Student workshop on scientific computing 2022

May 26 - 29, 2022. Děčín, Czech Rep. + Online

Departments of Software Engineering and Mathematics
FNSPE CTU in Prague, Czech Republic

List of abstracts

On stress integration method for lattice Boltzmann method in 2D
Jan Bureš
FNSPE CTU in Prague


Iterated Function Systems, Their Invariant Sets and Measure
Michaela Diasová
FNSPE CTU in Prague


This contribution deals with iterated function systems (IFS), its invariant sets and the chaos game algorithm, which is used to display them. In order to analyze these sets some properties of the inductive, Hausdorff, similarity and box-counting dimension are shown. Subsequently, the changes inside invariant sets caused by recurrent IFS are studied. The aproximation of the box-counting dimension for some of these sets is introduced.

Lattice Boltzmann method and Boundary conditions
Pavel Eichler
FNSPE CTU in Prague, FNSPE CTU in Prague


Classical problems for the incompressible fluid flow simulations are given in the macroscopic description, i.e., using the initial and boundary conditions for the fluid velocity and pressure. In the case of the mesoscopic simulations, the macroscopic conditions must be transferred to the mesoscopic description. The commonly used way is based on the setting of the discrete density function to its equilibrium part. This method neglects the non-equilibrium part and is correct only for cases with constant pressure and velocity in space and time.

In this contribution, the other commonly used approximations of the boundary conditions are discussed and analyzed on the 3D periodic fluid flow between parallel plates. Finally, the newly derived momentum boundary conditions for the D3Q27 are introduced and tested. These boundary conditions present a more accurate alternative to the other mesoscopic boundary conditions.

In vitro experiments and computational simulations of blood flow
Radek Galabov, Jan Rydlo, Jaroslav Tintěra
FNSPE CTU in Prague, IKEM Prague, Institute for Clinical and Experimental Medicine, Prague


Computational models of flow dynamics have a potential to enhance medical decision-making. The accuracy of flow models depends on a number of conditions such as fluid properties, vessel anatomy, vessel wall properties and flow regime. These properties can be controlled in physical models of blood flow. In this talk, such a physical model of the abdominal aorta is presented together with a pumping system providing pulsatile flow. Flow through the system can be measured by a magnetic resonance imaging scanner (MRI). This system and MRI-obtained data will be used later to adjust a lattice Boltzmann method-based computational model of blood flow through aorta.

Properties of Diffusion over Sparse Grids
František Gašpar, Jaromír Kukal
FNSPE CTU in Prague, Department of Software Engineering, FNSPE, Czech Technical University in Prague


The contribution presents the statistical properties of the diffusion process over fractal sets represented as sparse grids. The summary of differences between regular grid diffusion and sparse grid diffusion is presented together with  an overview of dimension estimation methods. The main focus is given to less than one dimensional sets which allow for analytical study of return probability. Properties of sparse grid diffusion are demonstrated using data from simulations and improved dimension estimation method is shown.

SPH method for free surface flow in discharge object
Tomáš Halada, Luděk Beneš, Jiří Fürst
FME CTU in Prague


Smoothed particle hydrodynamics, a meshfree particle method based on Lagrangian description is used for simulation of free surface flow in 3D complex geometries of discharge objects of turbine and pump stations. Possibilities and benefits of the method are demonstrated as well as drawbacks mostly related to boundary condition are shown. Arising problems are not connected with particular case but these are general topics of research in SPH method. Motivated by that, we focus on comparasement of some realization of boundary conditions. Moreover, modern SPH formulation based on partially Lagrangian partially Eulerian description and approximate Riemann solvers (R-ALE-SPH) with new proposed scheme is presented as possible improvement of the method.

Mathematical modeling of flow around obstacles using the lattice Boltzmann method
Dominik Horák
FNSPE CTU in Prague


Mathematical modeling of transport and transfer of contrast agent in myocardial perfusion problems
Lenka Horvátová
FNSPE CTU in Prague


Modeling vapor transport in air using LBM and MHFEM
Jakub Klinkovský, Andrew C. Trautz, Radek Fučík, Tissa H. Illangasekare
FNSPE CTU in Prague, USACE ERDC in Vicksburg, FNSPE CTU in Prague, CSM in Golden


We present an efficient computational approach for simulating component transport within single-phase free flow in the boundary layer over porous media. A numerical model based on this approach is validated using experimental data generated in a climate-controlled wind tunnel coupled with a 7.3 m long soil test bed. The developed modeling approach is based on a combination of the lattice Boltzmann method (LBM) for simulating the fluid flow and the mixed-hybrid finite element method (MHFEM) for solving constituent transport. Both those methods individually, as well as when coupled, are implemented entirely on a GPU accelerator in order to utilize its computational power and avoid the hardware limitations caused by slow communication between the GPU and CPU over the PCI-E bus. We describe the mathematical details behind the computational method, focusing primarily on the coupling mechanisms. The performance of the solver is demonstrated on a modern high-performance computing system. Flow and transport simulation results are validated and compared herein with experimental velocity and relative humidity measurements made above a flat partially saturated soil layer exposed to steady air flow. Model robustness and flexibility is demonstrated by introducing rectangular bluff-bodies to the flow in several different experimental scenarios.

Mathematical modeling of myocardial perfusion using lattice Boltzmann method
Jan Kovář
FNSPE CTU in Prague


Discrete Torsion
Jiří Minarčík
FNSPE CTU in Prague


High resolution modeling with LES models
Jelena Radović, First part – TURBAN project: Michal Belda1, Jaroslav Resler2, Pavel Krč2, Martin Bureš2, Kryštof Eben2, Jan Geletič2; Second part - “The Role of coherent structures’ dynamics on scalar transport and dispersion in the urban canopy layer” project: Vladimír Fuka1, Štěpán Nosek 3
Faculty of Mathematics and Physics, Charles University, 1 - Department of Atmospheric Physics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic; 2 - Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic ;3 - Institute of Thermomechanics AS CR, v.v.i., Dolejškova 1402/5, Prague 8 182 00, Czech Republic


This work is a combination of two different studies conducted within two independent projects in which the high-resolution Large Eddy Simulations (LES) were performed by using two different numerical models: The Parallelized Large-Eddy Simulation Model (PALM) and the OpenFOAM model.

In the course of the first study in which the PALM model was used, three LES simulations were performed using three different sets of initial and boundary conditions obtained from the mesoscale numerical model called WRF. The simulations were performed on an 8 x 8 km domain in 10 m resolution which is capturing a real city area in the southeast part of Prague. In order to obtain preliminary conclusions, a comparison of the WRF model and PALM model outputs against observations obtained from the University of Wyoming (UW) was performed as well.  The ultimate goal of this still ongoing study is to develop a mechanism for determining the best possible initial and boundary conditions for the initialization of the PALM model, perform a series of different simulations on a real urban environment and validate the accuracy of the model for given conditions.  This study is a part of an international project called the Turbulent-resolving urban modeling of air quality and thermal comfort (TURBAN).

The high-resolution LES simulations in the second study were performed on a 3D urban array by the model OpenFOAM with the goal of capturing the turbulent flow in the street canyons of the mentioned urban array. The configuration and the setup of these simulations are built upon the results previously published by Nosek et al., 2018, BAE 138; Kluková et al., 2021, JWEIA 208. The final objective of this study is to determine and investigate to what extent the coherent structures’ dynamics influence the scalar transport and dispersion in the urban canopy layer. The outputs of the OpenFOAM model simulations will be compared to the data obtained during the wind tunnel experiment. This research experiment is a part of the GAČR funded project named “The Role of coherent structures’ dynamics on scalar transport and dispersion in the urban canopy layer”. 

A Lagrange--Galerkin Scheme of second order in time for the shallow water equations with a transmission boundary condition
Md Mamunur Rasid, Hirofumi Notsu, Masato Kimura, Erny Rahayu Wijayanti and Md Masum Murshed
Kanazawa University


This study presents a Lagrange-Galerkin(LG) scheme of second order in time for the shallow water equations (SWEs) with a transmission boundary condition. Firstly, we confirm the experimental order of convergence of the scheme. Secondly, we apply the scheme to a practical case, i.e., a complex domain with a transmission boundary condition. Finally, based on the numerical experiments, we summarize the advantages of our scheme, second-order accuracy in time, mass conservation, and no significant reflection from the transmission boundaries.

Numerical computation for 2-phase viscous fluids Hele-Shaw flow with sink/source by the method of fundamental solutions
Yusaku Shimoji, Shigetoshi Yazaki
Meiji University, Meiji University


The boundary between two viscous fluids is known to destabilize depending on the situation, producing a finger-like pattern, which is called the Saffman-Taylor instability. We were able to simulate the Saffman-Taylor instability in a Hele-Shaw cell by using the method of fundamental solutions (MFS for short). MFS is a mesh-free numerical solution method for mainly potential problems. Here, we present the implementation of MFS for 2-phase viscous fluids Hele-Shaw flow with sink/source and its numerical results.

A lifting theorem for the Dirichlet-data for the Navier-Stokes equations with open boundary condition
John Sebastian Simon, Hirofumi Notsu
Kanazawa University, Kanazawa University

Abstract: We shall present a Navier-Stokes equation coupled with a general class of nonlinear Robin-type boundary condition. The lifting theorem allows a prescription of a non-homogeneous Dirichlet condition on a portion of the boundary that excludes where the open boundary condition is prescribed. We present the existence of weak solutions, and end by illustrating particular forms of the boundary condition and show their differences numerically.

Investigation of brine leakage from a deep aquifer
Jakub Solovský
FNSPE CTU in Prague


Damage to the caprock and potential leakage of brine from a deep aquifer is one of the risks during CO2 sequestration.

To reduce the complexity of the numerical solutions the fractures are considered one-dimensional objects whereas the rest of the domain is considered two-dimensional.

In this work, we assume that the flow is described by Darcy's law both in porous media and fractures. We present the mathematical model of single-phase flow and transport in porous media and its coupling between 1D and 2D computational domains.

The numerical solution is based on the mixed-hybrid finite element method with fully implicit time discretization.

The capabilities of the model are demonstrated in scenarios arising from the laboratory experiments mimicking the brine leakage from a deep aquifer.

Application of Neural Networks and Mathematical Models for T1 Relaxation Time Estimation
Kateřina Škardová
FNSPE CTU in Prague


In this contribution, we discuss how mathematical models and machine learning methods can be combined in parameter estimation framework. We propose a two-stage method: in the first stage, we combine machine learning and mathematical model in order to obtain a fast first parameter estimation; in the second stage, the estimation is refined by numerical optimization. The proposed method is applied to the problem of estimating the relaxation time T1 from a series of images obtained by the standard Modified Look-Locker Inversion (MOLLI) restoration technique. We present the results of the proposed method applied to phantom and in vivo data and demonstrate some advantages of such a combined approach.

Forecasting cryptocurrency price dynamics using reinforcement learning
Jan Thiele, Quang Van Tran


Maximal monotone operator technique for solving Hamilton-Jacobi-Bellman equation arising from optimal portfolio selection problem
Cyril Izuchukwu Udeani, Daniel Sevcovic
Comenius University in Bratislava


This study investigates a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) parabolic equation using the monotone operator technique. We consider the HJB equation arising from portfolio optimization selection, where the goal of an investor is to maximize the conditional expected value of the terminal utility of the portfolio. The fully nonlinear HJB equation is transformed into a quasilinear parabolic equation using the so-called Riccati transformation method. The transformed parabolic equation can be viewed as the porous media type of equation with the source term. Under some assumptions, we obtain that the diffusion function to the quasilinear parabolic equation is globally Lipschitz continuous, which is a crucial requirement for solving the Cauchy problem. We employ Banach's fixed point theorem to obtain the existence and uniqueness of a solution to the general form of the transformed parabolic equation in a suitable Sobolev space in an abstract setting. Some financial applications of the proposed result are presented in one-dimensional space.