tools presented through different examples connected to the analysis of noncylindrical partial differential equations, such as the Navier-Stokes equations for incompressible fluids in moving domains.
Features:
- Provides various tools to handle moving domains on the level of intrinsic definition, computation, optimization, and control
- Addresses real-world engineering problems with applications
- Emphasizes the Eulerian approach using evolution and derivation tools for controlling fluids and systems
- Includes two chapters devoted to fluid control described using Navier-Stokes equations
- Features new approaches to deal with boundary control fluid-structure interaction systems
Contents
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
- 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
- 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
- Elements of Non-Cylindrical Shape Calculus
- Elements of Tangential Calculus
- State Derivative Strategy
- Min-Max and Function Space Parameterization
- Min-Max and Function Space Embedding
Tube Derivative in a Lagrangian Setting
- Evolution Maps
- Navier-Stokes Equations in Moving Domain
Sensivity Analysis for a Simple Fluid Solid Interaction System
- Mathematical Settings
- Well-Posedness of the Coupled System
- Inverse Problem Settings
- KKT Optimality Conditions
Sensitivity Analysis for a General Fluid Structure Interaction System
- Mechanical Problem and Main Result
- KKT Optimality Conditions
Index