Abstract
This paper deals with shape optimization of systems governed by the Stokes flow with threshold slip boundary conditions. The stability of solutions to the state problem with respect to a class of domains is studied. For computational purposes the slip term and impermeability condition are handled by a regularization. To get a finite dimensional optimization problem, the optimized part of the boundary is described by Bézier polynomials. Numerical examples illustrate the computational efficiency.
Highlights
Jaroslav HaslingerDepartment of Numerical Mathematics, Faculty of Mathematics and Physics Charles University Prague, Sokolovska 83, 186 75 Prague 8, Czech Republic Department of Mathematical Information Technology University of Jyvaskyla, P.O. Box 35 (Agora) FIN-40014 Jyvaskyla, Finland
The standard kinematic boundary condition in mathematical models of fluid mechanics is represented by the no-slip condition, namely the fluid has the zero velocity u on the boundary of a solid impermeable wall
Due to the threshold character of the slip boundary conditions, the respective control-to-state mapping which with any admissible domain associates the solution to the state problem (M) is non-differentiable in the classical sense
Summary
Department of Numerical Mathematics, Faculty of Mathematics and Physics Charles University Prague, Sokolovska 83, 186 75 Prague 8, Czech Republic Department of Mathematical Information Technology University of Jyvaskyla, P.O. Box 35 (Agora) FIN-40014 Jyvaskyla, Finland
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