This diploma thesis is focused on waves and oscillations in the solar corona, which takes place in a large number of phenomena that occurs here. In recent years these waves have been observed in Earth observation same like as cosmic observation.The task of this thesis is to familiarize with the problems of waves and oscillations in solar corona and subsequent interpretation into numerical simulations that are performed by FLASH code. The aim of the work will be to modify numerical simulations and thus to achieve more realistic of the observed phenomena.

en.txt After an introduction into current sheet physics, with emphasis to solar physics we showed some formulations of finite element method. We implemented and evaluated new discontinuous finite element with Taylor basis and introduced deal.II library with an example of burgers equation. While the program is dimension independent, we compared our solution with a one-dimensional analytical solution. Finally, using previously derived LSFEM formulation, we solved simple current sheet problem using deal.II. Stránka 1

Theoretical part of this thesis is dedicated to the theoretical basis of electric conduction phenomena in fluids and method of calculation of magnetohydrodynamic phenomena. In the experimental part, computational modules have been developed to complement and augment the use of commercial simulation programs for simulation in the field of magnetohydrodynamics. On practical examples of mass spectrometer simulation, Einzel lens, electron movement and electric circuit breaker, the functionality of the computational models and the correctness of the obtained results were documented. Created computational modules can be used to design and optimize products using magnetohydrodynamic phenomena.

In the present work we study the properties of accretion tori orbiting black hole. Our approach to this problem comes from the solving of general relativistic magnetohydrodynamic equations, which follow from conservation of the energy-momentum tensor, the particle number and from Maxwell's equations. We solve these equations by numerical methods which are described in Chapter 1. The formalism of tori which we consider here is described in Chapter 2. We are interested in tori with constant density of angular momentum and Fishbone-Moncrief tori mainly. We study accretion rates in these tori when the mass of black hole is increased suddenly and so the equilibrium in the torus is corrupted. For tori with constant density of angular momentum we study the influence of the presence of toroidal magnetic field on accretion rates.