2025-01-19
00:08 |
Dynamic mode decompositions of phonation onset – Comparison of different methods
Valášek, Jan ; Sváček, P.
Four dynamic mode decomposition (DMD) methods are used to analyze a simulation of the phonation onset carried out by in-house solver based on the nite element method. The dataset consists of several last periods of the flow-induced vibrations of vocal folds (VFs). The DMD is a data-driven and model-free method typically used for finding a low-rank representation of a high-dimensional system. In general, the DMD decomposes a given dataset to modes with mono-frequency content and associated complex eigenvalues providing the growth/decay rate that allows a favourable physical interpretation and in some cases also a short-term prediction of system behaviour. The disadvantages of the standard DMD are non-orthogonal modes and sensitivity to an increased noise level which are addressed by following DMD variants. The recursive DMD (rDMD) is an iterative DMD decomposition producing orthogonal modes. The total least-square DMD and the higher order DMD (hoDMD) are methods substantially reducing a high DMD sensitivity to noise. All methods identi ed very similar DMD modes as well as frequency spectra. Substantial difference was found in the real part of the spectra. The nal dataset reconstruction is the most accurate in the case of the recursive variant. The higher order DMD method also outperforms the standard DMD. Thus the rDMD and the hoDMD decompositions are promising to be used further for the parametrization of a VF motion.
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2024-11-26
10:48 |
Synchronization of airflows at varying heights
Filimonova, N. ; Kellnerová, Radka ; Bodnár, Tomáš ; Friedmann, E.
We propose a method to study the dynamics of energetic events in airflows at different heights. The method is based on a mathematical model for invariant pattern recognition by a visual system, which is combined with a wavelet analysis method. Here we use the first four Krawtchoukfunctions as the mother wavelets. The method allows to determine the time-frequency characteristics of the local impulse components for continuous signals. These extracted impulsecomponents of airflow velocities can be effectively utilized in cross-correlation analysis aimed at identifying potential synchronizations among airflows at different heights.
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2024-03-10
03:13 |
Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius 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 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.
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2024-03-10
03:13 |
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2024-03-10
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 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.
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2024-03-10
03:13 |
Numerical evaluation of mass-diffusive 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 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.
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2024-03-10
03:13 |
Programs and Algorithms of Numerical Mathematics 21 : Jablonec nad Nisou, June 19-24, 2022 : Proceedings of Seminar
Chleboun, J. ; Kůs, Pavel ; Papež, Jan ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub
These proceedings contain peer-reviewed 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 19-24, 2022.\nThe seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EU-MATHS-IN.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 1983-2020. 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 multi-processor applications of computational methods.
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2024-02-18
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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2023-12-17
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 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.
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2023-12-17
00:02 |
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