Applied shape optimization for fluids

• Main Authors: Mohammadi, B. (Author), Pironneau, Olivier (Author)
• Format: Electronic eBook
• Language: English
• Published: Oxford ; New York : Oxford University Press, ©2010.
• Edition: 2nd ed.
• Series: Numerical mathematics and scientific computation.
• Subjects: Fluid dynamics > Mathematics.; Mathematical optimization.; Shape theory (Topology); elektronické knihy; electronic books
• ISBN: 9780199546909; 0199546908; 9780191574214; 019157421X; 9780191720482; 0191720488; 9781523121236; 1523121238
• Physical Description: 1 online resource (xiv, 277 pages) : illustrations

Examining shape optimization problems for fluids, with the equations needed for their understanding and the simulation of these problems, this text introduces automatic differentiation, approximate gradients, and automatic mesh refinement.

Table of 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 problem2.5.2 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