PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2010 | Vol. 39, no 3 | 677-713
Tytuł artykułu

Shape derivatives for general objective functions and the incompressible Navier-Stokes equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier-Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equations and linear elasticity. This article tries to be self contained, also presenting many useful results from the literature. We conclude with a comparison of different objective functions for the shape optimization of an obstacle in a channel, which can be done quite conveniently when one knows the general form of the shape gradient.
Wydawca

Rocznik
Strony
677-713
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
autor
Bibliografia
  • AMROUCHE, C., NEČASOVA, Š. and SOKOLOWSKI, J. (2007) Shape sensitivity analysis of the Neumann problem of the Laplace equation in the half-space. Technical Report preprint 2007-12-20, Institute of Mathematics, AS CR, Prague.
  • ATKINSON, K. and HAN, W. (2007) Theoretical Numerical Analysis: A Functional Analysis Framework. Texts in Applied Mathematics, 39. Springer, 2nd edition.
  • BOISGÉRAULT, S. and ZOLÉSIO, J.P. (1993) Shape derivative of sharp functionals governed by Navier-Stokes flow. In: W. Jager, J. Necas, O. John, K. Najzar and J. Stara, eds., Partial Differential Equations: Theory and Numerical Solution. Research Notes in Mathematics. Chapman & Hall/CRC, 49-63.
  • DELFOUR, M.C. and ZOLÉSIO, J.P. (2001) Shapes and Geometries: Analysis, Differential Calculus, and Optimization. Advances in Design and Control. SIAM, Philadelphia.
  • GUNZBURGER, M.D. (2003) Perspectives in Flow Control and Optimization. Advances in Design and Control. SIAM, Philadelphia.
  • HINTERMÜLLER, M. and RING, W. (2004) An inexact Newton-CG-type active contour approach for the minimization of the Mumford-Shah functional. Journal of Mathematical Imaging and Vision, 20, 19-42.
  • ITO, K., KUNISCH, K., GUNTHER, G. and PEICHL, H. (2008) Variational approach to shape derivatives. Control, Optimisation and Calculus of Variations, 14, 517-539.
  • MOHAMMADI, B. and PIRONNEAU, O. (2001) Applied Shape Optimization for Fluids. Numerical Mathematics and Scientific Computation. Clarendon Press, Oxford.
  • PIRONNEAU, O. (1973) On optimum profiles in Stokes flow. Journal of Fluid Mechanics, 59 (1), 117-128.
  • PIRONNEAU, O. (1974) On optimum design in fluid mechanics. Journal of Fluid Mechanics, 64 (1), 97-110.
  • PLOTNIKOV, P.I., RUBAN, E.V. and SOKOLOWSKI, J. (2008) Inhomogeneous boundary value problems for compressible Navier-Stokes equations: Well-posedness and sensitivity analysis. Journal on Mathematical Analysis, 40 (3), 1152-1200.
  • PLOTNIKOV, P.I. and SOKOLOWSKI, J. (2005) On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier-Stokes equations. Journal of Mathematical Fluid Mechanics, 7 (4), 529-573.
  • PLOTNIKOV, P.I. and SOKOLOWSKI, J. (2008) Stationary boundary value problems for compressible Navier-Stokes equations. Handbook of Differential Equations, 6, 313-410.
  • SCHMIDT, S., ILIC, C., GAUGER, N. and SCHULZ, V. (2008) Shape gradients and their smoothness for practical aerodynamic design optimization. Technical Report Preprint SPP1253-10-03, DFG-SPP 1253. Submitted to OPTE.
  • SCHMIDT, S. and SCHULZ, V. (2009) Impulse response approximations of discrete shape Hessians with application in CFD. SIAM Journal on Control and Optimization, 48 (4), 2562-2580.
  • SOKOLOWSKI, J. and ZOLÉSIO, J.P. (1992) Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0055-0024
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.