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Korteweg fluids - modeling, analysis and computer simulations
Blaškovičová, Monika ; Málek, Josef (advisor) ; Řehoř, Martin (referee)
We present two possible thermodynamical approaches towards a derivation of a model, proposed by Korteweg at the beginning of the 20th century, that is suitable to describe phase transitions liquid-vapor with non-sharp interfaces. The first approach (Dunn, Serrin (1985)) is based on classical rational continuum thermodynamics. The second approach (Heida, Málek (2010)) stems from the principles of classical nonequilibrium continuum thermodynamics. We compare both approaches in favor of the second one. The considered constitutive equation for the Cauchy stress is nonlinear. Nonlinearity and higher order derivatives of the density makes the analysis of relevant problems for the Navier-Stokes- Korteweg (NSK) fluid more difficult in comparison to problems concerning Navier-Stokes equations. Special attention is devoted to the appropriate choice of the boundary conditions. We also investigate the influence of compressibility on the stability of bubbles by comparing numerical simulations for compressible NSK fluid and its incompressible variant. Instabilities observed for a compressible NSK fluid are due to the pressure that has a different meaning for incompressible fluid. Powered by TCPDF (www.tcpdf.org)
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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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Bingham-Korteweg fluids - modeling, analysis and computer simulations
Los, Tomáš ; Málek, Josef (advisor) ; Bulíček, Miroslav (referee)
Flow of granular materials is usually initiated when the shear stress is large enough and exceeds certain critical value. This can result in the presence of the dead-zones in which the flow itself does not take place. Motions of such materials are frequently described by Bingham model. Flows of granular fluids are frequently connected with the presence of free surface. In the thesis Bingham model is incorporated into a more general framework of Bingham-Korteweg fluids, which is a suitable way how to transfer free- boundary problems into the problems on fixed domains. A part of the thesis concerns mathematical analysis of interesting relevant problems for incompressible fluids. 1
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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor) ; Pražák, Dalibor (referee) ; Breit, Dominic (referee)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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Korteweg fluids - modeling, analysis and computer simulations
Blaškovičová, Monika ; Málek, Josef (advisor) ; Řehoř, Martin (referee)
We present two possible thermodynamical approaches towards a derivation of a model, proposed by Korteweg at the beginning of the 20th century, that is suitable to describe phase transitions liquid-vapor with non-sharp interfaces. The first approach (Dunn, Serrin (1985)) is based on classical rational continuum thermodynamics. The second approach (Heida, Málek (2010)) stems from the principles of classical nonequilibrium continuum thermodynamics. We compare both approaches in favor of the second one. The considered constitutive equation for the Cauchy stress is nonlinear. Nonlinearity and higher order derivatives of the density makes the analysis of relevant problems for the Navier-Stokes- Korteweg (NSK) fluid more difficult in comparison to problems concerning Navier-Stokes equations. Special attention is devoted to the appropriate choice of the boundary conditions. We also investigate the influence of compressibility on the stability of bubbles by comparing numerical simulations for compressible NSK fluid and its incompressible variant. Instabilities observed for a compressible NSK fluid are due to the pressure that has a different meaning for incompressible fluid. Powered by TCPDF (www.tcpdf.org)
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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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