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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20230424 23:56 
Spherical basis function approximation with particular trend functions
Segeth, Karel
The paper is concerned with the measurement of scalar physical quantities at nodes on the $(d1)$dimensional unit sphere surface in the hbox{$d$dimensional} Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider $d=3$. We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful in the interpretation of many physical measurements. We show an example concerned with the measurement of anisotropy of magnetic susceptibility having extensive applications in geosciences and present numerical difficulties connected with the high condition number of the matrix of the system defining the interpolation.
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20220928 00:47 
Cosmology on Small Scales 2022: Dark Energy and the Local Hubble Expansion Problem
Křížek, Michal ; Dumin, Y. V.
One hundred years ago, Russian mathematician and physicist Alexander A. Friedmann applied the system of Einstein equations to the threedimensional sphere with a time varying radius. In this way, he obtained a nonlinear ordinary differential equation which is called the Friedmann equation after him and serves now as a cornerstone of the standard cosmological model. Unfortunately, it is well known that this model exhibits a number of paradoxes. Thus, the main goal of the CSS 2022 Conference Proceedings is to discuss whether and how the Friedmann equation can be applied at the various spatial scales, from our local cosmic neighborhood up to the whole Universe, and if the existence of dark matter and dark energy are merely artifacts of the excessive extrapolations.
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20220928 00:47 
100 years of the Friedmann equation
Křížek, Michal
In 1922, Alexander Friedmann applied Einstein’s equations to a threedimensional sphere to describe the evolution of our universe. In this way he obtained a nonlinear ordinary differential equation (called after him) for the expansion function representing the radius of that sphere. At present, the standard cosmological ΛCDM model of the universe is based just on the Friedmann equation. It needs a significant amount of dark matter, about six times that of the usual baryonic matter, besides an even larger amount of dark energy to be consistent with the real universe. But to date, both dark matter and dark energy have remained without concrete evidence based on direct physical measurements. We present several arguments showing that such a claimed amount of dark matter and dark energy can only be the result of vast overestimation, incorrect extrapolations, and that it does not correspond to the real universe. The spatial part of our universe seems to be locally flat and thus it can be locally modeled by the Euclidean space. However, Friedmann did not consider the flat space with zero curvature. Therefore, in the second part of this paper we will derive a general form of the corresponding metric tensor satisfying Einstein’s equations with zero righthand side.
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20220928 00:47 
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20220928 00:47 
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.
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