|
|
Modelling of plasma-solid interaction
Nožka, Jan ; Hrach, Rudolf (advisor) ; Hron, Jaroslav (referee)
Title: Modelling of plasma-solid interaction Author: Jan Nožka Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Rudolf Hrach, DrSc., Department of Surface and Plasma Science Abstract: This work is devoted to computer modeling of the low-temperature argon plasma discharge. We created one basic particle model and one basic fluid model. Furthermore, we created a model of electron-electron interaction in three dimensions. This model is able to stabilize nonequilibrium electron gas in the expected equilibrium. This model was developed to investigate the influence of electron-electron scattering on the acceleration of electrons above the speed that is sufficient for excitation or ionization of neutral argon atom. At the end of this work there are results that shed a light on the importance of this interaction in comparison with the amount of fast electrons that are present in the plasma due to electric filed field.
|
|
|
Matematické modelování viskoplastických materiálů
Touška, Kryštof ; Hron, Jaroslav (advisor) ; Stebel, Jan (referee)
In the first chapter of the thesis we present an introduction to the visco- plasticity and overview of the presented problems. The constitutive relation for Bingham fluid is derived and in the second chapter. Further there is demon- strated a procedure of proving existence and uniqueness with classical varia- tional method. This method is compared with the same process using modern implicit theory. The last chapter starts with summary of used problem formu- lations and used software. It is then followed by the main part with results of numerical simulations, both for the purpose of used formulations comparison and then verification of the preferred one in more complicated simulations. We expect a possible application of tested approaches on different materials. 1
|
|
|
Behaviour of new types of material models in a squeeze flow geometry
Řehoř, Martin ; Průša, Vít (advisor) ; Hron, Jaroslav (referee)
Investigation of material behaviour in a squeeze flow geometry provides an impor- tant technique in rheology and it is relevant also from the technological point of view (some types of dampers, compression moulding). To our best knowledge, the sque- eze flow has not been solved for fluids-like materials with pressure-dependent material moduli. In the main scope of the present thesis, an incompressible fluid whose visco- sity strongly depends on the pressure is studied in both the perfect-slip and the no-slip squeeze flow. It is shown that such a material model can provide interesting departures compared to the classical model for viscous (Navier-Stokes) fluid even on the level of analytical solutions, which are obtained using some physically relevant simplificati- ons. Numerical simulation of a free boundary problem for the no-slip squeeze flow is then developed in the thesis using body-fitted curvilinear coordinates and spectral collocation method. An interesting behaviour is expected especially in the corners of the computational domain where the stress singularities are normally located. Unfor- tunately, numerical results reveal some fundamental drawbacks related to the physical model and its possible improvement is discussed at the end of the thesis.
|
|
|
Immersed boundary methods in air-flow models
Benešová, Stanislava ; Brechler, Josef (advisor) ; Hron, Jaroslav (referee)
This work focuses on the immersed boundary methods and their aplications to modeling flow in urban areas. In the first part Navier-Stokes equations are derived. In the second part we describe the main priciples of the immersed boundary methods. Two main groups of methods are introduced accompanied by examples. Based on the properties of these methods one method is selected which is suitable to describe the geometry in the modeling of airflow in urban areas. The method MIB from the article Mark et al. (2008) is chosen. This method is compared with the method introduced in the article Kim et al. (2001). Both methods are described in detail and compared according to several criteria in the third chapter. Such a criterion is the accuracy of the continuity equation. Simulations of a several test problems were carried out for the purpose of comparison of the chosen methods. Flow around a circular cylinder and a square cylinder for Reynolds numbers of 10 and 30 is solved. The divergence value of~the~velocity field in the modeled area was observed during the calculation of both methods. The results yields that MIB method solves the continuity equation more accurate.
|
|
|
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...
|
|
|
Matematické modelování proudění krve
Michalová, Marie ; Hron, Jaroslav (advisor) ; Průša, Vít (referee)
At first we point out some important properties and behaviour of blood and blood particles. In the next part we approximate steady two-dimensional Pois- seiulle flow between two parallel plates. We show analytical solutions for New- tonian and power-law models. According to observations of Fahraeus-Lindquist effect we show two-layer models combining previously mentioned models. In the last section we model pulsatile Poisseuille flow and we show analytical and nu- merical results for some pressure and viscosity values. In the end we show our best model, where we shift pressure gradient and get closer to the real blood flow characteristics. 1
|
|
| |
|
| |
|
| |
|
|
Variational methods for segmentation of digital images
Kotera, Jan ; Zitová, Barbara (advisor) ; Kružík, Martin (referee) ; Hron, Jaroslav (referee)
The text covers the theory of the Mumford and Shah model for digital image segmentation. The strong and weak formulation is presented and the questions of existence, uniqueness, and solution regularity is answered. Then, a particular variant of the model called `active contours without edges' is numerically implemented. This implementation is tested on several images, the results are presented in detail and theoretically explained.
|
guest ::
RSS feed.