Shape optimization in fluid mechanics. (English) Zbl 1076.76020

Mohammadi, Bijan; Pironneau, Olivier

Annu. Rev. Fluid Mech. 36, 255-279 (2004).

Summary: This paper is a short and nonexhaustive survey of some recent developments in optimal shape design (OSD) for fluids. OSD is an interesting field both mathematically and for industrial applications. Existence, sensitivity, and compatibility of discretizations are important theoretical issues. Efficient algorithmic implementations with low complexity are also critical. We discuss topological optimization, algorithmic differentiation, gradient smoothers, computer aided design (CAD)-free platforms and shock differentiation; all these are applied to a multicriterion optimization for a supersonic business jet.
For the entire collection see [Zbl 1048.76003].

MSC:

76B75	Flow control and optimization for incompressible inviscid fluids
76N25	Flow control and optimization for compressible fluids and gas dynamics
76M30	Variational methods applied to problems in fluid mechanics
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
49Q10	Optimization of shapes other than minimal surfaces
76D55	Flow control and optimization for incompressible viscous fluids
76M25	Other numerical methods (fluid mechanics) (MSC2010)

Keywords:

topological optimization; algorithmic differentiation; supersonic business jet