Shape optimization for Navier-Stokes flow

Inverse Problems in Science and Engineering

Volumn 16, Issue 5, 2008, Pages 583-616

  Gao, Z M ^a   Ma, Y C ^a   Zhuang, H W ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b ENGINEERING COLLEGE OF ARMED POLICE FORCE   (China)

Author keywords

Gradient algorithm; Material derivative; Minimax formulation; Navier Stokes equations; Shape derivative; Shape optimization

Indexed keywords

BOOLEAN FUNCTIONS; FLUID DYNAMICS; FLUID MECHANICS; FUNCTIONAL ANALYSIS; GRADIENT METHODS; SHAPE OPTIMIZATION; VISCOUS FLOW;

ADJOINT; COST FUNCTIONALS; DIFFERENTIABILITY; FUNCTION SPACES; LAGRANGIAN; MINI MAX; NAVIER STOKES EQUATIONS; NAVIER-STOKES FLOWS; NEWTONIAN; NON-HOMOGENEOUS; NUMERICAL EXAMPLES; OPTIMAL SHAPE DESIGNS; PARAMETRIZATION; STATE DERIVATIVE; VISCOUS INCOMPRESSIBLE FLUIDS;

NAVIER STOKES EQUATIONS;

EID: 47849106320     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970701743319     Document Type: Article

References (18)

1. Céa, J., 1981, Problems of shape optimal design. In: E. J. Haug and J. Céa (Eds) Proceedings of the Optimization of Distributed Parameter Structures, Vol. II (The Netherlands: Sijthoff and Noordhoff, Alphen aan denRijn), pp. 1005-1048.
2. Delfour, M.C. and Zolesio, J.P., 2002, Shapes and geometries: analysis, differential calculus, and optimization. Advance in Design and Control (Philadelphia, USA: SIAM).
3. Pironneau, O., 1984, Optimal Shape Design for Elliptic systems (Berlin: Springer).
4. Sokolowski, J. and Zolesio, J.P., 1992, Introduction to Shape Optimization: Shape Sensitivity Analysis (New York: Springer-Verlag).
5. Pironneau, O., 1974, On optimum design in fluid mechanics. Journal of Fluid Mechanics, 64(1), 97-110.
6. Simon, J., 1990, Domain variation for drag in Stokes flow. In: L. Xunjing, (Ed.) Proceedings of the Lecture notes in Control and Information Science (New York: Springer).
7. Gao, Z. Ma, Y. and Zhuang, H., 2006, Optimal shape design for Stokes flow via minimax differentiability. Mathematical and Computer Modelling, JMCM (Oxford: Taylor & Francis) (submitted).
8. Gao, Z. Ma, Y. and Zhuang, H., 2007, Shape optimization for Navier-Stokes flow (This article is in this issue please reference).
9. Gao, Z. and Ma, Y., 2007, Shape reconstruction of an inverse boundary value problem for the stationary heat conduction with a Robin condition. Indian Journal Pure and Applied Mathematics, 38(2), 105-121.
10. Gao, Z. and Ma, Y., 2006, Shape sensitivity analysis for a Robin problem via minimax differentiability. Applied Mathematics and Computer, 181(2), 1090-1105.
11. Hadamard, J., 1907, Mémoire sur le problème d'analyse relatif â l'équilibre des plaques élastiques encastrées. Proceedings of the Mémoire des savants étrangers, 33, 1907.
12. Simon, J., 1980, Differentiation with respect to the domain in boundary value problems. Numerical Function Analytical Optimization, 2, 649-687.
13. Zolesio, J.P., 1979, Identification de domaines par déformation. PhD thesis, Université de Nice.
14. Temam, R., 2001, AMS Chelsea (Ed.) Navier-Stokes Equations, Theory and Numerical Analysis (Rhode Island: American Mathematical Society).
15. Boisgerault, S., 2000, Optimisation de forme: systemes nonlineaires et mecanique des fluides, PhD thesis, Ecole des Mines de Paris.
16. Dziri, R., 1995, Problemes de frontiere libre en fluides visqueux, PhD thesis, Ecole des Mines de Paris, Robotique, Automatique.
17. Correa, R. and Seeger, A., 1985, Directional derivative of a minmax function. Nonlinear Analysis, Theory Methods and Applications, 9, 13-22.
18. Hecht, F. Pironneau, O. Hyaric, A.L. and Ohtsuka, K., 2006, FreeFem++ Manual. Available on line at:http://www.freefem.org