Browsing by Author "Stebel, Jan"
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- ItemShape optimization for a time-dependent model of a carousel press in glass production(ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS, ZITNA 25, PRAHA 1, 115 67, CZECH REPUBLIC, 2019) Salač, Petr; Stebel, JanThis contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption of rotational symmetry, supplemented by suitable boundary conditions. The cost functional is defined as the squared weighted L-2 norm of the difference between a prescribed constant and the temperature of the plunger surface layer at the moment before separation of the plunger and the glass piece. The existence and uniqueness of the solution to the state problem and the existence of a solution to the optimization problem are proved.
- ItemTopics in Mathematical Fluid Mechanics and Shape Optimization(Technical university of Liberec, 2019-07-08) Stebel, JanThis habilitation thesis is based on the author's contributions to the mathematical theory of incompressible uids and to the shape optimization in uid mechanics. In Chapter 2, an overview of basic equations, theory of weak solutions and nite-element approximation for incompressible uids is given. Chapter 3 is devoted to the formulation of shape optimization problems, to the questions of existence of solutions, approximation and di erentiability. Finally, in Chapter 4 some results obtained by the author are mentioned, namely on the theory of non-Newtonian piezoviscous uids, applied shape optimization and sensitivity analysis.