2025-07-05
00:00 |
Simplified mathematical models of fluid-structure-acoustic interaction problem motivated by human phonation process
Valášek, Jan ; Sváček, P.
Human phonation process represents an interesting and complex problem of fluid-structure-acoustic interaction, where the deformation of the vocal folds (elastic body) are interplaying with the fluid flow (air stream) and the acoustics. Due to its high complexity, two simplified mathematical models are described - the fluid-structure interaction (FSI) problem describing the self-induced vibrations of the vocal folds, and the fluid-structure-acoustic interaction (FSAI) problem, which also involves aeroacoustic phenomena. The FSI model is based on the incompressible Navier-Stokes equations in the ALE formulation coupled with the linear elasticity model. Both the fluid and structural models are approximated using finite element methods, and the influence of different inlet boundary conditions is discussed in detail. For the FSAI model, an aeroacoustic hybrid approach is used, incorporating the Lighthill analogy or the perturbed convective wave equation. The acoustic results strongly depend on the proper choice of the computational acoustic domain (i.e. vocal tract model). Further, the spatial and frequency distributions of sound sources computed from the FSI solution are compared for both used approaches. The final frequency spectra of acoustic pressure at the mouth position are also analyzed for both approaches.
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2025-07-05
00:00 |
On fluid structure interaction problems of the heated cylinder approximated by the finite element method
Vacek, Karel ; Sváček, P.
This study addresses the problem of the flow around circular cylinders with mixed convection. The focus is on suppressing the vortex-induced vibration (VIV) of the cylinder through heating. The problem is mathematically described using the arbitrary Lagrangian-Eulerian (ALE) method and Boussinesq approximation for simulating fluid flow and heat transfer. The fluid flow is modeled via incompressible Navier-Stokes equations in the ALE formulation with source term, which represent the density variation due to the change of temperature. The temperature is driven by the additional governing transport equation. The equations are numerically discretized by the finite element method (FEM), where for the velocity-pressure couple the Taylor-Hood (TH) finite element is used and the temperature is approximated by the quadratic elements. The proposed solver is tested on benchmark problems.
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2025-07-05
00:00 |
Spherical RBF interpolation employing particular geodesic metrics and trend functions
Segeth, Karel
The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient for its existence. Particular formulae with specified geodesic metrics, trend and SRBFs are then constructed and tested on a series of magnetic susceptibility examples. The results show that this interpolation is sufficiently robust in general.
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2025-07-05
00:00 |
Performance of parallel QR factorization methods on the NVIDIA Grace CPU Superchip
Břichňáč, V. ; Šístek, Jakub
This article studies several algorithms for QR factorization based on hierarchical Householder reflectors organized into elimination trees, which are particularly suited for tall-and-skinny matrices and allow parallelization. We examine the effect of various parameters on the performance of the tree-based algorithms. The work is accompanied with a custom implementation that utilizes a task-based runtime system (OpenMP or StarPU). The same algorithm is implemented in the PLASMA library. The performance evaluation is done on the recent NVIDIA Grace CPU Superchip.
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2025-07-05
00:00 |
Coupled vibroacoustic problem inspired by human phonation
Valášek, Jan ; Hubálek, J.
The contribution deals with the 2D vibro-acoustic model inspired by human phonation. Its aim is to demonstrate the in uence of vocal fold compliance on acoustic resonant frequencies. Vibro-acoustic coupling is highlighted under speci c conditions, particularly when elastic and acoustic frequencies coincide, as seen in phonation into tubes or straws of suitable lengths used in voice therapy. Here, vocal folds vibrations are modelled using linear elasticity theory and acoustics is described by wave equation. Both coupled subproblems are formulated in the frequency domain and numerically approximated by the nite element method. In the end the numerical results of the obtained resonant frequencies and their analysis are presented.
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2025-07-05
00:00 |
On flutter analysis by the finite element method using Taylor-Hood and Scott-Vogelius elements
Vacek, Karel ; Sváček, P.
This paper presents a numerical study of a complete fluid-structure interaction (FSI) problem of incompressible fluid flow interacting with a flexible supported airfoil whose motion is described by two degrees of freedom. The governing equations for the fluid flow are formulated in the arbitrary Lagrangian-Eulerian (ALE) framework and coupled to a system of ordinary differential equations describing the airfoil motion. The numerical solution is obtained using the finite element method (FEM), where both the Taylor-Hood (TH) and Scott-Vogelius (SV) elements are used. Stabilization techniques, including the streamline upwind Petrov-Galerkin (SUPG) method and grad-div stabilization, are applied to treat convection dominance and numerical oscillations. The results are validated against theoretical benchmarks, confirming the robustness and accuracy of the presented methods.
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2025-07-05
00:00 |
Aeroacoustic simulations in thermally non-homogeneous fluid flows
Caggio, Matteo ; Schmid, Michal ; Valášek, Jan ; Nečasová, Šárka ; Bodnár, Tomáš ; Starynskyi, O.
The cooling system, comprising heat exchangers and cooling fans, is essential for maintaining the power performance and acceptable operational conditions of a vehicle. However, running of the cooling fan produces unwanted noise, which often becomes dominant sound produced by the vehicle. To model the noise generated by turbulent flow and heat transfer around cooling fan blades, an appropriate flow model is essential. This study employs the compressible Navier-Stokes equations with an restricted relation between temperature and density for efficient handling of non-homogeneous temperature fields, combined with Delayed Detached Eddy Simulation (DDES) for advanced turbulence modeling. For the aeroacoustic analysis, a hybrid aeroacoustic approach is adopted, utilizing the Acoustic Perturbation Equation (APE) to model acoustic generation and propagation. The main aim of this study is to model the flow and the acoustic problem in the consistent way for the considered simple test case of heated cylinder walls in cross-flow. As most prior investigations focused only on isothermal conditions the model considered in this study presents an important generalization. A part of the problem is to select an efficient numerical software capable to treat temperature non-homogeneities in the flow and the aeroacoustic solver while being prepared for a possible future industrial application. The obtained results for varying thermal conditions show the significant sensitivity of produced sound pressure levels.
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2025-07-05
00:00 |
Design and numerical simulation of an axial blood pump
Bodnár, Tomáš ; Linkeová, I. ; Pirkl, L.
This paper shows a first version of a new geometrical and computational model of a Ventricular Assist Device (VAD). The main aim and purpose of this model is to serve as a computational test case and benchmark for mutual cross-comparison of numerical simulations employing different grids, solvers, and additional mathematical model extensions. The simplified VAD was designed as a fully parametric adjustable geometry, allowing for easy change of the essential model shape parameters to assess their effect on the VAD’s performance. The description of the newly developed VAD geometry is presented, briefly describing its structure and main shape parameters. The first numerical simulations of the flow in the resulting VAD model are presented, based on the OpenFOAM finite-volume solver implemented in the TCAE Engineering Simulation Environment. The presented first numerical results show the applicability of the newly developed VAD’s model geometry for computational fluid dynamics (CFD) evaluation and benchmarking.
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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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