
On the development of a numerical model for the simulation of air flow in the human airways
Lancmanová, Anna ; Bodnár, Tomáš ; Sequeira, A.
This contribution reports on an ongoing study focusing on reduced order models for incompressible viscous fluid flow in two dimensional channels. A finite difference solver was developed using a simple implementation of the immersed boundary method to represent the channel geometry. The solver was validated for unsteady flow by comparing the obtained twodimensional numerical solutions with analytical profiles computed from the Womersley solution. Finally the 2D model was coupled to a simple 1D extension simulating the flow in axisymmetric elastic vessel (tube). Some of the coupling principles and implementation issues are discussed in detail.

 

Numerical assessment of stratification influence in simple algebraic turbulence model
Uhlíř, V. ; Bodnár, Tomáš ; Caggio, Matteo
This paper presents rst few results obtained using a newly developed test code aimed at validation and crosscomparison of turbulence models to be applied in environmental flows. A simple code based on nite di erence discretization is constructed to solve steady flows of incompresible nonhomogeneous (variable denstity) fluids. For the rst tests a simple algebraic turbulence model was implemented, containing stability function depending on the stratification via the gradient Richardson number. Numerical tests were performed in order to explore the capabilities of the new code and to get some insight into its behavior under di erent stratification. The twodimensional simulations were performed using immersed boundary method for the flow over low smooth hill. The resulting flow fields are compared for selected Richarson numbers ranging from stable up to unstable strati cation conditions.


Numerical validation of a simple immersed boundary solver for branched channels simulations
Lancmanová, A. ; Bodnár, Tomáš ; Keslerová, D.
This contribution reports on an ongoing study of incompressible viscous fluid flow in two dimensional branched channels. A new finite difference solver was developed using a simple implementation of an immersed boundary method to represent the channel geometry. Numerical solutions obtained using this new solver are compared with outputs of an older finite volume code working on classical wall tted structured multiblock grid. Besides of the comparative evaluation of obtained solution, the aim is to verify whether the immersed boundary method is suitable (accurate and e cient enough) for simulations of flow in channels with complicated geometry where the the grid generation might be challenging.


Numerical tests of vanishing diffusion stabilization in OldroydB fluid flow simulations
Pires, M. ; Bodnár, Tomáš
This work presents some numerical tests of finite element solution of incompressible OldroydB fluids flows, using different types of numerical stabilization. In this study the diffusive term (Laplacian of extra stress) is added to the tensorial constitutive relation where it is multiplied by a coefficient, that is variable in time. The goal is to make this diffusion coefficient vanish in time, so that the final solution remains unaffected by the added diffusion term. A series of numerical tests was performed for the steady twodimensional OldroydB fluid flow in corrugated channel (tube) to compare different versions of the vanishing stabilization terms and assess their efficiency in enforcing the solution convergence, without affecting the final steady state.


Secondorder model for atmospheric turbulence without critical Richardson number
Caggio, M. ; Schiavon, M. ; Tampieri, F. ; Bodnár, Tomáš
The purpose of this communication is to present a derivation of the nondimensional vertical gradients of the mean wind speed and mean potential temperature expressed in terms of the socalled similarity functions for very stable conditions of the atmosphere where theoretical approaches provide conflicting results (see e.g. Luhar et al. [19]). The result is based on the analysis of the secondorder model equations in the boundary layer approximations in which new heat flux equations are proposed. The model employs a recent closure for the pressuretemperature correlation, avoiding the issue of a critical treshold for the Richardson number.


Fluidstructure interaction between blood and dissipating artery wall
Fara, Jakub ; Tůma, Karel (advisor) ; Bodnár, Tomáš (referee)
In this thesis we introduce a new fluidstructure interaction model in the Eulerian description. This model is developed for blood flow in viscoelastic artery. For the fluid part a nonNewtonian model OldroydB is used and for the structure part KelvinVoigt model is employed. KelvinVoigt model will be reached by a limiting process of the OldroydB model. Interface between these two materials is guaranteed by conservative levelset method. Numerical tests of this model is performed by finite element method. This model is used for a simulation of two problems: a two dimensional channel with viscoelastic walls and pulsating inflow and TurekHron FSI benchmark. 1


When can a contract constitute the relation of influence or control and their potential consequences?
Bodnar, Tomáš ; Čech, Petr (advisor) ; Černá, Stanislava (referee)
When can a contract constitute the relation of influence or control and their potential consequences? The aim of my thesis is the description of the regulation of group entities (with the exception of concern law) with emphasis on the possibility to establish such relationship by a contract. I am trying to prove that establishment of the relationship of influence and control is possible. I am further trying to prove that such situations are not common in practice. Controlling relationship established by a contract is even quite unique. Another aim of my thesis is to describe the legal consequences of group entities under the Act on Corporations, especially the compensation for damages. However I would also like to take into consideration other consequences of group entities within the Act on corporations.


On the influence of diffusion stabilization in OldroydB fluid flow simulations
Pires, M. ; Bodnár, Tomáš
This work presents some numerical tests of finite element solution of incompressible OldroydB fluid flows. The effect of numerical stabilization using artificial stress diffusion is investigated in detail. The limits of Weissenberg number We for which it is possible to obtain the numerical solution were studied depending on the Reynolds number Re and the diffusion parameter. Series of numerical tests were performed for steady twodimensional OldroydB fluid flow in corrugated channel (tube). The numerical results clearly proved the advantage (higher attainable We) of stabilized numerical method over the classical formulation without the artificial stress diffusion.


Fluidstructure interaction between blood and dissipating artery wall
Fara, Jakub ; Tůma, Karel (advisor) ; Bodnár, Tomáš (referee)
In this thesis we introduce a new fluidstructure interaction model in the Eulerian description. This model is developed for blood flow in viscoelastic artery. For the fluid part a nonNewtonian model OldroydB is used and for the structure part KelvinVoigt model is employed. KelvinVoigt model will be reached by a limiting process of the OldroydB model. Interface between these two materials is guaranteed by conservative levelset method. Numerical tests of this model is performed by finite element method. This model is used for a simulation of two problems: a two dimensional channel with viscoelastic walls and pulsating inflow and TurekHron FSI benchmark. 1
