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Shape Optimization for Navier-Stokes Equations with Viscosity
Stebel, Jan ; Haslinger, Jaroslav (advisor) ; Feistauer, Miloslav (referee) ; Feireisl, Eduard (referee)
We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making 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 the 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 is to analyze theoretically this problem (proof of the existence of a solution), its discretization and the numerical realization.
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Matematické modelování viskoplastických materiálů
Touška, Kryštof ; Hron, Jaroslav (advisor) ; Stebel, Jan (referee)
In the first chapter of the thesis we present an introduction to the visco- plasticity and overview of the presented problems. The constitutive relation for Bingham fluid is derived and in the second chapter. Further there is demon- strated a procedure of proving existence and uniqueness with classical varia- tional method. This method is compared with the same process using modern implicit theory. The last chapter starts with summary of used problem formu- lations and used software. It is then followed by the main part with results of numerical simulations, both for the purpose of used formulations comparison and then verification of the preferred one in more complicated simulations. We expect a possible application of tested approaches on different materials. 1
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Aerodynamic Optimization of Airfoils and Wings Using Fast Solver
Hájek, Jaroslav ; Šafařík, Pavel (advisor) ; Maršík, František (referee) ; Stebel, Jan (referee)
This thesis is concerned with aerodynamic optimization of airfoils and wings. It focuses at using very fast solvers based on hybrid potential methods to evaluate the aerodynamic performance of the airfoils and wings. Compared to more widely used CFD solvers which are more computationally demanding, use of fast solvers brings different possibilities and different problems to tackle, some of which are analyzed in this work. A state-of-the-art fast solver for airfoils is resented, and a fast solver for slender wings is developed, and some of its aspects are discussed. An innovative evolutionary optimization algorithm is presented and both solvers are hen utilized to solve real-life airfoil and wing optimization problems.
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Matematické modelování viskoplastických materiálů
Touška, Kryštof ; Hron, Jaroslav (advisor) ; Stebel, Jan (referee)
In the first chapter of the thesis we present an introduction to the visco- plasticity and overview of the presented problems. The constitutive relation for Bingham fluid is derived and in the second chapter. Further there is demon- strated a procedure of proving existence and uniqueness with classical varia- tional method. This method is compared with the same process using modern implicit theory. The last chapter starts with summary of used problem formu- lations and used software. It is then followed by the main part with results of numerical simulations, both for the purpose of used formulations comparison and then verification of the preferred one in more complicated simulations. We expect a possible application of tested approaches on different materials. 1
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Shape Optimization for Navier-Stokes Equations with Viscosity
Stebel, Jan ; Haslinger, Jaroslav (advisor) ; Feistauer, Miloslav (referee) ; Feireisl, Eduard (referee)
We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making 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 the 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 is to analyze theoretically this problem (proof of the existence of a solution), its discretization and the numerical realization.
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|
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Aerodynamic Optimization of Airfoils and Wings Using Fast Solver
Hájek, Jaroslav ; Šafařík, Pavel (advisor) ; Maršík, František (referee) ; Stebel, Jan (referee)
This thesis is concerned with aerodynamic optimization of airfoils and wings. It focuses at using very fast solvers based on hybrid potential methods to evaluate the aerodynamic performance of the airfoils and wings. Compared to more widely used CFD solvers which are more computationally demanding, use of fast solvers brings different possibilities and different problems to tackle, some of which are analyzed in this work. A state-of-the-art fast solver for airfoils is resented, and a fast solver for slender wings is developed, and some of its aspects are discussed. An innovative evolutionary optimization algorithm is presented and both solvers are hen utilized to solve real-life airfoil and wing optimization problems.
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