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Fluid-structure interaction of compressible flow
Hasnedlová, Jaroslava ; Feistauer, Miloslav (advisor) ; Křížek, Michal (referee) ; Kozel, Karel (referee) ; Rannacher, Rolf (referee)
Title: Fluid-structure interaction of compressible flow Author: RNDr. Jaroslava Hasnedlová Department: Department of Numerical Mathematics, Institute of Applied Mathematics Supervisors: Prof. RNDr. Miloslav Feistauer, DrSc., Dr. h. c., Prof. Dr. Dr. h. c. Rolf Rannacher Supervisors' e-mail addresses: feist@karlin.mff.cuni.cz, rannacher@iwr.uni-heidelberg.de Abstract: The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The DGFE method is applied sep- arately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. The main result is the proof of error estimates in L2 (L2 )-norm and in DG-norm formed by the L2 (H1 )-seminorm and penalty terms. The second part of the thesis deals with the realization of fluid-structure interaction problem of the compressible viscous flow with the elastic structure. The time-dependence of the domain occupied by the fluid is treated by the ALE (Arbitrary Lagrangian-Eulerian) method, when the compress- ible Navier-Stokes equations are formulated in...
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Numerical simulation of transonic flow of wet steam
Nettl, Tomáš ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
This thesis is concerned on the simulation of wet steam flow using discontinuous Galerkin method. Wet steam flow equations consist of Naviere-Stokes equations for compressible flow and Hill's equations for condensation of water vapor. The first part of this thesis describes the mathematical formulation of wet steam model and the derivation of Hill's equations. The model equations are discretized with the aid of discontinuous Galerkin method and backward difference formula which leads to implicit scheme represented by nonlinear algebraic system. This system is solved using Newton-like method. The derived scheme was implemented in program ADGFEM which is used for solving non-stationary convective-diffusive problems. The numerical results are presented in the last part of this thesis. 1
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Numerical modelling of compressible flow using spectral element method
Jurček, Martin ; Dolejší, Vít (advisor) ; Kučera, Václav (referee)
The development of computational fluid dynamics has given us a very powerful tool for investigation of fluid dynamics. However, in order to maintain the progress, it is necessary to improve the numerical algorithms. Nowadays, the high-order methods based on the discontinuous projection seem to have the largest potential for the future. In the work, we used open-source framework Nektar++, which provides the high-order discretization method. We tested the abilities of the framework for computing the compressible sonic and transonic flow. We successfully obtained simulations of the viscous and inviscid flow. We computed the lift and the drag coefficients and showed that for a higher polynomial order we can obtain the same accuracy with less degrees of freedom and lower computational time. Also, we tested the shock capturing method for the computation of the inviscid transonic flow and confirmed the potential of the high order methods. 1
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Incompressible and compressible viscous flow with low Mach numbers
Balázsová, M. ; Feistauer, M. ; Sváček, Petr ; Horáček, Jaromír
In this paper we compare incompressible flow and low Mach number compressible viscous flow. Incompressible Navier-Stokes equations were treated with the aid of discontinuous Galerkin method in space and backward difference method in time. We present numerical results for a flow in a channel which represents a simplified model of the human vocal tract. Presented numerical results give a good correspondence between the incompressible flow and the compressible flow with low Mach numbers.
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Numerical simulation of transonic flow of wet steam
Nettl, Tomáš ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
This thesis is concerned on the simulation of wet steam flow using discontinuous Galerkin method. Wet steam flow equations consist of Naviere-Stokes equations for compressible flow and Hill's equations for condensation of water vapor. The first part of this thesis describes the mathematical formulation of wet steam model and the derivation of Hill's equations. The model equations are discretized with the aid of discontinuous Galerkin method and backward difference formula which leads to implicit scheme represented by nonlinear algebraic system. This system is solved using Newton-like method. The derived scheme was implemented in program ADGFEM which is used for solving non-stationary convective-diffusive problems. The numerical results are presented in the last part of this thesis. 1
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Fluid-structure interaction of compressible flow
Hasnedlová, Jaroslava ; Feistauer, Miloslav (advisor) ; Křížek, Michal (referee) ; Kozel, Karel (referee) ; Rannacher, Rolf (referee)
Title: Fluid-structure interaction of compressible flow Author: RNDr. Jaroslava Hasnedlová Department: Department of Numerical Mathematics, Institute of Applied Mathematics Supervisors: Prof. RNDr. Miloslav Feistauer, DrSc., Dr. h. c., Prof. Dr. Dr. h. c. Rolf Rannacher Supervisors' e-mail addresses: feist@karlin.mff.cuni.cz, rannacher@iwr.uni-heidelberg.de Abstract: The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The DGFE method is applied sep- arately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. The main result is the proof of error estimates in L2 (L2 )-norm and in DG-norm formed by the L2 (H1 )-seminorm and penalty terms. The second part of the thesis deals with the realization of fluid-structure interaction problem of the compressible viscous flow with the elastic structure. The time-dependence of the domain occupied by the fluid is treated by the ALE (Arbitrary Lagrangian-Eulerian) method, when the compress- ible Navier-Stokes equations are formulated in...
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Numerical tests of flow in human vocal tract
Pořízková, P. ; Kozel, K. ; Horáček, Jaromír
This study deals with a numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract. The authors present several numerical tests of computational domain, of modified numerical scheme and types of mesh for the wall motion frequency 100 Hz.
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