Student workshop on scientific computing 2019

May 30 - June 2, 2019

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

List of abstracts

Rotational spectrum as a Tool for Alzheimer disease diagnostics
Martin Dlask
FNSPE, CTU in Prague, FNSPE, CTU in Prague


Biomedical data often carry chaotic character that can be investigated with the tools of fractal geometry. Correlation dimension is a suitable measure that can be used for the analysis of EEG signal in order to discover Alzheimer disease (AD). However, its estimation is often biased and inaccurate.We present the rotational spectrum method that estimates the correlation dimension without bias for arbitrary set in Euclidean space and apply it to the EEG. Using multiple testing we discovered channels with significant difference of fractal dimension between CN and AD patients. Using space reconstruction theorem it was possible to prove that the left occipital and temporal part of human brain carries the most important information of the disease in human body.

A modified IB-LB method for incompressible fluid flow in 2D and 3D on GPU
Pavel Eichler, Radek Fučík
FNSPE, CTU in Prague

Abstract: Fluid-solid interaction in 2D and 3D is an important topic in fluid dynamics and accurate simulations are desirable in the field of applications dealing with this phenomenon, e.g., blood flow across the aortic valve, air flow in the boundary layer, etc. To accurately represent the position of the solid obstacle, immersed boundary method (IBM) based on the Lagrangian description was introduced. The advantage of this method is that it does not depend on the numerical method used for the fluid simulations and thus modern numerical method such as Cascaded lattice Boltzmann method (CLBM) in 2D and Cumulant lattice Boltzmann method (CuLBM) in 3D can be used. In this contribution, a computational study on optimal spacing of Lagrangian nodes discretizing a rigid and immobile immersed body boundary in 2D and 3D is presented to show how the density of the Lagrangian points affects the numerical results of the Immersed Boundary–Lattice Boltzmann Method (IB–LBM). The study is based on the implicit velocity correction-based IB–LBM proposed by Wu and Shu (2009, 2010); however, this method often fails for densely spaced Lagrangian points. Thus, we introduce a modification that improves the stability of the original method and compare the performance of both methods using several benchmarks problems. In these problems, we show how the spacing of the Lagrangian points affects the numerical results, mainly the overall drag force and the permeability of the discretized body boundary.

Limitations of using the Magnetic Resonance Imaging for flow measurements
Radek Galabov
FNSPE, CTU in Prague


Magnetic Resonance Imaging (MRI) is a method used in medicine to obtain medical images carrying diverse information. The Phase Contrast sequence of MRI imaging (PC MRI) can provide information on flowing blood velocity. This data can be coupled with and compared to the Computational Flow Dynamics (CFD). The PC MRI data are sometimes also compared to the data obtained by the MRI data acquisition simulator (Bloch simulator). For both purposes, the knowledge of the MRI limitation is substantial.

Several artifacts arise in the PC MRI, which is designed to measure constant flow correctly. Pulsatile flow leads to a recognizable ghosting artifact. Accelerated flow results in spatial mismatch. The summation of spins in one voxel reduces the correct mean velocity and in the case of turbulent flow may even lead to a complete signal void. As PC MRI does not allow real-time measurement, flow data are time averaged with a complicated weighting over several heart cycles. If flow periodicity is not held, results may be misleading. Other artifacts exist as well, including metal and motion artifacts and eddy currents.

In conclusion, MRI images do not show reality and must be approached adequately before being coupled with CFD of when interpreting Bloch simulator outputs.

Imperfect Classification via SOM and Hidden Classes
Radek Hřebík
FNSPE, CTU in Prague


Various approaches to data self-organisation are discussed. New alternative strategies to traditional Kohonen SOM learning are based on basic and anomalous diffusive learning algorithms. Both diffusions are used to improve the basic system behaviour. New approach is compared to the traditional one using real datasets. The quality of self organisation is based on distance penalization and topographic error. Correlation based measures are also discussed. The basic characteristics of hidden class unions are based on elementary characteristics of classification quality as accuracy, sensitivity and critical sensitivity.

Numerical simulation of multiphase flow in a fluidized bed boiler on unstructured grids
Tomáš Jakubec
FNSPE CTU in Prague


This presentation is aimed at numerical simulation of two-phase flow in 2D geometry of the combustion chamber of a fluidized bed boiler. Firstly, the governing equations and the problem formulation are introduced. Eulerian description for both the solid and the gaseous phase is employed. The resulting problem is solved by finite volume method on unstructured grids together with explicit Euler scheme. Some details of the implementation are briefly discussed. Finally, solutions of several representative flow patterns in the combustion chamber are demonstrated.

Semi-Automated Finder of Invariant Regions
Jakub Kantner, Michal Beneš
FNSPE, CTU in Prague


Invariant regions can be used to bound solutions of several systems of partial-differential equations. However, their localization requires lot of manual work especially when the equations include several parameters. For each set of such parameter values a new invariant region has to be found.

In this contribution, a proof of existence of invariant region for special class of right hand side functions of PDEs is given. Based on this proof an algorithm is proposed that automatizes their search.

Massively parallel LBM simulations using CUDA and MPI on multiple GPUs
Jakub Klinkovský, Pavel Eichler, Radek Fučík, Tomáš Oberhuber
FNSPE, CTU in Prague

Abstract: In this talk, we summarize our progress towards an efficient multi-GPU LBM solver for single-phase fluid flow. It is known that LBM is suitable for massive parallelization on GPUs and the implementation for a single GPU in the CUDA framework is straightforward. The single-GPU implementation can be extended with a standard domain decomposition approach in order to utilize multiple GPUs. A domain decomposition solver can be implemented either as a single-process solver using a threading library such as OpenMP, or as a multi-process solver using message passing. Recently, we have extended our former single-process LBM solver into a multi-process solver using the MPI library in order to utilize many GPUs spread across multiple nodes on HPC clusters. We describe the optimization strategies and techniques used in the solver, compare the performance with the original single-process solver on a single node, and finally show the results of preliminary high-resolution simulations for problems investigated in our research projects.

The solution of modified Allen-Cahn equation with the lattice Boltzmann method
Michal Malík
FNSPE, CTU in Prague


Phase-field models are popular in identifying and tracking multiple domains with different physical properties. Thus the correct and time effective solution is crucial in many applications, e.g., multiphase flow, etc.

In this entry,  the single relaxation time lattice Boltzmann method for the solution of the modified Allen-Cahn equation is presented. First, the basics of the discrete mathematical model are introduced. Next, some basic numerical experiments demonstrating the efficiency of the lattice Boltzmann method are carried out.

Properties of codimension-two curve shortening flow
Jiří Minarčík
FNSPE, CTU in Prague


This contribution deals with problems associated with generalization of the curve shortening flow into higher dimensional space. Specifically, the motion in normal and binormal direction of closed curves embedded in $\mathbb{R}^3$ is analyzed and compared to the standard two-dimensional case. Although the motion of space curves in normal direction is similar to that in the plane, new phenomena may be observed in $\mathbb{R}^3$. Namely, embedded curves may develop new types of singularities, stop being simple or lose their convexity during the evolution. We discuss some specific examples and present theoretical results addressing these problems. The motion in the binormal direction, discussed in the second part of the talk, has been studied mainly in the context of vortex dynamics. Aside from its application in physics, this motion has many interesting properties. The local rate of parametrization as well as length, total torsion, elastic energy and other global properties of closed curves are preserved and the motion law is equivalent to a non-linear Schrödinger equation obtained by the Hasimoto's transformation.

Numerical Modeling of Compressible Gas Flow in Zeolite Bed and above its Surface
Ondřej Pártl, Jiří Mikyška
FNSPE, CTU in Prague


We shall present mathematical and numerical models for non-isothermal compressible flow of a mixture of two gases in a heterogeneous porous medium and in the coupled atmospheric boundary layer above the surface of this porous medium, where one of the flowing components adsorbs on the porous matrix, and we shall discuss the application of these models to the simulation of the hydration of a zeolite bed.

In our models, the domain in which the flow occurs is divided into the porous medium subdomain and the free flow subdomain. In each subdomain, the flow is described by corresponding balance equations for mass, momentum and energy. On the interface between the subdomains, coupling conditions are prescribed.

In both subdomains, the spacial discretization of the governing equations is carried out via the finite volume method. As for the time discretization, the stiff source terms which describe the adsorption effects are handled via the operator splitting.

In this contribution, we shall also present the results of the simulations of the hydration of a zeolite bed via humid air which comes to this bed through a pipe.

Experimental Study of Gas Mass Transfer between Entrapped Air and Water in Satiated Sand
Tomáš Princ, Michal Sněhota
Czech Technical University in Prague


Aim of this study is obtaining time development of the mass transfer coefficient and relationship between the actual hydraulic conductivity and the saturation by the entrapped gas bubbles during the course of entrapped air dissolution in otherwise water-saturated sand. The changes in gas saturation occur only because of the gas mass transfer between bubbles and partly degassed water flowing through the sand column. In the experimental set-up water driven by a peristaltic pump first passes through vacuum membrane degasser into total dissolved gas probe. Then, it enters vessel with submerged sand column. Given the water level in the vessel is kept at a constant level, mass of water and air in the sample can be determined gravimetrically. The samples were prepared from the coarse sand. Initial full saturation of the samples was achieved by packing the samples under degassed deionized water. Samples were subsequently drained at suction pressure 5 kPa and then submerged in air-saturated water for re-saturation that induced bubbles trapping. Then series of inflow outflow experiments was conducted. Firstly, the ponded infiltration experiment with water in equilibrium with atmosphere removed the mobile bubbles from the porous space. Then the degasser was turned on and air bubbles dissolution phase of the experiment started. Total dissolved gas probes recorded the concentration of dissolved air at the inflow and at outflow. The hydraulic conductivity was determined using a Darcy law from known hydraulic gradient and measured water flux. The experiment was maintained until the sample mass (and therefore the water and gas saturation) remained constant. The outcome of the experiment is a replicated record of time development of the mass transfer between air bubbles and flowing water in a coarse sand. Additionally, the relationship between hydraulic conductivity and gas saturation was developed during the same experiment.

Global optimization method for solving the $VTN$-phase stability testing problem
Tomáš Smejkal, Jiří Mikyška
FNSPE, CTU in Prague


In this contribution we will present a new global optimization method for solving the phase stability problem at constant volume, temperature, and mole numbers (VTN-specification) of a multicomponent mixture. This method is based on the Branch and Bound strategy and the convex-concave splitting of the objective function. The Branch and Bound strategy consists of a local optimization method (the Newton-Raphson method) and a convex optimimization method (the Barrier method). Different strategies for constructing the convex-concave split will be presented. The performance of the method will be shown on examples from the literature. Comparison with the standard Newton-Raphson method with line-search and with modified Cholesky decomposition will be presented.

Imaging Models in Image Registration
Kateřina Solovská
FNSPE, CTU in Prague


Image registration plays an important role in post-processing of medical data. Te process of registration consists of deforming a (moving) source image to match a (fixed) target image.

One of the biggest problems in the task of image registration is corruption of the input image data. Noise, missing values or partial volume artifact are some of the aspects, that can negatively effect the result of registration.

This talk will describe an approach to extracting motion from medical image series, based on a model of the imaging modality.

The goal is to be able to generate data corresponding to the real image, and provide better registration. The method will be illustrated on examples of synthetically generated 2D tagged images.