|
|
Analysis of Methods of Differences for Partial Differential Equations Solving
Zpěváková, Jana ; Zbořil, František (referee) ; Šátek, Václav (advisor)
In this thesis, we discuss the numerical solution of ordinary differential equation and numerical methods of solving partial differential equations. We propose and implement an application, that converts partial differential hyperbolic equation to a set of ordinary differential equations using finite difference method. After that, the system of equations is solved using the Taylor method programmed in Matlab environment. Finally, we compare the time complexity of proposed solution with parallel numerical computation.
|
|
|
Numerical simulation of sound propagation by difference methods
Prochazková, Zdeňka ; Zatočilová, Jitka (referee) ; Čermák, Libor (advisor)
The goal of this thesis is to introduce the finite difference method (FDM) adjusted for usage in modeling of sound propagation, and other approaches that are used together with this method. These approaches include selective filtering and time integration using the Runge-Kutta method, which has low computer memory requirements. An important topic in modeling sound propagation are boundary conditions. The thesis examines and verifies several types of boundary conditions. Included in the thesis are solutions to example problems implemented in Matlab.
|
|
|
Numerical solution of the simplified Richards equations
Kváčová, Radka ; Dolejší, Vít (advisor) ; Knobloch, Petr (referee)
In this Bachelor's thesis we study a numerical solution of the simplified Richards equation which describes flows in porous media. At first we derive Richards equation from the Darcy law and the continuity equation. We solve the 1D variant of this using semi-implicit discretization with respect to time. This problem leads to a solving system of a linear algebraic equations for each time level. We implement this method in the Matlab environment and we perform some numerical experiments for particular porous medium - gravel and clay and we compare obtained results. 1
|
|
|
Design optimization of packed bed for thermal energy storage
Krist, Thomas ; Charvát, Pavel (referee) ; Klimeš, Lubomír (advisor)
Tato diplomová práce se zabývá tématem výměny tepla v zásobníku tepla typu ”packed bed”. Cílem je popsat přenos tepla v zásobníku tepla obsahující kamínky malých průměrů, skrz který proudí horký vzduch. Toto je modelováno v prostředí MATLAB. Na začátku je krátký úvod do problematiky zahrnující ukládání tepla a jeho možné využití. Dále je uveden krátký přehled o základech přenosu tepla, typech přenosu tepla a termofyzikální vlastnosti systému vzduch-kámen. Ve třetí kapitole je představen zásobník tepla typu ”packed bed” a rozličné modely a dané podmínky jsou vysvětleny. Další kapitola se zabývá s numerickými metodami, převážně s metodou konečných diferencí použitou v této práci. Pátá kapitola se zaměřuje na obecnou optimalizaci daného problému přenosu tepla. Populačně založený metaheuristický optimalizační algoritmus zvaný Genetický algoritmus je popsán. Sestavení modelu je ukázáno v šesté kapitole, stejně jako prezentace výsledků získaných z programu MATLAB. V poslední kapitole je pak diskutován závěr a doporučení.
|
|
| |
|
|
Modification of Navier_Stokes equations asuming the quasi-potential flow
Navrátil, Dušan ; Pochylý, František (referee) ; Fialová, Simona (advisor)
The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.
|
|
|
Heat transfer solution of solidifying steel system with phase change with moving edge conditions
Fedorko, Tomáš ; Mauder, Tomáš (referee) ; Štětina, Josef (advisor)
Cílem diplomové práce je vytvoření 2D numerického modelu pohybujícího se řezu s proměnnými okrajovými podmínkami skutečné geometrie plynulého odlévání a chlazení předlitku v prostředí MATLAB. Model se zabývá vysoce nelineárními termofyzikálními podmínkami oceli během tuhnutí a chlazení. V práci je simulovaná nejen nelinearita termofyzikálních podmínek, ale také nelinearita při fázové změně. Fázová změna je modelovaná pomocí metody entalpie, metody zdánlivé kapacity a metody teplotního zotavení. Všechny výsledky práce jsou porovnány z více hledisek, jako např. z hlediska přesnosti, rychlosti výpočtu, nebo vhodnosti časového diskretizačního kroku pro nelineární problémy, a paralelizace.
|
|
|
Computational modeling of radial hydrodynamic bearings for water machines
Pokorný, Jan ; Šimek,, Jiří (referee) ; Návrat, Tomáš (advisor)
The aim of this thesis is to calculate the stiffness and damping coefficients for radial hydrodynamic bearings. Cylindrical and lemon hydrodynamic bearings are considered. The solution to this problem mainly depends on the hydrodynamic pressure in the bearing. The numerical solution of the Reynolds equation is used to calculate the pressure. The effect of variable viscosity and density of the lubricant due to temperature changes is considered. The static equilibrium position of the journal centre is also solved. The stiffness and damping coefficients are determined using small amplitude journal motions about the equilibrium position. Three methods for determining these coefficients are presented. The outcome of this thesis is an algorithm for the calculation of stiffness and damping coefficients for cylindrical and lemon bearings. Results for lemon bearings are presented and comparison with the commercial software DynRot BR is made. The benefit of this thesis is the creation of an algorithm for the calculation of journal centre equilibrium position, a new way of incorporating the temperature changes in the viscosity and the density of the lubricant, and the modification of a method for calculating stiffness and damping coefficients based on experimental analogy.
|
|
|
Analysis of Methods of Differences for Partial Differential Equations Solving
Zpěváková, Jana ; Zbořil, František (referee) ; Šátek, Václav (advisor)
In this thesis, we discuss the numerical solution of ordinary differential equation and numerical methods of solving partial differential equations. We propose and implement an application, that converts partial differential hyperbolic equation to a set of ordinary differential equations using finite difference method. After that, the system of equations is solved using the Taylor method programmed in Matlab environment. Finally, we compare the time complexity of proposed solution with parallel numerical computation.
|
|
| |
guest ::
