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Numerical tests of far-field boundary conditions for stably stratified flows
Bodnár, Tomáš; Fraunié, P.; Řezníček, Hynek
2019 - English
This numerical study presents the results of simulations of stably stratified wall-bounded flows. The effect of artificial far-field boundary conditions is studied in detail. The standard homogeneous Neumann condition for pressure is replaced by a non-homogeneous condition depending on local velocity and its gradient. The two-dimensional 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 far-field artifcial boundary condition. The model is based on Boussinesq approximation of non-homogeneous Navier-Stokes equations, solved using artificial compressibility method, looking for a steady solution.
Keywords:
boussinesq approximation; stable stratification; far-field boundary condition
Available in digital repository of the ASCR
Numerical tests of far-field boundary conditions for stably stratified flows
This numerical study presents the results of simulations of stably stratified wall-bounded flows. The effect of artificial far-field boundary conditions is studied in detail. The standard homogeneous ...
Analysis of the turbulence parameterisations for the atmospheric surface layer
Caggio, Matteo; Bodnár, Tomáš
2018 - English
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer 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.
Keywords:
atmospheric boundary layer; Monin-Obukhov similarity theory; turbulence parameterisations; strong strati cation
Available in digital repository of the ASCR
Analysis of the turbulence parameterisations for the atmospheric surface layer
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer in function of the stability of the atmosphere. The case of ...
Classification of distances in cosmology
Křížek, Michal; Mészáros, A.
2018 - English
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single natural distance, since the universe is expanding, curved, and we look back in time. In this survey paper we will concentrate on geometrical interpretations of the above-mentioned distances.
Keywords:
standard cosmological model; cosmological principle; Friedmann equation; cosmological parameters; Einstein static universe
Available in digital repository of the ASCR
Classification of distances in cosmology
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single ...
Neglected gravitational redshift in detections of gravitational waves
Křížek, Michal; Somer, L.
2018 - English
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the authors have not taken into account a large gravitational redshift of this binary system, which is a direct consequence of time dilation in a strong gravitational field. Thus the proposed masses are overestimated. In our paper we also give other arguments for this statement.
Keywords:
gravitational redshift; time dilatation; black holes; wavelets
Available in digital repository of the ASCR
Neglected gravitational redshift in detections of gravitational waves
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the ...
Parallel domain decomposition solver for flows in hydrostatic bearings
Hanek, Martin; Šístek, Jakub; Burda, P.; Stach, E.
2018 - English
We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used for discretization. The arising nonlinear system of algebraic equations is linearized using the Picard’s iteration, and the Balancing Domain Decomposition based on Constraints (BDDC) method is used to solve the linear systems of equations. The solver is first validated with an experiment for the case of a bearing without motion, and it is then applied to simulation of flow in a sliding bearing.
Keywords:
hydrostatic bearings; BDDC
Available in digital repository of the ASCR
Parallel domain decomposition solver for flows in hydrostatic bearings
We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used ...
Cosmology on Small Scales 2018: Dark Matter Problem and Selected Controversies in Cosmology
Křížek, Michal; Dumin, Y. V.
2018 - English
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.
Keywords:
cosmology
Fulltext is available at external website.
Cosmology on Small Scales 2018: Dark Matter Problem and Selected Controversies in Cosmology
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 ...
Artificial far-field pressure boundary conditions for wall-bounded stratified flows
Bodnár, Tomáš; Fraunié, P.
2018 - English
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 in-house developed high-resolution numerical code, based on compact finite-difference discretization in space and Strong Stability Preserving Runge-Kutta method for (pseudo-) time stepping.
Keywords:
Boussinesq approximation; stable stratification; compact finite-difference; pressure boundary condition
Available in digital repository of the ASCR
Artificial far-field pressure boundary conditions for wall-bounded stratified flows
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 ...
Programs and Algorithms of Numerical Mathematics 18 : Janov nad Nisou, June 19-24, 2016 : proceedings of seminar
Chleboun, J.; Kůs, Pavel; Přikryl, Petr; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
2017 - English
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 19-24, 2016. All the papers have been peer-reviewed. The 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. 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 1983-2014. 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 multi-processor applications of computational methods.
Keywords:
numerical mathematics
Available in digital repository of the ASCR
Programs and Algorithms of Numerical Mathematics 18 : Janov nad Nisou, June 19-24, 2016 : proceedings of seminar
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 ...
The role of Sommerville tetrahedra in numerical mathematics
Hošek, Radim
2017 - English
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by its direct generalization to any dimension.
Keywords:
simplicial tessellations; simplicial mesh; Sommerville tetrahedron
Available in digital repository of the ASCR
The role of Sommerville tetrahedra in numerical mathematics
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine ...
A particular smooth interpolation that generates splines
Segeth, Karel
2017 - English
There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $it smooth interpolation$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.
Keywords:
data interpolation; smooth interpolation; spline interpolation
Available in digital repository of the ASCR
A particular smooth interpolation that generates splines
There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one ...
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