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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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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 solution of flow past an airfoil
Prokopová, Jaroslava ; Feistauer, Miloslav (advisor) ; Najzar, Karel (referee)
Nazev prace: Numorioke feseni obtekani leleckeho profilu Autor: .Javoslava Prokopova Katedra (ustav): Katedra numerieke maternal,iky Vedoucf bakalarske prace: Prof- RNDr. Miloslav Feistauer, DrSc. e-mail vedoudho: feiyf'^kaTlin.niff. ouni.cz Abstrakt: Pfedkladaiia prace se vennjo problematic^1 obtekani izolovanelio le- teckeho profilu. .Tso\ zdc popsany rovnice charaktcvizuji nova^kn, Tu^tlacitol- no. novifivc'% stacioiiarni, rovinnr proudorif a nvixUnia koni])lo1,iii cliaraktrriH- lika danclio problonm ]K)inoci ryrhloati i ijroud(jvc tunkc^. Hlavnf uaplni jo ])ak stiulium niol.ody fuukci kuinploxni promonne a melody kouecnych prvku. Pfi aplikaci tfx-hto met.orl so zainonijoino na fescni oljtokaiii Znkov- skcho profilu. Di'ky ostro odtokovo hrano tuhoto profiln jsou zdo studovany odtokovo podmiiiky a jejich vyuziti vo stiulovanych motodacU. Poslodni casti Leto prace jo srovnain' vysledkii dosazeuycli ].)omorf tool)to nu^tod pro zvo- loriy Z\ikovskoho profil. Klicova slova: neva.xke, uoatlaoitolno, lunn'ri^'e, sta.oioiu'i.nii, ruvimio proudoni; mctoda fuukei koinploxni proruonnr; moUnla k(jneciiyoh ])rvkii: Znkovskeho profil; odtokova pochuiuka Title: Numerical .solution of flow past an airfoil Author: Jaroslava Prokopova Department: Department of Numoricn,! Matlieniatica Supervisor: Prof. RNDr. Miloslav...
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Adaptive space-time discontinuous Galerkin method for the solution of non-stationary problems
Vu Pham, Quynh Lan ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
This thesis studies the numerical solution of non-linear convection-diffusion problems using the space- time discontinuous Galerkin method, which perfectly suits the space as well as time local adaptation. We aim to develop a posteriori error estimates reflecting the spatial, temporal, and algebraic errors. These estimates are based on the measurement of the residuals in dual norms. We derive these estimates and numerically verify their properties. Finally, we derive an adaptive algorithm and apply it to the numerical simulation of non-stationary viscous compressible flows. Powered by TCPDF (www.tcpdf.org)
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