Applied Shape Optimization for Fluids

Name: Applied Shape Optimization for Fluids
Brand: OUP Oxford
Price: 94.8 EUR
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Bijan Mohammadi Olivier Pironneau(Autor*in)

OUP Oxford (Verlag)

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Erschienen am 24. September 2009

292 Seiten

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Inhalt

Intro
Contents
1 Introduction
2 Optimal shape design
2.1 Introduction
2.2 Examples
2.2.1 Minimum weight of structures
2.2.2 Wing drag optimization
2.2.3 Synthetic jets and riblets
2.2.4 Stealth wings
2.2.5 Optimal breakwater
2.2.6 Two academic test cases: nozzle optimization
2.3 Existence of solutions
2.3.1 Topological optimization
2.3.2 Suficient conditions for existence
2.4 Solution by optimization methods
2.4.1 Gradient methods
2.4.2 Newton methods
2.4.3 Constraints
2.4.4 A constrained optimization algorithm
2.5 Sensitivity analysis
2.5.1 Sensitivity analysis for the nozzle problem
2.5.2 Numerical tests with freefem++
2.6 Discretization with triangular elements
2.6.1 Sensitivity of the discrete problem
2.7 Implementation and numerical issues
2.7.1 Independence from the cost function
2.7.2 Addition of geometrical constraints
2.7.3 Automatic differentiation
2.8 Optimal design for Navier-Stokes flows
2.8.1 Optimal shape design for Stokes flows
2.8.2 Optimal shape design for Navier-Stokes flows
References
3 Partial differential equations for fluids
3.1 Introduction
3.2 The Navier-Stokes equations
3.2.1 Conservation of mass
3.2.2 Conservation of momentum
3.2.3 Conservation of energy and and the law of state
3.3 Inviscid flows
3.4 Incompressible flows
3.5 Potential flows
3.6 Turbulence modeling
3.6.1 The Reynolds number
3.6.2 Reynolds equations
3.6.3 The k - e model
3.7 Equations for compressible flows in conservation form
3.7.1 Boundary and initial conditions
3.8 Wall laws
3.8.1 Generalized wall functions for u
3.8.2 Wall function for the temperature
3.8.3 k and e
3.9 Generalization of wall functions
3.9.1 Pressure correction
3.9.2 Corrections on adiabatic walls for compressible flows
3.9.3 Prescribing ?[sub(w)]
3.9.4 Correction for the Reichardt law
3.10 Wall functions for isothermal walls
References
4 Some numerical methods for fluids
4.1 Introduction
4.2 Numerical methods for compressible flows
4.2.1 Flux schemes and upwinded schemes
4.2.2 A FEM-FVM discretization
4.2.3 Approximation of the convection fluxes
4.2.4 Accuracy improvement
4.2.5 Positivity
4.2.6 Time integration
4.2.7 Local time stepping procedure
4.2.8 Implementation of the boundary conditions
4.2.9 Solid walls: transpiration boundary condition
4.2.10 Solid walls: implementation of wall laws
4.3 Incompressible flows
4.3.1 Solution by a projection scheme
4.3.2 Spatial discretization
4.3.3 Local time stepping
4.3.4 Numerical approximations for the k - e equations
4.4 Mesh adaptation
4.4.1 Delaunay mesh generator
4.4.2 Metric definition
4.4.3 Mesh adaptation for unsteady flows
4.5 An example of adaptive unsteady flow calculation
References
5 Sensitivity evaluation and automatic differentiation
5.1 Introduction
5.2 Computations of derivatives
5.2.1 Finite differences
5.2.2 Complex variables method
5.2.3 State equation linearization
5.2.4 Adjoint method
5.2.5 Adjoint method and Lagrange multipliers
5.2.6 Automatic differentiation
5.2.7 A class library for the direct mode
5.3 Nonlinear PDE and AD
5.4 A simple inverse problem
5.5 Sensitivity in the presence of shocks
5.6 A shock problem solved by AD
5.7 Adjoint variable and mesh adaptation
5.8 Tapenade
5.9 Direct and reverse modes of AD
5.10 More on FAD classes
References
6 Parameterization and implementation issues
6.1 Introduction
6.2 Shape parameterization and deformation
6.2.1 Deformation parameterization
6.2.2 CAD-based
6.2.3 Based on a set of reference shapes
6.2.4 CAD-free
6.2.5 Level set
6.3 Handling domain deformations
6.3.1 Explicit deformation
6.3.2 Adding an elliptic system
6.3.3 Transpiration boundary condition
6.3.4 Geometrical constraints
6.4 Mesh adaption
6.5 Fluide-structure coupling
References
7 Local and global optimization
7.1 Introduction
7.2 Dynamical systems
7.2.1 Examples of local search algorithms
7.3 Global optimization
7.3.1 Recursive minimization algorithm
7.3.2 Coupling dynamical systems and distributed computing
7.4 Multi-objective optimization
7.4.1 Data mining for multi-objective optimization
7.5 Link with genetic algorithms
7.6 Reduced-order modeling and learning
7.6.1 Data interpolation
7.7 Optimal transport and shape optimization
References
8 Incomplete sensitivities
8.1 Introduction
8.2 Efficiency with AD
8.2.1 Limitations when using AD
8.2.2 Storage strategies
8.2.3 Key points when using AD
8.3 Incomplete sensitivity
8.3.1 Equivalent boundary condition
8.3.2 Examples with linear state equations
8.3.3 Geometric pressure estimation
8.3.4 Wall functions
8.3.5 Multi-level construction
8.3.6 Reduced order models and incomplete sensitivities
8.3.7 Redefinition of cost functions
8.3.8 Multi-criteria problems
8.3.9 Incomplete sensitivities and the Hessian
8.4 Time-dependent flows
8.4.1 Model problem
8.4.2 Data mining and adjoint calculation
References
9 Consistent approximations and approximate gradients
9.1 Introduction
9.2 Generalities
9.3 Consistent approximations
9.3.1 Consistent approximation
9.3.2 Algorithm: conceptual
9.4 Application to a control problem
9.4.1 Algorithm: control with mesh refinement
9.4.2 Verification of the hypothesis
9.4.3 Numerical example
9.5 Application to optimal shape design
9.5.1 Problem statement
9.5.2 Discretization
9.5.3 Optimality conditions: the continuous case
9.5.4 Optimality conditions: the discrete case
9.5.5 Definition of ?[sub(h)]
9.5.6 Implementation trick
9.5.7 Algorithm: OSD with mesh refinement
9.5.8 Orientation
9.5.9 Numerical example
9.5.10 A nozzle optimization
9.5.11 Theorem
9.5.12 Numerical results
9.5.13 Drag reduction for an airfoil with mesh adaptation
9.6 Approximate gradients
9.6.1 A control problem with domain decomposition
9.6.2 Algorithm
9.6.3 Numerical results
9.7 Conclusion
9.8 Hypotheses in Theorem 9.3.2.1
9.8.1 Inclusion
9.8.2 Continuity
9.8.3 Consistency
9.8.4 Continuity of ?
9.8.5 Continuity of ?[sub(h)](a[sub(h)])
9.8.6 Convergence
References
10 Numerical results on shape optimization
10.1 Introduction
10.2 External flows around airfoils
10.3 Four-element airfoil optimization
10.4 Sonic boom reduction
10.5 Turbomachines
10.5.1 Axial blades
10.5.2 Radial blades
10.6 Business jet: impact of state evaluations
References
11 Control of unsteady flows
11.1 Introduction
11.2 A model problem for passive noise reduction
11.3 Control of aerodynamic instabilities around rigid bodies
11.4 Control in multi-disciplinary context
11.4.1 A model problem
11.4.2 Coupling strategies
11.4.3 Low-complexity structure models
11.5 Stability, robustness, and unsteadiness
11.6 Control of aeroelastic instabilities
References
12 From airplane design to microfluidics
12.1 Introduction
12.2 Governing equations for microfluids
12.3 Stacking
12.4 Control of the extraction of infinitesimal quantities
12.5 Design of microfluidic channels
12.5.1 Reduced models for the flow
12.6 Microfluidic mixing device for protein folding
12.7 Flow equations for microfluids
12.7.1 Coupling algorithm
References
13 Topological optimization for fluids
13.1 Introduction
13.2 Dirichlet conditions on a shrinking hole
13.2.1 An example in dimension 2
13.3 Solution by penalty
13.3.1 A semi-analytical example
13.4 Topological derivatives for fluids
13.4.1 Application
13.5 Perspective
References
14 Conclusions and prospectives
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W

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