Workshop on scientific computing

June 12-15, 2014
Department of Mathematics, FNSPE CTU in Prague
Děčín, Czech Republic

TOUGH2 Simulation of water and air flow in heterogenous porous media

Tomáš Princ, Michal Sněhota


Abstract:The contribution deals with TOUGH2 modeling of water and air flows in heterogeneous porous media during ponded infiltration. Flow was simulated in two-dimensional vertical domain that consisted of three materials. Analysis of scenarios results showed that water penetrated first through continuous preferential pathways, while infiltration to the fine material was slower. The full water saturation was not reached in coarse material. Retained air was then gradually dissolved in the partially air-saturated water in the simulated experiment.

This research was provided by the GAČR14-03691S and SGS14/131/OHK1/2T/11.

Temporal and spatial distribution of water and air during ponded infiltration on a sand sample recorded by neutron imaging

Jan Šácha, Michal Sněhota, Martina Sobotková, Vladimíra Jelínková

Czech Technical University in Prague, Civil Engineering, Department of Irrigation, Drainage and Landscape Engineering, Prague 6, Czech Republic

Abstract:Significant temporal variation of quasi saturated hydraulic conductivity (Kqs) has been observed in number of infiltration experiments conducted mainly on heterogeneous soil of Cambisol. The change of quasi-saturated hydraulic conductivity cannot be precisely described by existing mathematical models. The Kqs variation has been recently attributed to a changing distribution of the entrapped air and water within the sample. It is expected that air is moved to the preferential pathway and acts as a barrier there. To support this assumption a ponded infiltration experiment was conducted on a soil sample packed into the quartz glass column of inner diameter of 34 mm. The sample composition represents simplified heterogeneity of the natural soil but also allow the easy quantitative water content determination in individual subdomains of the sample. The sample consists of two sand fractions. The coarse sand represents preferential flow pathways and it constitutes the continuous pathways across the sample. The matrix is formed by fine sand. The Kqs was determined from the known hydraulic gradient and measured volume flux. The experiment was monitored by neutron radiography (NR). The raw images from NR had to be corrected for the beam hardening, background noise, fluctuations of neutron flux and inhomogeneity of beam and detector. Volume of water in the sample calculated from neutron projections was compared with actually infiltrated water volume into the sample during first 40 second after beginning of infiltration. Results of the comparison were in a good agreement. The 3D tomography images were reconstructed from the corrected radiographic images to obtain the spatial distribution of the water content within the sample. The difference between the water volume calculated from radiography and the one calculated from tomography never exceeded 5%. While the total amount of water determined by NR within the sample during the quasi steady state flow remains practically constant (27.9 cm3 at the beginning and 28.6 cm3 in the end of infiltration) the water content in the coarse fraction decreases (from 0.333 to 0.324) and the water content in the fine fraction increases (from 0.414 to 0.436) in 5 hours. The results support the hypothesis that the effect of the gradual Kqs variations is caused by the entrapped air redistribution, which acts as a barrier in preferential pathways.

This research was provided by the GAČR14-03691S and SGS14/131/OHK1/2T/11.
The neutron imaging was carried out in the NEUTRA beam line at the Paul Scherrer Institute, Villigen, Switzerland. The technical support of the SINQ team is greatly appreciated.

Experimental investigation of the entrapped air redistribution in near-saturated soil

Michal Sněhota, Jan Šácha, Martina Sobotková, Vladimíra Jelínková, Martina Fryčová, Milena Císlerová


Abstract:In structured soils the preferential flow appearance may be accompanied by temporal variations of the soil hydraulic properties often occurring in the time frame of one infiltration event. These variations do not have to be related to the changes in soil structure. The experimental evidence of the large short term variations of hydraulic conductivity in satiated soil columns during Darcy’s type of the experiment were reported seven decades ago by Christiansen (1944), but to date are not considered in models. The described instability is attributed to changes in amount of entrapped air remaining in soil pores despite the pressure head of water have become positive. Such flow regime can be called the quasi-saturated flow characterized by a certain value of quasi saturated hydraulic conductivity (KQS). It is hypothesized that the total volume of entrapped air bubbles, which effectively restricts the water flow, may vary even during the infiltration resulting in considerable changes of KQS.
Our team at FCE CTU in Prague has investigated the above effect by means of recurrent ponded infiltration–outflow (RPI) experiment (Cislerova et al., 1990) in which the first and second infiltration runs are started into the soil under different initial water content. While at the top of the sample a constant pressure head is maintained, the bottom is supported by a perforated plate to induce free outflow (a seepage face boundary condition). The initial transient infiltration stage as well as the steady state flow stage needed to determine KQS are acquired in one run of RPI experiment. For some structured soils the RPI experiment exhibited a significant gradual decrease of quasi-saturated hydraulic conductivity during the first infiltration and even lower quasi saturated hydraulic conductivity during the second infiltration.
The presentation will mainly focus on results of series of experiments conducted on undisturbed soil samples (Dystric Cambisol) of two different sizes. RPI experiments on larger samples (7×103 cm3) were performed with concurrent monitoring of the fluxes, pressure heads (tensiometers), water contents (TDR) and tracer breakthrough (Br- and deuterium) during the RPI experiments (Snehota et al., 2008). Smaller samples (approx. 1 × 102 cm3) were used to monitor internal processes during the same experiment by means of non-invasive methods of magnetic resonance imaging (MRI) (Jelinkova et al., 2011; Snehota et al., 2010). The imaging has allowed visualizing and quantifying the bubbles of entrapped air. Internal structure of all samples was visualized by X-ray computer tomography (CT). Scaling factors of hydraulic conductivity and porosity, calculated in particular voxels of the CT scan were used as nodal input information into three-dimensional (3D) water flow model based on Richards’ equation (Dohnal et al., 2013). Voxels containing entrapped air bubbles, located by MRI, were included as no-flow nodes in the model. Results support the hypothesis (Snehota et al., 2010) that the effect of the gradual decrease of the flow rates is caused by entrapped air redistribution and gradual build-up of bubbles in preferential pathways. The air comes probably from the soil matrix where the residual air encapsulated during the primary fast breakthrough of gravitational water is being gradually replaced by water attracted to fine pores by strong capillary forces. The trapped air forms bubbles which may thus block some preferential pathways and cause overall lower infiltration and outflow flux rates. When the same experiment was repeated on undisturbed sample of the same soil but taken from more compact part of the soil without presence of continuous preferential pathways, the described effect didn’t occur. This shows a close connection between preferential flow and temporal variations of quasi-saturated hydraulic conductivity.
As the next step the process of infiltration in near-saturated soil and fate of residual air bubbles was studied using neutron imaging in NEUTRA beamline of the Paul Sherrer Institut, Switzerland. Experiments were conducted on undisturbed samples of soil from the Cambisol series and on an artificially packed sample composed of coarse sand and fine ceramic. The neutron radiography and tomography data showed quantitatively exchange of water and air between domains of fine and coarse materials during quasi-steady state flow in the sample.

This research was provided by the GAČR14-03691S and SGS14/131/OHK1/2T/11.
The neutron imaging was carried out in the NEUTRA beam line at the Paul Scherrer Institute, Villigen, Switzerland.

Christiansen, J.E., 1944. Effect of entrapped air upon the permeability of soils. Soil Sci. 58, 355–365.
Cislerova, M., Vogel, T., Simunek, J., 1990. The infiltration-outflow experiment used to detect flow deviations. Field-Scale Water and Solute Flux in Soils. Birkhauser Verlag, Basel.
Dohnal, M., Jelinkova, V., et al., 2013. Three-dimensional numerical analysis of water flow, affected by entrapped air: Application of noninvasive imaging techniques, Vadose Zone J., 12(1)
Jelinkova, V., Snehota, M., et al., 2011. Effects of entrapped residual air bubbles on tracer transport in heterogeneous soil: Magnetic resonance imaging study. Org. Geochem. 42(8), 991–998.
Snehota, M., Sobotkova, M., Cislerova, M., 2008. Impact of the entrapped air on water flow and solute transport in heterogeneous soil: experimental set-up. J. Hydrol. Hydromech. 56(4), 247–256.
Snehota, M., Cislerova, M., et al., 2010. Tracing the entrapped air in heterogeneous soil by means of magnetic resonance imaging. Vadose Zone J. 9(2), 373–384.

Fluctuation analysis of high frequency electricity power load in the Czech Republic

Hynek Lavička


Abstract:We analyse the electricity power load in the Czech Republic (CR) which exhibits seasonality as well as other oscillations typical for European countries. Moreover we detect 1/f noise property that was separated from modulating signal and analysed. The presented approach uses Multi-fractal Detrended Fluctuation Analysis method (MF-DFA) from statistical physics to analyse extremely large power load datasets with minute resolution. Extracting of noise part of the signal using Fourier transform allows us to apply this method to obtain fluctuation function and to estimate Hurst exponent. The resulting fluctuation function of the dataset is characterized by heavy-tail distribution with no finite moment. Generalized Euclidean metric with variable exponent q is used to analyze this fluctuation function. We found that the autocorrelation function exhibits persistent behavior for q<1 and it is anti-persistent for q>1.

Sand in the Wheels or Wheels in the Sand? Tobin Taxes and Market Crashes

Hynek Lavička


Abstract:The recent crisis revived interest in financial transaction taxes (FTTs) as a means to offset negative risk externalities. However, up-to-date academic research does not provide sufficient insights into the effects of transaction taxes on financial markets as the literature has here-to-fore been focused too narrowly on Gaussian variance as a measure of volatility. In this paper, we argue that it is imperative to understand the relationship between price jumps, Gaussian variance, and FTTs. While Gaussian variance is not necessarily a problem in itself, the non-normality of return distribution caused by price
jumps affects not only the performance of many risk-hedging algorithms but directly influences the frequency of catastrophic market events. To study the aforementioned relationship, we use an agent-based model of financial markets. Its results show that FTTs may increase the variance while decreasing the impact of price jumps. This result implies that regulators may face a trade-off between overall variance and price jumps when designing optimal tax. However, the results are not robust to the size of the artificial market as non-linearities emerge when the size of the market is increased.

A mechanism for cell motility by active polar gels

Wieland Marth

TU Dresden

Abstract:We present a model which describes cell motility as a result of contractile stresses between actin filaments. We therefore consider the actomyosin solution inside the cell as a active polar gel. Together with a classical Helfrich type model to account for bending and stiffness effects of the cell membrane we obtain a model for two phase complex fluids. The coupled model is formulated within a phase field approach and solved using adaptive finite elements.

Crystallization on a Sphere

Christian Köhler

TU Dresden

Abstract:By means of numerical simulations we investigate crystallization according to a 2D Phase Field Crystal model on the curved surface of a sphere. The focus is laid on the development and characterization of defects by monitoring the temporal evolution of the crystal boundary.

Up-wind principle in geodetic computations

Marek Macák, Karol Mikula

SvF STU, Bratislava

Abstract:We present a new mathematical formulation of the geodetic boundary value problem (GBVP) for the disturbing potential. From the mathematical point of view, the GBVP is formulated in the form of the Laplace partial differential equation for the unknown potential in the external domain. As boundary conditions (BC) defined on the Earth surface we consider the oblique BC. Since the GBVP is defined in the infinite domain we present a construction of the bounded domain. On artificial boundary the Dirichlet BC is applied. For numerical solution of the Laplace equation we use the finite volume method. As a discretization technique for the oblique BC we use the so-called up-wind principle. From this discretization we obtain the linear system of equations with the M-matrix property. Finally we test this approach numerically to show its order of accuracy in several experiments.

Nonlinear PDE based numerical methods for cell tracking in 4D biomedical images

Róbert Špir, Karol Mikula

SvF STU, Bratislava

Abstract:We present results obtained for large-scale 3D+time two-photon laser scanning microscopy images of early stages of zebrafish (Danio rerio) embryo development. Our approach consists of three basic steps - the image filtering, the cell centers detection and the cell trajectories extraction yielding the lineage tree reconstruction. In all three steps we use nonlinear partial differential equations. The core of our new tracking method is an original approach to cell trajectories extraction based on finding a continuous centered paths inside the spatio-temporal tree structures representing cell movement and divisions. Such paths are found by using a suitably designed distance function from cell centers detected in all time steps of the 3D+time image sequence and by a backtracking in steepest descent direction of a potential field based on this distance function.

Velocity Field Extraction from Image Sequences

Viera Kleinová

SvF STU, Bratislava

Abstract:In computer vision there are many methods that are dealing with optical flow estimation. In this work we focused on one of them, specifically Lucas-Kanade method. The goal of this work is to extract velocity field from image sequences using Lucas-Kanade method and visualization of the evolution of this extracted velocity field.

Creation of Digital Terrain Models using surface evolution

Michal Kollár

SvF STU, Bratislava

Abstract:This work discusses the creation of the digital terrain models using surface evolution method. To achieve this goal we developed a discretization of the Laplace-Beltrami operator using the finite volume method. This approach is based on an approximation of arbitrary surface by triangular mesh and deriving the weak formulation for the Laplace-Beltrami operator on the manifold. A system of linear equations obtained by the finite volume approximation of the weak formulation is solved in each discrete time step by an iterative solver. The numerical experiments consist of theoretical ones, where we are interested in a minimal surface and a surface with a given mean curvature, and practical ones, where our aim is to create the digital terrain models obtained by using a remote sensing technology LiDAR.

A Quasi-1D Model of Biomass Co-Firing in a Circulating Fluidized Bed Boiler

Michal Beneš, Pavel Strachota, Radek Máca, Vladimír Havlena, Jan Mach


Abstract:We introduce an outline of the mathematical model of combustion in circulating fluidized bed boilers. The model is concerned with multiphase flow of flue gas, bed material, and two types of fuels (coal and biomass) that can be co-fired in the furnace. It further considers phase interaction resulting in particle attrition, devolatilization and burnout of fuel particles, and energy balance between heat production and consumption (radiative and convective transfer to walls). Numerical solution by means of the finite volume method together with a Runge-Kutta class time integration scheme is mentioned only briefly as the used methods are generic and well documented elsewhere. Some representative results are also presented.


Jaromír Kukal


Abstract:Estimates of capacity, information, and correlation dimensions are not unbiased, which is a well known fact.
The talk will be about methodological and statistical origins of the estimation bias. Three directions of research will be presented. Entropy estimates from small data sets will be presented first including natural Bayes and Jeffreys approaches. The second approach is based on n-dimensional fBm hypothesis and stabilzation of n-dimensional power spectrum via numeric integration. The third method of fractal set investigation is based on properties of point set intersection, which enables to convert fractal analysis of n-dimensional functions to investigation of long time series fractality. Many thanks for theoretical and programming suport to my students Martin Dlask, David Blatsky, Lucie Jungerova, Lucie Tylova, and Vaclav Hubata-Vacek.

Two approaches for solving optimal topology design problems

Roman Kukumberg

Comenius University, Bratislava

Abstract:Optimal topology design problems may lead to minimization of a non-differentiable convex function of large number of variables. We apply and compare two competing methods of convex optimization for solving the optimal topology design problem, namely proximal gradient method and interior-point method. In proximal gradient method we use three different approaches known from literature and one our modification of the method. We test these methods on two topology design problems with 16 500 and 186 000 variables. Both methods are compared, analyzed and a discussion on the performance is provided.

Repeated support splitting and merging phenomena in the initial-boundary value problem for a porous media equation

Kenji Tomoeda

Kyoto University, Graduate School of Informatics Kyoto University, Kyoto 606-8501, Japan


Lattice Boltzmann Method - An Introduction for JM

Robert Straka

AGH Krakow

Abstract:We will focus on development and use of the LBM for simulating a fluid flow. First the Boltzmann transport (BTE) equation will be introduced and its discretization in the space of finite velocities and on the lattice, next the BGK approximation together with the equilibrium distribution function of Maxwell-Boltzmann will be used to show that solving the BTE gives the solution of the athermal Navier-Stokes equations. In the last part of talk, brief overview of several concepts of collision terms approximation will be presented with particular attention to the Factorized Central Moment Cascaded LBM and it's use for 2D CFD.

A continuous theory for active polar liquid crystals

Simon Praetorius

TU Dresden

Abstract:Soft active matter (dry and wet) is currently in the focus of many researchers. We want to focus on active crystals, i.e. matter with polar and translational order and with an active drift. Therefore we have extended the phase-field crystal model to include hydrodynamic interactions and combine it with a polarization model to give the crystal an orientation.

Passive Transport in Neurons

Francesco Alaimo

TU Dresden

Abstract:We aim at studying passive transport of particles inside a neuron showing a complex geometry. In doing so, we use adaptive finite elements to study the diffusion of particles in this geometry. In particular, we focus on to two important quantities of the system: the mean first passage time (MFPT) and the variance. An accurate analysis of these two quantities allows us to understand how the geometry of the system affects the transport of particles.

Phase Field Modeling of Pillar-like Crystal Surface Morphology

Marco Salvalaglio1, Roberto Bergamaschini1, Rainer Backofen2, Francesco Montalenti1, Leo Miglio1, Axel Voigt2

1Università degli Studi di Milano-Bicocca and 2TU Dresden

Abstract:The description of the surface morphology in real crystals is an interesting field of research in which the mathematical modeling provides informations for a broad range of applications, from pure materials science to the design of technology devices. We present here a suitable Phase Field Model of surface diffusion, able to reproduce, within a continuum approach, arbitrary morphologies according to the selected surface energy density function. A description of the general anisotropic surface diffusion problem is given and the results are compared with experimental cases of pillar structures [1]. This model predicts the equilibrium surface morphology (i.e. the Wulff Shape) and its evolution in time, for instance during annealing experiments. It can also be considered as a starting point about the study of more complex surface morphology phenomena and their kinetic evolution.

[1] C. V. Falub, H. von Kanel, F. Isa, R. Bergamaschini, A. Marzegalli, D. Chrastina, G. Isella, E. Muller, P. Niedermann and L. Miglio, Science 335, 1330 (2012).

Parallel multi-mesh method on AMDiS

Siqi Ling

TU Dresden

Abstract:Multi-mesh finite element method is currently one good method to modeling multiphysics problems. Compared to standard adaptive finite element method, it creates less overall Degree of Freedoms by resolving the local nature of different components independently of each other. But so far, this method is only applied in sequential mode. My concentration is focused on how parallel multi-mesh method works, including the strategy of meshes partition and repartition, the detailed implementation based on existing finite element codes, and the numerical results on examples such as dendritic growth.