Workshop on scientific computing 2018

June 14-17, 2018

Department of Mathematics, FNSPE CTU in Prague
Děčín, Czech Republic

List of abstracts

Achilles, Turtoise and Motion of Curves
Michal Beneš
FNSPE, CTU in Prague


In the contribution we discuss the formulation and numerical solution of the planar mean curvature flow with the area or length constraint. The motion law is treated by means of the direct method [4] and by means of the phase-field method (see [3]) with non-local terms. This problem is originally mentioned in [1] and analyzed partially in [2]. We identify basic properties of this motion, generalize it by including anisotropy in relative geometry and discuss the quantitative numerical results, their mutual relation, and present qualitative behavior of the solution.

[1] J. Rubinstein and P. Sternberg: Nonlocal reaction-diffusion equation and nucleation, IMA J.Appl. Math. (1992) 48, 249--264.  

[2] L. Bronsard and B. Stoth: Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg-Landau equation, SIAM Journal on Mathematical Analysis (1997) 28 No. 4, 769--807. 

[3] M. Benes: Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow, Applications of Mathematics (2003) 48 No. 6, 437--453.  

[4] D. Sevcovic (BVP Driver) and S. Yazaki: Evolution of plane curves with a curvature adjusted tangential velocity. Japan J. Industrial and Applied Mathematics (2011) 28, 413--442.

LES of turbulence above rough surfaces and domain nesting
Vladimír Fuka
FMP, CU in Prague

Abstract: The paper will present simulations of turbulent flow over rough rough surfaces in a wind tunnel. The computations are performed using the finite difference code ELMM (Extended Large-Eddy Microscale Model). The model uses the immersed boundary method to treat solid obstacles, such as the roughness elements and the turbulence-generating spires. The time-scale sub-grid model is used to model the effect of unresolved scales of turbulence. The simulated problem features a large area to be simulated (a 2 m long section of the wind-tunnel with cross section 0.24 x 0.24 m) but at the same time the roughness elements are small. Therefore the whole domain is simulated in a coarse resolution of 2 mm and a nested domain with a higher resolution (1 mm) is located in the are of the highest interest. The presentation will discuss the numerical method of domain nesting and the results of the simulations with several types of rough surfaces and inflow turbulence generators.

Lattice-Boltzmann simulation of turbulent flow in 3D on GPU
Radek Fučík
FNSPE CTU in Prague

Abstract: Three-dimensional turbulent flows of fluids around obstacles are investigated using the lattice-Boltzmann method in 3D with applications to blood flow across aortic valve (under newtonian regime) or air flow in the boundary layer. First, the numerical method is briefly presented together with implementaion details and then, the method is validated against experimental data provided by collaborating institutions: IKEM Praha, Czech republic and CESEP, Colorado School of Mines, Golden, USA.

Coherent structures in turbulent flow - cooperation of the physical and numerical modelling
Klára Jurčáková
Institute of Thermomechanics, CAS

Abstract: The contribution will introduce project ”Large structures in the boundary layers over complex surfaces in high Reynolds numbers” supported by Czech science foundation. The project aims to verify the existence of very-large-scale motions and other structures in a fully turbulent boundary layer above a rough surface. The joint effort of experimental and numerical modelling has several benefits for both partners. The numerical model can be validated on the basis of experimental data and adjusted for the particular task. On the other hand, numerical modelling can be used for systematic parameter studies and only selected interesting cases could be afterwards modelled physically. Also analysis of full 3D numerical solution can point out regions with high gradients or turbulence generation, which can be measured in detail on physical model without tedious measurement of the whole flow field. The presentation will introduce the project teams, the models which are under development and the pending tasks.

Dynamic portfolio optimization by means of Riccati transformation of corresponding HJB equation
Soňa Kiliánová
Comenius University, Bratislava


We consider a problem of dynamic stochastic portfolio optimization modeled by a Hamilton-Jacobi-Bellman (HJB) equation. Using the Riccati transformation the HJB equation is transformed to a simpler quasi-linear PDE. An auxiliar quadratic  programming problem is obtained, which uses a vector of expected asset returns and a covariance matrix of returns as input parameters. Since this problem can be sensitive to the input data, the problem can be modified from fixed input parameters to worst-case optimization over convex or discrete uncertainty sets both for asset returns and covariance matrix. Qualitative properties of the value function are analyzed along with providing illustrative numerical examples.

Anomalous Diffusion on Spherical Surface
Jaromír Kukal
FNSPE, CTU in Prague

Abstract: Anomalous diffusion is supposed to be driven by fractional gradient of Riesz-Feller type. Based on mass balance, the fractional PDE is obtained for analytic solution and stochastic simulation. Using technique of variable separation, the general solution is expressed as infinite weighted sum of non-orthogonal functions, which makes numerical difficulties in approximation of Green function. The verification of resulting Green function is performed via Monte Carlo simulations using multidimensional alpha stable distribution. The roles of simulation step, space discretization and approximation order are also discussed.

Development of hybrid model based on LBM and CA for modeling of diffusion phase transformation
Lukasz Lach
AGH, UST, Krakow


The phenomenon of phase transformation is one of the most important elements of hot forming processes and heat treatment, which supports to obtain the proper microstructure. The aim of the work is a development of the phase transformation model. The proposed hybrid model uses two modeling methods: Lattice Boltzmann Method and Cellular Automata. In the part related to modeling of the microstructure evolution, a cellular automat is used, whereas diffusion is modeled using LBM. The modeling system and the structure of the hybrid model as well as some sample results will be presented.

Mathematical modeling and experimental validation of flow through aortic valve
Petr Pauš
FNSPE CTU in Prague

Abstract: The fluid flow through the aortic valve is simulated using 3D LBM method and compared with the experimental data obtained from magnetic resonance measurements. The experiment is performed  by a phantom device with know parameters scanned using MR.

The Effect of Entrapped Air on Hydraulic Conductivity of Coarse Sand
Tomáš Princ
FCE, CTU in Prague

Abstract: The relationship between gas residual saturation (Sgr) and corresponding hydraulic conductivity (K), was studied experimentally for two coarse sands. Air entrapping was achieved by drainage-imbibition cycles done on columns of packed sand. The value of K was determined using a constant head infiltration experiment and evaluated using Darcy’s law from measured steady-state flux. The Sgr was determined gravimetrically after each infiltration run. One point of K(Sgr) relationship was determined from each infiltration experiment that followed the drainage imbibition cycle. The sample was fully saturated at the beginning and drainage was done using a tension imposed at the bottom of the sample. Four samples were used to obtain the K(Sgr) relationship. Additionally, air bubbles were visualized by micro-computed X-ray tomography (CT) for selected runs to obtain information on entrapped air cluster sizes, shapes and distribution. The spatial distribution of air bubbles within the sample, the histogram of air bubble sizes and residual air content were obtained from binarized CT images. The resulting K(Sgr) relationship confirmed the trend of decreasing K with increasing Sgr. The highest amount of the entrapped air content and the largest air bubbles were detected in the upper half of sample. The results confirmed that the trend of the K(Sgr) relationship was a consequence of changes in entrapped air bubbles distribution.

Freezing and thawing experiments in fully saturated packed sand sample
Martina Sobotková
FCE, CTU in Prague


Freezing and thawing experiment were carried out in the laboratory on fully saturated packed sand sample (15 cm in diameter and 20 cm in height). The experimental setup consisted of plastic tube covered on its sides and bottom by insulation layers. The sample assembly was placed into the precisely controlled freezer chamber. The top of the sample was covered by a stainless steel plate. Initially the sample was equilibrated at $+10^\circ$ C and then the temperature inside the chamber was changed to $-10^\circ$ C. The inner temperature of sand sample was monitored in four depths by thin temperature sensors (109 SS, Campbell Scientific) horizontally inserted into the sample. Temperature development in four temperature sensors was obtained during freezing and thawing cycles. The experiment aims to provide information on freezing dynamics and thermo-mechanical changes during the freezing and thawing cycles. 

Challenges and Methods in Mathematical Modeling of Oxyfuel Biomass Combustion in Fluidized Bed Boilers
Pavel Strachota, Michal Beneš, Miroslav Kolář, Alexandr Žák, Jakub Solovský, Jakub Klinkovský
FNSPE, CTU in Prague

Abstract: For the upcoming five years, our research team will participate in the project of the Czech Operational Programme "Research, Development and Education" Research centre for low-carbon energy technologies, No. CZ.02.1.01/0.0/0.0/16\_019/0000753. Our aim is to develop and implement parallel algorithms for simulation of the complex processes during combustion in fluidized bed boilers. In contrast to traditional application of fluidized bed boilers in energy production, focus is put on the oxyfuel regime where pure oxygen is used as the oxidizer instead of air. The purpose of this approach is the ability to purify and capture carbon dioxide, which can be further utilized or stored, minimizing environmental impact. The first part of the contribution represents an overview of the processes to be dealt with, including multiphase flow in the combustion chamber in the bubbling and circulating regime, the recirculation of the multiphase mixture, chemical reaction chain in the standard and oxyfuel regime, and heat release and transfer. Fuel particle devolatilization, burnout, and attrition will be discussed for both coal and biomass, the latter being the fuel of choice within the framework of the project. In the second part, we introduce our current achievements in fluidized bed combustion simulations, point out the known limitations and outline the advanced approaches to their resolution. Euler-Euler and Euler-Lagrange (Multiphase Particle in Cell) methods will shortly be compared and illustrative results will be presented.

Lattice Boltzmann Method: analysis of accuracy by an equivalent finite difference scheme.
Robert Straka
AGH, UST, Krakow


One possible way of analyzing an accuracy of any Lattice Boltzmann Method (LBM) is to examine recurrent expressions for distribution functions. Taking appropriate moments of these recurrent expressions one gets an equivalent finite difference scheme (EFDS) for a macroscopic quantity which evolution is solved by the LBM. Once we have the EFDS we can use standard techniques to check e.g. accuracy of the EFDS and to establish which free parameters of the LBM could help us make the LBM solution more accurate and stable. For the sake of "simplicity" we will consider 1D diffusion problem and derive EDFSs in the case of D1Q3 (i.e. 1D with 3 characteristic velocity lattice model) for single and multiple relaxation time collision operators.

The Stock Markets Development and the Distribution of Their Indices Returns
Quang Van Tran
FNSPE, CTU in Prague

Abstract: The distribution of stock market index returns is well known for its fat tail and sharp peak. However, the problem whether there is any difference in the distributions of the returns across markets has not been fully investigated so far. To find the answer to this problem, two group of stock market indices are chosen: one for developed markets: SP500 (USA) and FTSE100 (GB) and the second one for emerging markets: BUX (Hungary), WIG (Poland) and PX (Czech Rep.). Also seven distributions with fat tails are selected as potential candidates for these indices returns. They are: logistic, generalized error distribution, generalized extreme value distribution, t-distribution, alpha stable distribution, normal inverse Gaussian distribution and skewed t-distribution. Using daily data from 2000 to 2018, first parameters of these distributions are estimated. Then the validity of each distribution for modeling stock market index returns is verified with chi2 goodness of fit test. The obtained results show the tail power depends on the development of the stock market.

Quantitative and qualitative properties eigenvalues of connected graphs
Daniel Ševčovič
Comenius University, Bratislava

Abstract: In this talk we present an overview of spectral properties of connected graphs. Spectrum of a graph consists of eigenvalues of its adjacency matrix. Special attention is focused on spectrum of the so-called positive and negatively invertible graphs. We also present descriptive statistics of spectrum of all connected graphs on $m\le10$  vertices. This is a joint work with S. Pavlikova.