**1192**

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**Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius elements**

Vacek, Karel; Sváček, P.

2024 - English
This paper addresses the problem of fluid flow interacting a vibrating solid cylinder described by one degree of freedom system and with fixed airfoil. The problem is described by the incompressible Navier-Stokes equations written in the arbitrary Eulerian-Lagrangian (ALE) formulation. The ALE mapping is constructed with the use of a pseudo-elastic approach. The flow problem is numerically approximated by the finite element method (FEM). For discretization of the fluid flow, the results obtained by both the Taylor-Hood (TH) element and the Scott-Vogelius (SV) finite element are compared. The TH element satisfies the Babuška-Brezzi inf-sup condition, which guarantees the stability of the scheme. In the case of the SV element the mesh, that is created as a barycentric refinement of regular triangulation, is used to satisfy the Babuška-Brezzi condition. The numerical results for two benchmark problems are shown.
Keywords:
*finite element method; arbitrary Lagrangian-Eulerian method; Scott-Vogelius element; Taylor-Hood element*
Available in digital repository of the ASCR
Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius elements

This paper addresses the problem of fluid flow interacting a vibrating solid cylinder described by one degree of freedom system and with fixed airfoil. The problem is described by the incompressible ...

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**Numerical study of the steady airflow in the human respiratory system during inhaling and exhaling**

Lancmanová, Anna; Bodnár, Tomáš

2024 - English
This paper presents some of the initial results of the numerical simulations of a steady turbulent flow in human upper airways during inhalation and exhalation. The mathematical model is based on the system of Reynolds-Averaged incompressible Navier-Stokes equations complemented by the SST k − ω turbulence model. The simulations were performed using finite-volume open source solver OpenFOAM on a realistic three-dimensional geometry. The main aim of this particular study is to verify the computational setup with special focus on appropriate choice and implementation of boundary conditions. The prescribed boundary conditions are chosen to mimic the physiological conditions during normal breathing cycle. This study aims to gain an insight into the airflow behavior during the inhalation and exhalation process by comparing the results of two distinct simulations corresponding to two different (opposite) flow rates . The obtained local flow rates and flow fields for both cases are presented and mutually compared. This initial work should serve as a foundation for future more complex simulations that will include the time-dependent and compressible effects.
Keywords:
*human airways; incompressible Navier-Stokes; OpenFOAM*
Available in digital repository of the ASCR
Numerical study of the steady airflow in the human respiratory system during inhaling and exhaling

This paper presents some of the initial results of the numerical simulations of a steady turbulent flow in human upper airways during inhalation and exhalation. The mathematical model is based on the ...

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**Numerical evaluation of mass-diffusive compressible fluids flows models**

Bodnár, Tomáš; Fraunié, P.

2024 - English
This contribution presents first numerical tests of some recently published alternative models for solution of viscous compressible and nearly incompressible models. All models are solved by high resolution compact finite difference scheme with strong stability preserving RungeKutta time stepping. The two simple but challenging computational test cases are presented, based on the double-periodic shear layer and the Kelvin-Helmholtz instability. The obtained time-dependent flow fields are showing pronounced shear and vorticity layers being resolved by the standard as well as by the new mass-diffusive modified models. The preliminary results show that the new models are viable alternative to the well established classical models.
Keywords:
*compressible Navier-Stokes; nearly incompressible flow; mass diffusion; compact finite-difference*
Available in digital repository of the ASCR
Numerical evaluation of mass-diffusive compressible fluids flows models

This contribution presents first numerical tests of some recently published alternative models for solution of viscous compressible and nearly incompressible models. All models are solved by high ...

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**Motion of fluids in the moving domain**

Nečasová, Šárka

2024 - English
It is a survay paper where the problem of the existence of weak solutions of compressible barotropic solutions in a moving bounded domain is studied.
Keywords:
*compressible fluid; moving domain; weak solutions*
Available in digital repository of the ASCR
Motion of fluids in the moving domain

It is a survay paper where the problem of the existence of weak solutions of compressible barotropic solutions in a moving bounded domain is studied.

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**Kam a kolik vody odvádí stromy? Modelování vlivu smrkových a bukových porostů na toky vody v půdě během extrémních klimatických podmínek**

Zelíková, Nikol; Šípek, Václav

2023 - Czech
Půdní vlhkost propojuje takové procesy, které ovlivňují celý hydrologický cyklus, a tím i dostupnost vodních zdrojů. Jedním z významných faktorů ovlivňující tyto procesy je přítomnost vegetace. Výzkum interakcí mezi vegetací, jejím managementem a procesy ovlivňující toky půdní vody nabývá na významu zejména v době probíhajících klimatických změn i změn krajinného pokryvu. Avšak komplexnost těchto interakcí, ovlivněná navíc jejich rozdílností mezi jednotlivými rostlinnými druhy tento výzkum ztěžuje. Proměna krajinného pokryvu probíhá také v českém lesnictví, konkrétně v podobě obměny smrkových monokultur buky. V této studii je proto zkoumán vliv dvou typů lesních porostů, smrku ztepilého (Picea abies) a buku lesního (Fagus sylvatica), na vodní režim půdy v experimentálním povodí Liz na Šumavě. A to (1) zjištěním rozdílů v množství půdní vláhy na základě dvaceti let naměřených dat a (2) získáním složek vodní bilance (transpirace a perkolace) na těchto dvou kontrastních plochách pomocí modelu bilance půdní vody. Z analýzy dlouhodobých dat půdních vlhkostí vyplývají nepatrně nižší hodnoty půdních vlhkostí pod porosty buku, které zanikají při srovnání průměrných ročních hodnot. Odlišnosti jsou patrné při hodnocení průměrných vlhkostí s hloubkou, kde v nejsvrchnější vrstvě půdního profilu smrk disponuje v průměru o 6 % vyššími zásobami půdní vody než buk. Z pohledu vývoje půdních vlhkostí během vegetační sezóny je půda z počátku sušší pod smrkem, který započíná svou transpiraci dříve. Tento rozdíl je v průběhu sezóny zredukován intenzivní transpirací buku. Výstupy bilančního modelu poukázaly na vyšší míru aktuální evapotranspirace buku a vyšší míru perkolace smrku během každého roku. Tento jev byl zvýrazněn během suchých let, kdežto v letech s dostatkem srážek byly rozdíly minimální. Zvýšení četnosti buku v krajině, tak může ovlivnit míru dotace podzemních vod. Soil moisture links processes that influence the entire hydrological cycle and thus the availability of water resources. One important factor influencing these processes is the presence of vegetation. Research on the interactions between vegetation, its management and the processes affecting soil water fluxes is of particular importance in times of ongoing climate change and land cover changes. However, the complexity of these interactions, further influenced by differences between plant species, makes this research more difficult. Land cover change is also taking place in Czechia, specifically in the replacement of spruce monocultures by beech. Therefore, this study investigates the influence of two types of forest stands, spruce (Picea abies) and beech (Fagus sylvatica), on the soil water regime in the experimental Liz catchment in Bohemian Forest, Czechia. This was performed by (1) evaluating differences in soil moisture based on twenty years of measured data and (2) obtaining the two components of the soil water balance (transpiration and percolation) at two plots (beech and spruce) using a soil water balance model. Analysis of the long-term soil moisture data show slightly lower soil moisture values under the beech stands, which disappear when comparing the annual mean values. Differences are evident when evaluating average soil moisture data with depth, where the topmost layer of the soil profile at the spruce site has on average 6% higher soil water content than beech. At the start of the growing season the soil moisture was initially drier under spruce, due to its earlier start of transpiration. This difference was reduced over the season by the intensive transpiration of beech. The outputs of the balance model indicated a higher rate of actual evapotranspiration of beech and a higher rate of percolation of spruce every year. This effect was more pronounced over the dry years, whereas in years with sufficient rainfall the differences were minimal. Thus, the replacement of spruce trees by beech trees may affect the rate of groundwater recharge.
Keywords:
*soil water balance; transpiration; percolation; land cover change; drought*
Fulltext is available at external website.
Kam a kolik vody odvádí stromy? Modelování vlivu smrkových a bukových porostů na toky vody v půdě během extrémních klimatických podmínek

Půdní vlhkost propojuje takové procesy, které ovlivňují celý hydrologický cyklus, a tím i dostupnost vodních zdrojů. Jedním z významných faktorů ovlivňující tyto procesy je přítomnost vegetace. Výzkum ...

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**On the structure and values of betweenness centrality in dense betweenness-uniform graphs**

Ghanbari, B.; Hartman, David; Jelínek, V.; Pokorná, Aneta; Šámal, R.; Valtr, P.

2023 - English
Betweenness centrality is a network centrality measure based on the amount of shortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of betweenness centrality. In this contribution, we focus on betweenness-uniform graphs with betweenness centrality below one. We disprove a conjecture about the existence of a BUG with betweenness value α for any rational numberαfrom the interval (3/4,∞) by showing that only very few betweenness centrality values below 6/7 are attained for at least one BUG. Furthermore, among graphs with diameter at least three, there are no betweenness-uniform graphs with a betweenness centrality smaller than one. In graphs of smaller diameter, the same can be shown under a uniformity condition on the components of the complement.
Keywords:
*betweenness; graphs*
Available in digital repository of the ASCR
On the structure and values of betweenness centrality in dense betweenness-uniform graphs

Betweenness centrality is a network centrality measure based on the amount of shortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of ...

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**On the development of a numerical model for the simulation of air flow in the human airways**

Lancmanová, Anna; Bodnár, Tomáš; Sequeira, A.

2023 - English
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 two-dimensional 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.
Keywords:
*reduced order model; incompressible Navier-Stokes equations; finite difference approximation; coupling method*
Available in digital repository of the ASCR
On the development of a numerical model for the simulation of air flow in the human airways

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 ...

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**Simulating particle-laden flows: from immersed boundaries towards model order reduction**

Isoz, Martin; Kubíčková, Lucie; Kotouč Šourek, M.; Studeník, Ondřej; Kovárnová, A.

2023 - English
Particle-laden flow is prevalent both in nature and in industry. Its appearance ranges from the trans-port of riverbed sediments towards the magma flow, from the deposition of catalytic material inside particulate matter filters in automotive exhaust gas aftertreatment towards the slurry transport in dredging operations. In this contribution, we focus on the particle-resolved direct numerical simulation (PR-DNS) of the particle-laden flow. Such a simulation combines the standard Eulerian approach to computational fluid dynamics (CFD) with inclusion of particles via a variant of the immersed boundary method (IBM) and tracking of the particles movement using a discrete element method (DEM). Provided the used DEM allows for collisions of arbitrarily shaped particles, PR-DNS is based (almost) entirely on first principles, and as such it is a truly high-fidelity model. The downside of PR-DNS is its immense computational cost. In this work, we focus on three possibilities of alleviating the computational cost of PR-DNS: (i) replacing PR-DNS by PR-LES or PR-RANS, while the latter requires combining IBM with wall functions, (ii) improving efficiency of DEM contact solution via adaptively refined virtual mesh, and (iii) developing a method of model order reduction specifically tailored to PR-DNS of particle-laden flows.
Keywords:
*particle-laden flow; CFD-DEM; arbitrarily-shaped particles; finite volume method*
Fulltext is available at external website.
Simulating particle-laden flows: from immersed boundaries towards model order reduction

Particle-laden flow is prevalent both in nature and in industry. Its appearance ranges from the trans-port of riverbed sediments towards the magma flow, from the deposition of catalytic material ...

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**On Reynolds-averaged turbulence modeling with immersed boundary method**

Kubíčková, Lucie; Isoz, Martin

2023 - English
The immersed boundary (IB) method is an approach in the computational fluid dynamics in which complex geometry conforming meshes are replaced by simple ones and the true simulated geometry is projected onto the simple mesh by a scalar field and adjustment of governing equations. Such an approach is particularly advantageous in topology optimizations (TO) where it allows for substantial speed-up since a single mesh can be used for all the tested topologies. In our previous work, we linked our custom IB variant, the hybrid fictitious domain-immersed boundary method (HFDIB), with a TO framework and successfully carried out an optimization under laminar flow conditions. However, to allow for optimizations of reallife components, the IB approach needs to be coupled with an affordable turbulence modeling. In this contribution, we focus on extending the HFDIB approach by the possibility to perform Reynolds-averaged simulations (RAS). In particular, we implemented the k − ω turbulence model and wall functions for closure variables and velocity.
Keywords:
*immersed boundary; RAS; wall functions; CFD; OpenFOAM*
Fulltext is available at external website.
On Reynolds-averaged turbulence modeling with immersed boundary method

The immersed boundary (IB) method is an approach in the computational fluid dynamics in which complex geometry conforming meshes are replaced by simple ones and the true simulated geometry is ...

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**Finite element modal analysis of a silicone vocal fold filled with fluid**

Hájek, P.; Radolf, Vojtěch; Horáček, Jaromír; Švec, J. G.

2023 - English
A three dimensional (3D) finite element (FE) model of a silicone vocal fold (VF) filled with fluid is presented here. The silicone part of the model is based on partial differential equations of the continuum mechanics and consider large deformations. The fluid domain encapsulated in the silicone VF is defined semianalytically as a lumped-element model describing the fluid in hydrostatic conditions. The elongated and pressurized silicone VF was subjected to perturbed modal analysis. Results showed that the choice of the fluid inside the VF substantially influences the natural frequencies. Namely, the water-filling lowers the natural frequencies approximately by half over the air-filling. Besides, the procedure of reverse engineering for obtaining the geometry of the VF from already 3D-printed mold is introduced.
Keywords:
*perturbed modal analysis; finite element method; vocal folds; reverse engineering; biomechanics of voice*
Fulltext is available at external website.
Finite element modal analysis of a silicone vocal fold filled with fluid

A three dimensional (3D) finite element (FE) model of a silicone vocal fold (VF) filled with fluid is presented here. The silicone part of the model is based on partial differential equations of the ...

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