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Nonnewtonian fluid flow simulation using lattice Boltzmann method
Kuriščák, Pavel ; Hron, Jaroslav (advisor) ; Málek, Josef (referee)
Title: Non-newtonian fluid flow simulation using lattice Boltzmann method Author: Bc. Pavel Kuriščák Department: Mathematical Institute, Charles University Supervisor: RNDr. Ing. Jaroslav Hron Ph.D. Supervisor's e-mail address: Jaroslav.Hron@mff.cuni.cz Abstract: The aim of this thesis is to find and estabilish a modification to the Lattice Boltzmann Method, allowing it to simulate non-newtonian behaviour of fluids. In the theoretical part of thesis, there is introduced a derivation, based on the work of [22], that is capable of arriving to macroscopical Navier-Stokes equa- tions completely a priori from the Boltzmann equation, utilizing the Hermite basis expansion. This derivation is afterwards applied to the method suggested by [11], that uses the changed equilibrium distribution to fine-tune the local fluid viscosity according to the non-newtonian model. In the last part of thesis, this method is implemented in the form of lattice kinetic scheme and tested on three sample problems. Keywords: Lattice Boltzmann Method, non-newtonian fluids, Hermite expansion, lattice kinetic scheme
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Generování a optimalizace meshů
Mokriš, Dominik ; Šír, Zbyněk (advisor) ; Hron, Jaroslav (referee)
This thesis is devoted to the problem of finding a suitable geometrical de- scription of the domain for the Finite Element Method (FEM). We present the most important methods used in generation and improvement of unstructured triangular meshes (grids) for two dimensional FEM. Possible measures of mesh quality are discussed with respect to their usage in linear Lagrange FEM. The relationship between mesh geometry (especially angles of particular triangles), discretization error and stiffness matrix condition number is examined. Two methods of mesh improvement, based on Centroidal Voronoi Tessellations (CVT) and Optimal Delaunay Triangulations (ODT), are discussed in detail and some results on convergence of CVT based methods are reviewed. Some aspects of these methods, e.g. the relation between density of boundary points and interior mesh vertices and the treatment of the boundary triangles is reconsidered in a new way. We have implemented these two methods and we discuss possible im- provements and new algorithms. A geometrically very interesting idea of recent alternative to FEM, Isogeometric Analysis (IGA), is outlined and demonstrated on a simple example. Several numerical tests are made in order to the compare the accuracy of solutions of isotropic PDEs obtained by FEM on bad mesh, mesh improved...
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Modelování nestlačitelných ionizovaných směsí
Havrda, Jaroslav ; Roubíček, Tomáš (advisor) ; Bulíček, Miroslav (referee) ; Hron, Jaroslav (referee)
In the present work we study the model of incompressible ionized mixtures from point of view of mathematical analysis and practical implementations. The model consists of the continuity equation, Navier-Stokes equations, Nernst-Planck equations and Poisson equation for the electric potential. We proove the existence of a weak solution for the model in three space dimensions. We also present a simple program for computing the solutions of Nernst-Planck equations and Poisson equation and use it to examine the problem that arrise during the computation. The results in thermodynamics of mixtures are refered as the physical part of the thesis.
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Application of spectral element method in fluid dynamics
Pech, Jan ; Maršík, František (advisor) ; Hron, Jaroslav (referee)
This work presents application of spectral element method (SEM) for solving partial differential equations. This method can be seen as combination of spectral method (SM) and finite element method (FEM). Computational domain is decomposed to smaller elements, what enable description of more general geometries. On each element is then used the spectral method, which brings high accuracy. In this work the basic theory is presented for SM and SEM with emphasize to facilitate application of this method in developing computer programs. Numerical scheme is presented on several appropriate examples. The result of this work is in comparison of solution of chosen problems obtained by SM and SEM from written program. Comparison with professional software is also done and shows power of spectral methods.
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Mixture theory applications in blood flow simulation
Michalová, Marie ; Hron, Jaroslav (advisor) ; Souček, Ondřej (referee)
In the beginning we outline some important properties of blood and de- scribe it from the biological point of view. In the next section we show how we derived our model based on the mixture theory. For the final model we suggest a mathematical method based on the finite element method and subject it to tests for flow in a simple domain. In the middle part we prove the existence of solution for a model with simplified constitutive relation for the stress tensor, which still includes an anisotropic model for the platelet diffusion. In the last section we show numerical results. We start with sim- ple testing computations in simple domains, followed by computations in a two-dimensional simulation of an aneurysm, and narrowed blood vessel re- spectively. In the end we also show some illustrative computations in three dimensions. 1
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Numerical methods for vortex dynamics
Outrata, Ondřej ; Hron, Jaroslav (advisor) ; Šístek, Jakub (referee)
Two aspects of solving the incompressible Navier-Stokes equations are described in the thesis. The preconditioning of the algebraic systems arising from the Finite Element Method discretization of the Navier-Stokes equations is complex due to the saddle point structure of the resulting algebraic problems. The Pressure Convection Diffusion Reaction and the Least Squares Commutator preconditioners constitute two possible choices studied in the thesis. Solving the flow problems in time-dependent domains requires special numerical methods, such as the Fictitious Boundary method and the Arbitrary Lagrangian Eulerian formulation of Navier-Stokes equations which are used in the thesis. The problems examined in the thesis are simulations of experiments conducted in liquid Helium at low temperatures. These simulations can be used to establish a relationship between vorticity and new quantity pseudovorticity in an experiment-like setting.
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