Mohammadi B., Pironneau O. Applied Shape Optimization for Fluids (Numerical Mathematics and Scientific Computation)

2nd edition. — Oxford University Press, 2010. — 292 p. — ISBN 978–0–19–954690–9.Computational fluid dynamics (CFD) and optimal shape design (OSD) are of practical importance for many engineering applications - the aeronautic, automobile, and nuclear industries are all major users of these technologies. Giving the state of the art in shape optimization for an extended range of applications, this new edition explains the equations needed to understand OSD problems for fluids (Euler and Navier Strokes, but also those for microfluids) and covers numerical simulation techniques. Automatic differentiation, approximate gradients, unstructured mesh adaptation, multi-model configurations, and time-dependent problems are introduced, illustrating how these techniques are implemented within the industrial environments of the aerospace and automobile industries.With the dramatic increase in computing power since the first edition, methods that were previously unfeasible have begun giving results. The book remains primarily one on differential shape optimization, but the coverage of evolutionary algorithms, topological optimization methods, and level set algortihms has been expanded so that each of these methods is now treated in a separate chapter.Presenting a global view of the field with simple mathematical explanations, coding tips and tricks, analytical and numerical tests, and exhaustive referencing, the book will be essential reading for engineers interested in the implementation and solution of optimization problems. Whether using commercial packages or in-house solvers, or a graduate or researcher in aerospace or mechanical engineering, fluid dynamics, or CFD, the second edition will help the reader understand and solve design problems in this exciting area of research and development, and will prove especially useful in showing how to apply the methodology to practical problems.Introduction.
Optimal shape design.Examples.
Existence of solutions.
Solution by optimization methods.
Sensitivity analysis.
Discretization with triangular elements.
Implementation and numerical issues.
Optimal design for Navier-Stokes flows.Partial differential equations for fluids.The Navier-Stokes equations.
Inviscid flows.
Incompressible flows.
Potential flows.
Turbulence modeling.
Equations for compressible flows in conservation form.
Wall laws.
Generalization of wall functions.
Wall functions for isothermal walls.Some numerical methods for fluids.Numerical methods for compressible flows.
Incompressible flows.
Mesh adaptation.
An example of adaptive unsteady flow calculation.Sensitivity evaluation and automatic differentiation.Computations of derivatives.
Nonlinear PDE and AD.
A simple inverse problem.
Sensitivity in the presence of shocks.
A shock problem solved by AD.
Adjoint variable and mesh adaptation.
Tapenade.
Direct and reverse modes of AD.
More on FAD classes.Parameterization and implementation issues.Shape parameterization and deformation.
Handling domain deformations.
Mesh adaption.
Fluide-structure coupling.Local and global optimization.Dynamical systems.
Global optimization.
Multi-objective optimization.
Link with genetic algorithms.
Reduced-order modeling and learning.
Optimal transport and shape optimization.Incomplete sensitivities.Efficiency with AD.
Incomplete sensitivity.
Time-dependent flows.Consistent approximations and approximate gradients.Generalities.
Consistent approximations.
Application to a control problem.
Application to optimal shape design.
Approximate gradients.Hypotheses in Theorem.Numerical results on shape optimization.External flows around airfoils.
Four-element airfoil optimization.
Sonic boom reduction.
Turbomachines.
Business jet: impact of state evaluations.Control of unsteady flows.A model problem for passive noise reduction.
Control of aerodynamic instabilities around rigid bodies.
Control in multi-disciplinary context.
Stability, robustness, and unsteadiness.
Control of aeroelastic instabilities.From airplane design to microfluidics.Governing equations for microfluids.
Stacking.
Control of the extraction of infinitesimal quantities.
Design of microfluidic channels.
Microfluidic mixing device for protein folding.
Flow equations for microfluids.
Coupling algorithm.Topological optimization for fluids.Dirichlet conditions on a shrinking hole.
Solution by penalty.
Topological derivatives for fluids.
Perspective.Conclusions and prospectives.