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Choice of the SUPG parameter for higher order finite elements
Kohutka, Jiří ; Knobloch, Petr (advisor) ; Dolejší, Vít (referee)
In this work, we deal with the finite element method Streamline Upwind/Petrov-Galerkin (SUPG) and use it to solve boundary value problem for the stationary convection-diffusion equation with dominant convection with Dirichlet boundary condition on the whole boundary of bounded polyhedral computational domain of dimension 1 and 2, respectively. We consider a quadratic Lagrangian finite elements on the line segments and triangles, respectively. The core of the work is a proposition of choice of stabilizing parameter of SUPG method as an elementwise affine function in outflow boundary layer and as an elementwise constant function in the rest of the computational domain. We show that this choice gives a more accurate solution than the choice of the stabilization parameter as a constant in each element. 1
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Numerical solution of the Navier-Stokes equations with a generalized state eqution
Ullrichová, Martina ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
Title: Numerical solution of the Navier-Stokes equations with a generalized state eqution Author: Martina Ullrichová Department: Department of numerical Mathematics Supervisor: doc. RNDr. Vít Dolejší, Ph.D., DSc. Supervisor's e-mail address: dolejsi@karlin.mff.cuni.cz Abstract: In the present work we study the simulation of viscous compressible flow. We consider a generalized model of gas described by a generalized state equation. We firstly summarize construction of this generalized equation and its consequences for the existence and uniquenes of the solution of the compressible flow problem. We suggest particular ways how define this generalized relations. Afterwards, we solve the Navier-Stokes problem by the discontinous Galerkin method. Considering the properties of the generalized model we choose explicit time discretization. Finally, we compare new generalized model with the standard model (ideal gas) for different flow regimes around the NACA0012 profil. Keywords: viscous compressible flow, Navier-Stokes equations, discontinous Ga- lerkin method, generalized state equation
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DES modelling of the turbulent flow
Benešová, Stanislava ; Brechler, Josef (advisor) ; Dolejší, Vít (referee)
This thesis deals with the study of hybrid RANS/LES methods for modeling of turbulent flow with a focus on the DES method and its modifications. The theoretical part focuses on the description of turbulent flow and classical methods for its modeling. The following describes the hybrid RANS/LES methods, their principles and categories. Finally, the DES method is described in detail together with its improvement in form of DDES and IDDES methods. The practical part is devoted to the testing of DES and DDES on benchmark problems. We describe here used software OpenFOAM and numerical methods used to discretize the equations. One part is devoted to grid generation. The DES and the DDES methods are tested on two benchmarks: flat plate with zero pressure gradient and backward facing step. The simulaton results are compared with experimental data, with a focus on good modeling of the velocity profile near wall, turbulent viscosity and skin friction coefficient. Powered by TCPDF (www.tcpdf.org)
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Vizualization of numerical solutions of partial differential equations with the aid of software Tecplot
Hejbal, Pavel ; Dolejší, Vít (advisor) ; Knobloch, Petr (referee)
Na/ev prace; Vi'/uali/ace nnmerickyeli resem' parcialm'ch diferenciahheh rovnii- pomoci bah'ku Tecplot Autor: Pavel Hejbal Katedra: Katedra numerieke matematiky YVdouci bakalafskc place: Doc. RiST)r. Vil Dolejsi, Ph.D. e-mail vedouci'ho: ViT.Doloj.si^'inff'.cuiii.c/, Al)stra.kt: V pfcdloxene praci se zabyvame vi7,ua!i/,ae:i numerickych fescm purciahii'ch elitereiicialnich rovnic /fska.nych iH'sj>ojit.oii Galcrkiiun'ou nus Uxlon, ktcra dava po rastt'ch polynomialm, ale lu-sijojitoii aproxiniat-i. IJrt) vizuali/a.t:i chccnic pon^i't konicrrui soft.ware TVtipiol, ktcry v.sak unio/MUJc vizualixoval pouzr s])ojitou, ]K> rastrch liurarni fnnkri. C'l'lcin trto ])i'Hce je vyt.vorit vhorlny interface mczi vyst.iipnn ]ics[jojit('' Galcr- kinovy inctddy a vstupem [>roj;ranni Tcr])lot, co/ /nunu'iia navrhnoiit a posleze iinpU'iiicntovat al^oritniy, ktcre aproxiimiji nospojitou, pu castech polynomial111funkci novon siiojitoii a po fastcch liMcanii fmikcf. Xa xavr.v se veinijcHH1 tvorbo sof'twarovyvh prostnxlkn. ktcrr |)ou/,itiui xini'iirnych al^orilinu iimoxni automaticky gpn(iro\at aniniacc nunuTirkolio fcscin'. Klfrova slova: Tccjjlot. Mcsjxtjita (ialrrkinova nictocla, trian^iilacu Title: Vi/uali/ation of nMincrical solutions of partial diti'crt'Mt ia.l (^quati- ons with the aid of soil ware T(icii)lot Author: Pavel...
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Goal-oriented a posteriori error estimates and adaptivity for the numerical solution of partial differential equations
Roskovec, Filip ; Dolejší, Vít (advisor) ; Kanschat, Guido (referee) ; Zeman, Jan (referee)
A posteriori error estimation is an inseparable component of any reliable numerical method for solving partial differential equations. The aim of the goal-oriented a posteriori error estimates is to control the computational error directly with respect to some quantity of interest, which makes the method very convenient for many engineering applications. The resulting error estimates may be employed for mesh adaptation which enables to find a numerical approximation of the quantity of interest under some given tolerance in a very efficient manner. In this thesis, the goal-oriented error estimates are derived for discontinuous Galerkin discretizations of the linear scalar model problems, as well as of the Euler equations describing inviscid compressible flows. It focuses on several aspects of the goal-oriented error estimation method, in particular, higher order reconstructions, adjoint consistency of the discretizations, control of the algebraic errors arising from iterative solutions of both algebraic systems, and linking the estimates with the hp-anisotropic mesh adaptation. The computational performance is demonstrated by numerical experiments.
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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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