20191019 16:35 
Numerical tests of farfield boundary conditions for stably stratified flows
Bodnár, Tomáš ; Fraunié, P. ; Řezníček, Hynek
This numerical study presents the results of simulations of stably stratified wallbounded flows. The effect of artificial farfield boundary conditions is studied in detail. The standard homogeneous Neumann condition for pressure is replaced by a nonhomogeneous condition depending on local velocity and its gradient. The twodimensional tests are performed for the case of flow over a low isolated hill. The simulations on computational domains with three different heights are discussed to evaluate the performance of the new farfield artifcial boundary condition. The model is based on Boussinesq approximation of nonhomogeneous NavierStokes equations, solved using artificial compressibility method, looking for a steady solution.
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20191019 16:35 
Note on the problem of compressible nonNewtonian fluids
Caggio, M. ; Nečasová, Šárka
The aim of the paper is to consider the compressible nonNewtonian fluids of power law type when the viscosity coeffcients depend not only on invariants of velocity field but also on the density. We introduce approximation scheme using model of multipolar fluids. After then passing with higher viscosity to zero we get the measure valued solution of the problem.
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20191019 16:35 
On the mechanisms of dimensional transition in stably stratified turbulent fluid layers
Caggio, M. ; Bodnár, Tomáš ; Schiavon, M.
The purpose of this short review communication is to present some recent results on the effects of stable density stratification on the threedimensional turbulent dynamics of 'thin' fluid layers forced at intermediate scales. In particular, how the strati cation and the confinement affect the mechanism of kinetic and potential energy transfer between different scales. Results on twodimensional vertically stratifed flows and possible applications for stably stratifed atmospheric boundary layer will be shortly discussed.
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20190725 09:14 
Talk about patterns in the mathematics classroom
Roubíček, Filip
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical patterns in a triangle grid and their transformation into arithmetic patterns or algebraic functions. It shows how pupils/students reason about relationships in these patterns and among these patterns, how they describe and express their generalizations in words or symbols.
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20190516 18:17 
Programs and Algorithms of Numerical Mathematics 18 : Janov nad Nisou, June 1924, 2016 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
This book comprises papers that originated from the invited lectures, survey lectures, short communications, and posters presented at the 18th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Janov nad Nisou, Czech Republic, June 1924, 2016. All the papers have been peerreviewed. The 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. It continued the previous seminars on mathematical software and numerical methods held (biennially, with only one exception) in Al šovice, Bratří kov, Janov nad Nisou, Ko řenov, L ázně Libverda, Dolní Maxov, and Prague in the period 19832014. The objective of this series of seminars is to provide a forum for presenting and discussing advanced theoretical as well as practical topics in numerical analysis, computer implementation of algorithms, new approaches to mathematical modeling, and single or multiprocessor applications of computational methods.
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20190516 18:17 
Programs and Algorithms of Numerical Mathematics 19 : Hejnice, June 2429, 2018 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
These proceedings contain peerreviewed papers that are based on the invited lectures, survey lectures, short communications, and posters presented at the 19th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in the International Center for Spiritual Rehabilitation, Hejnice, Czech Republic, June 2429, 2018. The 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 financial 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, and Prague in the period 19832016. 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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20190516 18:17 
Multivariate smooth interpolation that employs polyharmonic functions
Segeth, Karel
We study the problém of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomials therms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example is presented.
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20190213 17:43 
Cosmology on Small Scales 2018: Dark Matter Problem and Selected Controversies in Cosmology
Křížek, Michal ; Dumin, Y. V.
According to the standard cosmological model, our Universe needs a significant amount of dark matter, about six times more than that of the usual baryonic matter, besides an even larger amount of dark energy. But to date, both dark matter and dark energy have remained conceptually elusive, without concrete evidence based on direct physical measurements. Yet another subtle issue is that the Friedmann equation – the cornerstone of modern cosmology – was derived from the system of ten Einstein’s equations applied to a perfectly symmetric universe, which is homogeneous\nand isotropic for every fixed time instant. So, the question is whether one can perform such excessive extrapolations and, in particular, at which scale the effect of Hubble expansion is manifested.
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20190213 17:43 
Analysis of the turbulence parameterisations for the atmospheric surface layer
Caggio, Matteo ; Bodnár, Tomáš
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surfacelayer in function of the stability of the atmosphere. The case of very stable conditions (strong strati cation), where theoretical approaches provide conflicting results (see Luhar et al. [11]), is analysed in detail to provide some insight into the limits of applicability for some of the most popular models of turbulence. The problem of the existence of the critical flux Richardson number is also taken into account.
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20190213 17:43 
Artificial farfield pressure boundary conditions for wallbounded stratified flows
Bodnár, Tomáš ; Fraunié, P.
This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions on the arti cial boundaries of the computational domain. The simple three dimensional test case deals with the steady flow of an incompressible, variable density fluid over a low smooth model hill. The Boussinesq approximation model is solved by an inhouse developed highresolution numerical code, based on compact finitedifference discretization in space and Strong Stability Preserving RungeKutta method for (pseudo) time stepping.
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