|
| |
|
|
Time-domain modelling of global barotropic ocean tides
Einšpigel, David ; Martinec, Zdeněk (advisor) ; Haagmans, Roger (referee) ; Matyska, Ctirad (referee)
Traditionally, ocean tides have been modelled in frequency domain with forcing of selected tidal constituents. It is a natural approach, however, non-linearities of ocean dynamics are implicitly neglected. An alternative approach is time-domain modelling with forcing given by the full lunisolar potential, i.e., all tidal constituents are included. This approach has been applied in several ocean tide models, however, a few challenging tasks still remain to solve, for example, the assimilation of satellite altimetry data. In this thesis, we present DEBOT, a global and time-domain barotropic ocean tide model with the full lunisolar forcing. DEBOT has been developed "from scratch". The model is based on the shallow water equations which are newly derived in geographical (spherical) coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a physically consistent form. The numerical model employs finite differences in space and a generalized forward-backward scheme in time. The validity of the code is demonstrated by the tests based on integral invariants. DEBOT has two modes for ocean tide modelling: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. We introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing...
|
|
|
Numerical solution of the shallow water equations
Šerý, David ; Dolejší, Vít (advisor) ; Felcman, Jiří (referee)
The thesis deals with the numerical solution of partial differential equati- ons describing the flow of the so-called shallow water neglecting the flow in the vertical direction. These equations are of hyperbolical type of the first or- der with a reactive term representing the bottom topology. We discretize the resulting system of equations by the implicit space-time discontinuous Ga- lerkin method (STDGM). In the literature, the explicit techniques are used most of the time. The implicit approach is suitable especially for adaptive methods, because it allows the usage of different meshes for different time niveaus. In the thesis we derive the corresponding method and an adaptive algorithm. Finally, we present usage of the method in several examples. 1
|
|
| |
|
|
Numerical solution of the shallow water equations
Šerý, David ; Dolejší, Vít (advisor) ; Felcman, Jiří (referee)
The thesis deals with the numerical solution of partial differential equati- ons describing the flow of the so-called shallow water neglecting the flow in the vertical direction. These equations are of hyperbolical type of the first or- der with a reactive term representing the bottom topology. We discretize the resulting system of equations by the implicit space-time discontinuous Ga- lerkin method (STDGM). In the literature, the explicit techniques are used most of the time. The implicit approach is suitable especially for adaptive methods, because it allows the usage of different meshes for different time niveaus. In the thesis we derive the corresponding method and an adaptive algorithm. Finally, we present usage of the method in several examples. 1
|
|
|
Numerical solution of the shallow water equations
Šerý, David ; Dolejší, Vít (advisor) ; Felcman, Jiří (referee)
The thesis deals with the numerical solution of partial differential equati- ons describing the flow of the so-called shallow water neglecting the flow in the vertical direction. These equations are of hyperbolical type of the first or- der with a reactive term representing the bottom topology. We discretize the resulting system of equations by the implicit space-time discontinuous Ga- lerkin method (STDGM). In the literature, the explicit techniques are used most of the time. The implicit approach is suitable especially for adaptive methods, because it allows the usage of different meshes for different time niveaus. In the thesis we derive the corresponding method and an adaptive algorithm. Finally, we present usage of the method in several examples. 1
|
|
|
Time-domain modelling of global barotropic ocean tides
Einšpigel, David ; Martinec, Zdeněk (advisor) ; Haagmans, Roger (referee) ; Matyska, Ctirad (referee)
Traditionally, ocean tides have been modelled in frequency domain with forcing of selected tidal constituents. It is a natural approach, however, non-linearities of ocean dynamics are implicitly neglected. An alternative approach is time-domain modelling with forcing given by the full lunisolar potential, i.e., all tidal constituents are included. This approach has been applied in several ocean tide models, however, a few challenging tasks still remain to solve, for example, the assimilation of satellite altimetry data. In this thesis, we present DEBOT, a global and time-domain barotropic ocean tide model with the full lunisolar forcing. DEBOT has been developed "from scratch". The model is based on the shallow water equations which are newly derived in geographical (spherical) coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a physically consistent form. The numerical model employs finite differences in space and a generalized forward-backward scheme in time. The validity of the code is demonstrated by the tests based on integral invariants. DEBOT has two modes for ocean tide modelling: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. We introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing...
|
|
|
Flow of a subsurface ocean in shallow water approximation
Šafin, Jakub ; Čadek, Ondřej (advisor) ; Velímský, Jakub (referee)
In this thesis, we deal with the flow of a subsurface ocean in the so-called shallow water approximation. From the equations describing general flow of an incompressible fluid, we obtain simplified equations, applicable to a shallow global ocean on a rotating sphere. Based on these equations, we develop a program that can be used to model the flow of an ocean in 2D. We create short simulations of the flow on two icy moons, Europa and Enceladus, forced by the eccentricity and obliquity tidal potentials. The existence of subsurface oceans has been demonstrated on icy moons of outer planets; the mechanism which keeps them from freezing has remained unclear until now. Based on the flow simulations, we attempt to estimate the energy dissipation due to bottom friction. Powered by TCPDF (www.tcpdf.org)
|
|
|
Modelling of exoplanetary atmospheric circulation
Novák, Jiří ; Brechler, Josef (advisor) ; Raidl, Aleš (referee)
In this thesis we study the properties of exoplanetary atmospheres. The first part describes methods and instruments for searching exoplanets, statistics of discovered exoplanets and the sampling factor. The second part describes the properties of chosen planets and moons in the Solar system (Venus, Mars and Titan) and also possible properties of the exoplanetary atmospheres that are only briefly understood. The third part describes the atmospheric models which incorporate full 3D model of the atmosphere, dynamical core, shallow-water model and 1D spherically-symmetric model. We also show the results of exoplanetary atmospheric models published in the scientific journals. This part also describes the icosahedral geodetic grid that is advantageous for the global climatic models, and also discretisation on sphere and the application of the operators (gradient, divergence, vorticity) on geodetic grid. The fourth part discusses results of the numerical solution of the atmospheric circulation with the forcing on geodetic grid. In this part we also show global maps of the variables after a particular time of the numerical integration and also the evolution of the variables at chosen points in time. In the discussion part we examine the results of our program. The results of the numerical integrations (chosen...
|
|
|
ADER schemes for the shallow water equations
Monhartová, Petra ; Felcman, Jiří (advisor) ; Dolejší, Vít (referee)
In the present work we study the numerical solution of shallow water equations. We introduce a vectorial notation of equations laws of conservation from which we derive the shallow water equations (SWE). There is the simplify its derivation, notation and the most important features. The original contribution is to derive equations for shallow water without the using of Leibniz's formula. There we report the finite volume method with the numerical flow of Vijayasundaram type for SWE. We present a description of the linear reconstruction, quadratic reconstruction and ENO reconstruction and their using for increasing of order accuracy. We demonstrate using of linear reconstruction in finite volume method of second order accuracy. This method is programmed in Octave language and used for solving of two problems. We apply the method of the ADER type for the shallow water equations. This method was originally designed for the Euler's equation.
|
guest ::
