Shape optimization in problems governed by generalised Navier-Stokes equations: existence analysis

• Autorzy: Haslinger J. , Malek J. , Stebel J.
• Języki publikacji: EN

Abstrakty

EN

We study a shape optimization problem for a paper machine headbox which distributes a mixture of water and wood fibers in the paper manufacturing process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective of this paper is to prove the existence of an optimal shape.

Słowa kluczowe

EN

optimal shape design; paper machine headbox; incompressible non-Newtonian fluid; algebraic turbulence model

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 1
• Strony: 283--303
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Haslinger J.

• Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague 8, Czech Republic

autor

Malek J.

• Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague 8, Czech Republic

autor

Stebel J.

• Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague 8, Czech Republic

Bibliografia

• Hamalainen, J., Makinen, R.A.E. and Tarvainen, P. (2000) Optimal Design of Paper Machine Headboxes. Int. J. Numer. Meth. Fluids, 34, 685–700.
• Hamalainen, J. (1993)Mathematical Modelling and Simulation of Fluid Flows in Headbox of Paper Machines. Doctoral Thesis, University of Javaskyla.
• Haslinger, J. and Makinen, R.A.E. (2003) Introduction to Shape Optimization. Theory, Approximation, and Computation. SIAM, Advances in Design and Control.
• Ladyzhenskaya, O.A. (1968) O modifikatsiyakh uravnenii Navye–Stoksa dl’abolshikh gradientov skorosti (On modifications of Navier–Stokes equations for large gradients of the velocity). Zapiski nauchnych seminarov LOMI 5, 126–154, (in Russian).
• Ladyzhenskaya, O.A. (1969) The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York.
• Lions, J.L. (1969) Quelques Methodes de Resolution des Problemes aux Limites Non Lineaires. Dunod, Paris (in French).
• Malek, J., Necas, J., Rokyta, M. and Ruzicka, M. (1996) Weak and measure-valued solutions to evolutionary PDE’s. CRC Press, Applied Mathematics and Mathematical Computation 13.
• Malek, J., Rajagopal, K.R. and Ruzicka, M. (1995) Existence and Regularity of Solutions and Stability of the Rest State for Fluids with Shear Dependent Viscosity. Math. Models Methods in Appl. Sci. 6, 789–812.
• Pares, C. (1992) Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids. Applicable Analysis 43, 245–296.
• Rajagopal, K.R. (1993) Mechanics of non-Newtonian fluids. In: G.P. Galdi, J. Necas, eds., Recent Developments in Theoretical Fluid Mechanics, Series 291. Longman Scientific & Technical, Essex, 129–162.
• Sokolowski, J. and Zolesio, J.P. (1992) Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer–Verlag, Berlin.