20240310 03:13 
Finite element approximation of fluid structure interaction using TaylorHood and ScottVogelius elements
Vacek, Karel ; Sváček, P.
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 NavierStokes equations written in the arbitrary EulerianLagrangian (ALE) formulation. The ALE mapping is constructed with the use of a pseudoelastic 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 TaylorHood (TH) element and the ScottVogelius (SV) finite element are compared. The TH element satisfies the BabuškaBrezzi infsup 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 BabuškaBrezzi condition. The numerical results for two benchmark problems are shown.
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20240310 03:13 
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20240310 03:13 
Numerical study of the steady airflow in the human respiratory system during inhaling and exhaling
Lancmanová, Anna ; Bodnár, Tomáš
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 ReynoldsAveraged incompressible NavierStokes equations complemented by the SST k − ω turbulence model. The simulations were performed using finitevolume open source solver OpenFOAM on a realistic threedimensional 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 timedependent and compressible effects.
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20240310 03:13 
Numerical evaluation of massdiffusive compressible fluids flows models
Bodnár, Tomáš ; Fraunié, P.
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 doubleperiodic shear layer and the KelvinHelmholtz instability. The obtained timedependent flow fields are showing pronounced shear and vorticity layers being resolved by the standard as well as by the new massdiffusive modified models. The preliminary results show that the new models are viable alternative to the well established classical models.
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20240310 03:13 
Programs and Algorithms of Numerical Mathematics 21 : Jablonec nad Nisou, June 1924, 2022 : Proceedings of Seminar
Chleboun, J. ; Kůs, Pavel ; Papež, Jan ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub
These proceedings contain peerreviewed papers that are based on the invited lectures, short communications, and posters presented at the 21st seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Merkur Hotel, Jablonec nad Nisou, Czech Republic, June 1924, 2022.\nThe seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EUMATHSIN.CZ, Czech Network for Mathematics in Industry, and with the nancial support provided by the RSJ Foundation. It continued the previous seminars on mathematical software and numerical methods held (biennially, with only one exception) in Alšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, Prague, and Hejnice in the period 19832020. The objective of this series of seminars is to provide a forum for presenting and discussing advanced topics in numerical analysis, computer implementation of numerical algorithms, new approaches to mathematical modeling, and single or multiprocessor applications of computational methods.
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20240218 00:07 
Interpolation with restrictions  role of the boundary conditions and individual restrictions
Valášek, Jan ; Sváček, P.
The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative method not respecting conservation laws, a conservative interpolation method introducing constraints is described. The constraints have form of Lagrange multipliers enforcing conservation of desired flow quantities, like e.g. total fluid mass, flow kinetic energy or flow potential energy. Then the interpolation problem turns into an error minimization problem, such that the resulting quantities of proposed interpolation satisfy these physical properties while staying as close as possible to the results of Lagrangian interpolation in the L2 norm. The proposed interpolation scheme does not impose any restrictions on mesh generation process and it has a relatively low computational cost. The implementation details are discussed and test cases are shown.
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20231217 00:02 
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.
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20231217 00:02 
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20231217 00:02 
Hidden symmetry in turbulence and analytic study of shell models
Caggio, Matteo
This short communication concerns symmetries in developed turbulence and analytic study of shell models. However scaleinvariance is broken due to the intermittency phenomenon, is possible to established a hidden selfsimilarity in turbulent flows. Using a shell model, the author in [18] (see also [19]) addressed the problem deriving a scaling symmetry for the inviscid equations. Here, first we discuss the analysis presented in [18], then, from the mathematical perspective, we propose an analytic study for the shell model with the presence of the viscous terms. This brief paper should be understood as an introductory note to this new scaling symmetry with implications for mathematical analysis [5].
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20230424 23:56 
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