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HP-FEM for Coupled Problems in Fluid Dynamics
Dubcová, Lenka ; Feistauer, Miloslav (advisor) ; Segeth, Karel (referee) ; Dolejší, Vít (referee)
The thesis is concerned with the solution of multiphysics problems described by partial differential equations using higher-order finite element method (hp-FEM). Basics of hp-FEM are described, together with some practical details and challenges. The hp-adaptive strategy, based on the reference solution and meshes with arbitrary level hanging nodes, is discussed. The thesis is mainly concerned with the extension of this strategy to monolithical solution of coupled multiphysics problems, where each physical field exhibits different qualitative behavior. In such problems, each physical field is discretized on an individual mesh automatically obtained by the adaptive algorithm to suit the best the corresponding solution component. Moreover, the meshes can change in time, following the needs of the solution components. All described methods and technologies are demonstrated on several examples throughout the thesis, where comparisons with traditionally used approaches are shown.
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HP-FEM for Coupled Problems in Fluid Dynamics
Dubcová, Lenka
of dissertation hp-FEM FOR COUPLED PROBLEMS IN FLUID DYNAMICS Lenka Dubcová The thesis is concerned with the solution of multiphysics problems de- scribed by partial differential equations using higher-order finite element method (hp-FEM). Basics of hp-FEM are described, together with some practical details and challenges. The hp-adaptive strategy, based on the reference solution and meshes with arbitrary level hanging nodes, is dis- cussed. The thesis is mainly concerned with the extension of this strategy to monolithical solution of coupled multiphysics problems, where each physical field exhibits different qualitative behavior. In such problems, each physical field is discretized on an individual mesh automatically obtained by the adaptive algorithm to suit the best the corresponding so- lution component. Moreover, the meshes can change in time, following the needs of the solution components. All described methods and tech- nologies are demonstrated on several examples throughout the thesis, where comparisons with traditionally used approaches are shown.
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HP-FEM for Coupled Problems in Fluid Dynamics
Dubcová, Lenka ; Feistauer, Miloslav (advisor) ; Segeth, Karel (referee) ; Dolejší, Vít (referee)
The thesis is concerned with the solution of multiphysics problems described by partial differential equations using higher-order finite element method (hp-FEM). Basics of hp-FEM are described, together with some practical details and challenges. The hp-adaptive strategy, based on the reference solution and meshes with arbitrary level hanging nodes, is discussed. The thesis is mainly concerned with the extension of this strategy to monolithical solution of coupled multiphysics problems, where each physical field exhibits different qualitative behavior. In such problems, each physical field is discretized on an individual mesh automatically obtained by the adaptive algorithm to suit the best the corresponding solution component. Moreover, the meshes can change in time, following the needs of the solution components. All described methods and technologies are demonstrated on several examples throughout the thesis, where comparisons with traditionally used approaches are shown.
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HP-FEM for Coupled Problems in Fluid Dynamics
Dubcová, Lenka
of dissertation hp-FEM FOR COUPLED PROBLEMS IN FLUID DYNAMICS Lenka Dubcová The thesis is concerned with the solution of multiphysics problems de- scribed by partial differential equations using higher-order finite element method (hp-FEM). Basics of hp-FEM are described, together with some practical details and challenges. The hp-adaptive strategy, based on the reference solution and meshes with arbitrary level hanging nodes, is dis- cussed. The thesis is mainly concerned with the extension of this strategy to monolithical solution of coupled multiphysics problems, where each physical field exhibits different qualitative behavior. In such problems, each physical field is discretized on an individual mesh automatically obtained by the adaptive algorithm to suit the best the corresponding so- lution component. Moreover, the meshes can change in time, following the needs of the solution components. All described methods and tech- nologies are demonstrated on several examples throughout the thesis, where comparisons with traditionally used approaches are shown.
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Numerical simulation of interaction of fluids and solid bodies
Dubcová, Lenka ; Knobloch, Petr (referee) ; Feistauer, Miloslav (advisor)
The subject of this thesis is modelling and numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil. A solid airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the finite element solution of the Navier-Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. High Reynolds numbers up to 106 require the application of a suitable stabilization of the finite element discretization and application of a turbulent model. We apply the algebraic turbulent models, which were designed by Baldwin and Lomax and by Rostand. As a result a sufficiently accurate and robust method is developed, which was tested by the simulation of flow along a flat plate and applied to the computation of pressure distribution along the airfoil with forced vibrations.
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Numerical simulation of interaction of a vibrating airfoil with turbulent flax
Dubcová, L. ; Feistauer, M. ; Horáček, Jaromír ; Sváček, Petr
The report deals with numerical simulations of 2D viscous incompressible flow around a rotationaly vibrating profile. The flow is described by continuity and Navier-Stokes equations. Solution of the partial differential equations is based on finite element method. Because the Reynolds numbers higher than 10 000 are considered the solution is stabilized by SUPG method. Alge-braic turbulence model is taken into account and for simulations of the flow on moving grids the ALE method is used. the method was applied on harmonie vibrations of the profil NACA 0012 and the results are in good agreement with the experimental data obtained in ARTI.
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