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Vliv materiálových parametrů na stabilitu termální konvekce
Dostalík, Mark ; Matyska, Ctirad (advisor) ; Klika, Václav (referee)
The thesis is focused on the investigation of Rayleigh-Bénard problem in an extended setting approximating the conditions in the Earth's mantle. The aim is to evaluate the influence of depth- and temperature- dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on the qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection and characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly non-linear analysis. It has been found that the character of convection differ substantially from the standard case of Rayleigh-Bénard convection. Powered by TCPDF (www.tcpdf.org)
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The effect of a subsurface ocean on the heat transfer in an icy moon
Kvorka, Jakub ; Čadek, Ondřej (advisor) ; Souček, Ondřej (referee)
Successful space missions to Jupiter and Saturn provided important data bearing information about topography and internal structure of icy bodies in the outer Solar System. One of the possibilities how to explain the observed topography of an icy moon is to assume the existence of subsurface reservoir of liquid water transferring heat from the rocky core to icy crust causing its deformation. In this thesis, we develop a computer program to model the convective heat transfer in a rotating liquid shell, which we use to analyze heat flux anomalies on the top of the subsurface ocean. The results obtained for Titan are in agreement with those independently obtained from modelling the icy crust.
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Numerical tests of far-field boundary conditions for stably stratified flows
Bodnár, Tomáš ; Fraunié, P. ; Řezníček, Hynek
This numerical study presents the results of simulations of stably stratified wall-bounded flows. The effect of artificial far-field boundary conditions is studied in detail. The standard homogeneous Neumann condition for pressure is replaced by a non-homogeneous condition depending on local velocity and its gradient. The two-dimensional tests are performed for the case of flow over a low isolated hill. The simulations on computational domains with three different heights are discussed to evaluate the performance of the new far-field artifcial boundary condition. The model is based on Boussinesq approximation of non-homogeneous Navier-Stokes equations, solved using artificial compressibility method, looking for a steady solution.
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Artificial far-field pressure boundary conditions for wall-bounded stratified flows
Bodnár, Tomáš ; Fraunié, P.
This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions on the arti cial boundaries of the computational domain. The simple three dimensional test case deals with the steady flow of an incompressible, variable density fluid over a low smooth model hill. The Boussinesq approximation model is solved by an in-house developed high-resolution numerical code, based on compact finite-difference discretization in space and Strong Stability Preserving Runge-Kutta method for (pseudo-) time stepping.
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Vliv materiálových parametrů na stabilitu termální konvekce
Dostalík, Mark ; Matyska, Ctirad (advisor) ; Klika, Václav (referee)
The thesis is focused on the investigation of Rayleigh-Bénard problem in an extended setting approximating the conditions in the Earth's mantle. The aim is to evaluate the influence of depth- and temperature- dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on the qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection and characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly non-linear analysis. It has been found that the character of convection differ substantially from the standard case of Rayleigh-Bénard convection. Powered by TCPDF (www.tcpdf.org)
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On the boundary conditions in the numerical simulation of stably stratified fluids flows
Bodnár, Tomáš ; Fraunié, P.
This paper presents the results of a numerical study of the stably stratified flow over a low smooth hill. The emphasize is on certain problems related to artificial boundary conditions used in the numerical simulations. The numerical results of three-dimensional simulations are shown for a range of Froude and Reynolds numbers in order to demonstrate the varying importance of these boundary issues in different flow regimes. The simulations were performed using the Boussinesq approximation model solved by a high-resolution numerical code. The in-house developed code is based on compact finite-difference discretization in space and Strong Stability Preserving Runge-Kutta time integration.
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