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Interessen

Mathematik in den Geowissenschaften, dabei insbesondere Modellierung und Simulation reaktiven Schadstofftransports in porösen Medien, Beurteilung von Natural Attenuation, Geostatistik, effiziente und genaue Lösung von hydrogeochemischen Mehrkomponentenmodellen, Strukturbildung von Mikroaggregaten, insbesondere in der Rhizosphäre.

Mathematik in der Biologie, insbesondere räumlich-zeitliche Differentialgleichungsmodelle regulatorischer Netzwerke.

Entwicklung des Softwarepakets RICHY.

 

Sie finden folgend eine Liste von Projekten mit meiner Beteiligung oder Leitung, Publikationen, Review-Tätigkeiten, betreute Bachelor-, Master- und Diplomarbeiten, sowie eine Liste von Vorträgen bei Tagungen.

 

Projekte

  • Mehrskalenmodellierung mit veränderlicher Mikrostruktur: Ein Ansatz
    zur Emergenz in der Rhizosphäre mit effektiven Bodenfunktionen

    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)

    Titel des Gesamtprojektes: DFG Schwerpunktprogramm 2089 “Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”
    Laufzeit: 01-02-2019 - 31-01-2022
    Mittelgeber: DFG / Schwerpunktprogramm (SPP)
    URL: https://www.ufz.de/spp-rhizosphere/index.php?en=46495
    Abstract

    Im Projekt soll die Strukturbildung in der Rhizosphäre, welche durch geochemische, mikrobiologische und physikalische Einflüsse gesteuert wird, modellbasiert untersucht werden. Ziel ist die Entwickling eines mechanistischen Modellansatzes, welcher die dynamische strukturelle Reorganisation der Rhizosphäre auf der Skala einzelner Wurzeln (Mikroskala) ermöglicht (einschließlich expliziter Darstellung der Heterogenitäten des Porenraums). Dieses
    sich zeitlich verändernde Mikroskalenmodell ist wechselseitig mit der Makroskala gekoppelt mittels mathematischer Homogenisierung (upscaling) und erlaubt so die Ableitung effektiver Bodenfunktionen. Dabei betrachten wir also keine statische Rhizosphäre, sondern
    vielmehr eine dynamische, d.h. eine sich durch Bildung von Aggregaten und geochemische Strukturen verändernde. Insbesondere werden durch die Erkenntnisse aus dem
    Zentralexperiment - CT-Bilder in verschiedenen Wachstumsphasen und Feuchteverhältnissen - die Porenstruktur sowohl mit als auch ohne Wurzelhärchen deutlich, und damit auf deren Einfluss zur Aggregation schließen lassen. Mit Hilfe der Kooperationspartner soll
    auch eine explizite Wurzelsekretphase modelliert sowie die Anlagerungseigenschaften von Aggregaten an Wurzelhärchen aufgenommen.

  • Mechanistische Modellierung der Formation und Konsolidierung von Mikroaggregaten in Böden

    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)

    Titel des Gesamtprojektes: DFG RU 2179 “MAD Soil - Microaggregates: Formation and turnover of the structural building blocks of soils”
    Laufzeit: 01-01-2016 - 31-12-2018
    Mittelgeber: Deutsche Forschungsgemeinschaft (DFG)

  • MPFA (Multi Point Flux Approximation) und gemischt-hybride Finite Element Methoden für Fluss und Transport in porösen Medien

    (Drittmittelfinanzierte Einzelförderung)

    Laufzeit: 01-01-2012 - 31-12-2013
    Mittelgeber: Deutscher Akademischer Austauschdienst (DAAD)
    Abstract

    Nonlinear (multiphase) flow and reactive multicomponent transport problems in highly heterogeneous porous media and their numerical simulation are of great interest for evaluating site remediation, energy exploitation or CO2 sequestration scenarios.   The resulting advection-diffusion-reaction-systems are coupled nonlinear parabolic partial differential equations, and we have parabolic or elliptic nonlinear flow equations, possibly degenerate. The development of convergent and efficient numerical schemes is very challenging and the mixed (hybrid) finite element method M(H)FEM and the multipoint flux approximation MPFA are powerful locally mass conservative choices. They offer also the advantage of continuous flux approximations over the element faces.  Analogies between the two techniques should help to prove order of convergence estimates and monotonicity for the multicomponent transport problems, but also for multiphase flow.  Furthermore numerical diffusion of the schemes should be quantified to assess the accuracy of the methods.  Simulation examples should include realistic scenarios on heterogeneous, log normally distributed random parameter fields.

  • Entwicklung neuer photokatalytischer Filtersysteme zur Luftreinigung von Nanopartikeln, organischen Zusätzen und Bakterien mit Hilfe numerischer Simulationen

    (Drittmittelfinanzierte Einzelförderung)

    Laufzeit: 01-10-2009 - 30-09-2011
    Mittelgeber: Bundesministerium für Bildung und Forschung (BMBF)
    Abstract

    The project was a cooperation of a group of applied mathematicians with the Russian company Aeroservice for the development and optimization of new photocatalytic filter systems for air cleaning of nanoparticles and organic substances with the help of mathematical simulation tools. For the simulation of aerosol transport in the filter made of polypropylene fibers, which is used in hospitals or airports, e.g., mathematical models and efficient solution algorithms had to be developed. These allow on the one hand to take stochastic components into account, as the heterogeneous conductivity distribution in the filter. On the other hand these methods were coupled with highly accurate computation schemes as mixed finite element methods, which guarantee local mass conservation for the transport processes. The design parameters of real experiments can be optimized with the help of such simulation tools and their sensitivity with respect to filter efficiency analysed. Among the used methods are particle filtration in porous media, based on the Darcy equation, and coupled Eulerian and Lagrangeian simulation of transport processes, including Monte Carlo approaches with given filter geometries.

  • Der Einfluss von Kolloiden auf Wasserfluss und Stofftransport in Böden: Randaspekt oder Schlüsselprozess?

    (Drittmittelfinanzierte Einzelförderung)

    Laufzeit: 01-11-2006 - 31-12-2009
    Mittelgeber: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Abstract

    Soil colloids may influence the interaction between solutes and the immobile solid phase. A coupling to the fluid transport is possible by processes of sedimentation, flocculation, precipitation, filtration and deposition. The objective of this research project is the qualitative and quantitative examination of the crucial aspects of colloidal-influenced solute- and fluid transport by means of systematic, prognostic simulation. In detail,

    1. the attachment and detachment of colloids under consideration air-water interface of the soil,
    2. the transformation of the pore space and the thus induced coupling to the fluid transport in soil, and
    3. the transformation of the surface properties of the solid phase and the thus induced coupling to the solute transport

    have to be analyzed. The main hypothesis of this project states that the couplings incorporated in the model conception affect the praxis-relevant situations not only qualitatively, but also quantitatively in a significant way. The deterministic description of the physicochemical mechanisms on basis of the conservation laws for mass, impulse and energy results in systems of time-dependent non-linear partial differential equations. In order to make the model operative with respect to the problem formulation, one has to approximate it via numerical methods and to implement those in a software tool. For each level of complexity which has to be achieved, a comparison with existing experimental data has to be accomplished. In particular, these datasets have is to be used to obtain a realistic parametrization of the model via inverse modelling.

  • Modellierung des reaktiven Transports von Schadstoffen in der (un-)gesättigten Bodenzone zur Prognose der natürlichen Selbstreinigung

    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)

    Titel des Gesamtprojektes: Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Böden und Grundwässer (BMBF Förderschwerpunkt KORA)
    Laufzeit: 01-04-2004 - 31-03-2007
    Mittelgeber: BMBF / Verbundprojekt
    Abstract

    The evaluation of the potential of contaminated sites concerning natural attenuation needs comprehensive process descriptions and accurate, reliable numerical algorithms. Numerical errors may lead to qualitatively completely wrong conclusions concerning the potential of the site for degradation. It has been developed a comprehensive and flexible simulation tool, that is outstanding concerning the variety of processes, the quality and efficiency of the calculations ensured by modern numerical methods as well as the usability. The existing software platform RICHY has been extended, which is already intensely and successfully used by universities, institutes and consultants for the simulation of reactive transport and parameter identification. Among previous modules for coupled sufactant transport, preferential, unsaturated flow or carrier facilitated transport the project could realize new model components that surpass most of all existing software packages. The extensions contain complete descriptions of microbially catalysed degradation with arbitrary reaction partners and inhibition, general multicomponent reactions including the effects of ionic strength, as well as mineral dissolution and precipitation. The efficient and highly accurate, newly developed mathematical solution algorithms for the resulting coupled systems of partial differential equations could show their quality in complex international benchmark studies. Locally mass conserving, mixed hybrid finite element discretisations of the flow problem have been combined with globally implicit, reactive multicomponent models. Novel reduction methods for the latter rely on the linear transformation of the equation systems and variables and lead to the consideration of conservation quantities which can be handled efficiently, as a part of the transport – reaction – equations decouples. Another approach that has been pursued simultaneously relies on a modified Newton method and results in efficiency enhancements by the neglection of coupling terms in the Jacobian matrix. This algorithm can be applied fully adaptively, in 1D as well as in 2D. Both approaches could be combined with adaptive techniques for the automatic, efficient choice of time steps and spatial grid sizes, which makes the calculation of these complex problems feasible on PCs.

  • Entwicklung einer Simulationssoftware zur Prognose von Schadstoffausbreitung und -abbau in der (un-)gesättigten Bodenzone

    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)

    Titel des Gesamtprojektes: Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens
    Laufzeit: 01-06-2001 - 31-05-2003
    Mittelgeber: Bayerisches Staatsministerium für Umwelt und Gesundheit (StMUG) (bis 09/2013)
    URL: https://www.altlasten-bayern.de/projekte/verbundvorhaben-na/
    Abstract

    The project included the mathematical modelling of natural attenuation processes in the subsurface and the extension of a software tool for complex reactive multicomponent processes in the framework of mixed hybrid and conforming finite elements. New  parameter identification methods allow the parametrization of unknown functions or a formfree optimization, and help to overcome the dilemma of missing data in complex models. Work included instationary 3D simulations and scenarios of  contaminated sites explored by project partners. The findings of the joint research project resulted in guidelines for authorities and consulting engineers dealing with natural attenuation at contaminated sites.

  • Mathematische Modellsimulation und Parameteridentifizierung zur Transportprognose

    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)

    Titel des Gesamtprojektes: BMBF Förderschwerpunkt Sickerwasserprognose
    Laufzeit: 01-01-2001 - 31-12-2003
    Mittelgeber: Bundesministerium für Bildung und Forschung (BMBF)
    Abstract

    Mathematical simulation tools allow the quantitative integration of competing transport and transformation processes which are relevant for a seepage water risk prognosis. Therefore model simulations have to contain a comprehensive process description, while they can serve for parameter identification by inverse modelling of suitable column or batch experiments, and allow to quantify the dependence of a key variable on parameters through a simultaneous sensitivity analysis. The software platform RICHY1D has been extended and is already intensively and successfully used in universities, institutes and by consultants for the 1D simulation of complex reactive transport and for parameter identification. It stands out by the application of efficient and highly accurate mathematical solution strategies for the resulting systems of partial differential equations (e.g. locally mass conserving mixed hybrid finite element discretisations, modified Newton’s method). Besides the formerly existing modules for coupled surfactant-water transport, multiphase flow, saturated-unsaturated flow or carrier facilitated transport, the extensions contain in particular source terms (boundary conditions, distributed sources, arbitrarily time dependent, nonlinear and multiple (de-)sorption kinetics, mobilisation from a residual NAPL phase), preferential flow with solute transport, and heat transport in soils with coupling to reaction parameters of the contaminant transport like Monod degradation parameters, e.g.. The parameter identification is possible for the model extensions as well, which allows the identification of multiple complex parametrizations from suitable experiments (for example for source terms or microbially mediated degradation, sorption characteristics and hydraulic parameters). There is no need to impose a certain functional shape of these nonlinearities, the so-called form-free identification is also feasible, and furthermore a closed-flow experiment design can be accounted for. The sensitivity analysis is provided separately for the evaluation of the dependence of a key variable like the concentration of arbitrary model parameters, what represents a powerful tool in a transport simulation to identify controlling factors and evaluate uncertainties of the data.

Publikationen

 

Reviews

für BioSystems, Computer Methods in Applied Mechanics and Engineering, Environmental Pollution, Environmental Science & Technology, Geoderma, International Journal for Numerical Methods in Fluids,
Nonlinear Analysis: Real World Applications und Plant and Soil.

Betreute Arbeiten

Bachelorarbeiten:

Hutter, Jana: „Die Adsorptions-Advektions-Dispersionsgleichung“, 2009

Rupp, Andreas: „Numerische Studien zur Strukturbildung in Böden durch Mineralreaktionen„, 2014

Clarner, Jan-Patrick: „Modellierung und Simulation der Bildung und Transformation von Aggregaten in Böden„, 2016

Conrad, Marcus: „Integration von Reaktionstermen in das 1D-Flachwassermodell basierend auf dem Discontinuous-Galerkin-Verfahren„, 2016 (Integrated Life Sciences)

Klingberg, Tim: „Charakterisierung des stationären Eingangs-/Ausgangsverhaltens von Doppelphosphorylierungszyklen„, 2017 (Integrated Life Sciences)

Pindl, Kathrin: „Charakterisierung des Eingangs-/Ausgangsverhaltens der MAP Kinase Kaskade„, 2017 (Integrated Life Sciences)

Möckel, Marianna: „Einfluss der Autoregulation auf das dynamische Verhalten von Zwei-Komponenten Systemen„, 2017 (Integrated Life Sciences)

Eckstein, Nadja: „Charakterisierung der dynamischen Regulation von SCF Ligasen durch CAND1„, 2017 (Integrated Life Sciences)

Masterarbeiten:

Hutter, Jana: „Spatio-temporal modelling of cell cycle control„, 2011

Pérez Pardo, Beatriz: „Mathematical modeling and simulation of a microfluidic reactor. From real application towards a 2D computer simulation„, August 2012 (Computational Engineering)
Eckstein, Nadja: „Mathematical Modelling and Simulation of the Influence of Extracellular Polymeric Substances on Microaggregate Formation in Soils„, November 2018 (Integrated Life Sciences)

Diplomarbeiten:

Kastner, Stephan: „Mathematische Modellierung und numerische Simulation von Selbstreinigungsprozessen„, February 2002

Oßmann, Stephan: „Mathematische Modellierung und numerische Simulation von präferenziellem Fließen mit Stofftransport in strukturierten porösen Medien„, June 2004

Schumann, Robert: „Operator Splitting und voll gekoppelte Lösungsalgorithmen für Transport-Reaktionssysteme in porösen Medien„, May 2006

Frank, Florian: „Hydrogeochemical multi-component transport – mineral dissolution and precipitation with consideration of porosity changes in variably-saturated porous media„, 2008

Vorträge

    • „A Comprehensive Tool for the Simulation of Complex Reactive Transport and Flow in Soils“.
      XXV General Assembly of the European Geophysical Society (EGS), April 25-29, 2000, Nice, France.
    • „Accurate and Efficient Simulation of Coupled Water Flow and Nonlinear Reactive Transport in the Saturated and Vadose Zone – Application to Surfactant Enhanced and Intrinsic Bioremediation“.
      Computational Methods in Water Resources XIV, June 23-28, 2002, Delft, The Netherlands.
    • „Entwicklung einer Simulationssoftware zur Prognose von Schadstoffausbreitung und -abbau in der (un-)gesättigten Bodenzone“.
      Workshop Forschungsverbundvorhaben „Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens“, July 18-19, 2002, Freising, Germany.
    • Talks on „Mikrobiologie“, „Hydrochemie“ and „Modellierung“.
      Workshop Forschungsverbundvorhaben „Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens“, February 20-21, 2003, Freising, Germany.
    • „Modelling and numerical simulation of variably saturated flow and coupled reactive, biogeochemical transport“.
       Workshop on Modeling and Simulation in Chemical Engineering, June 30 – July 4, 2003, Coimbra, Portugal.
    • „Abbaukinetiken: Möglichkeiten der Modellierung und Simulation“.
      BMBF-Förderschwerpunkt KORA (Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Grundwässer und Böden), Fachgespräch Mikrobiologie, September 18-19, 2003, Karlsruhe, Germany.
    • „Handlungsempfehlung: Schwerpunkt Modellierung“.
      Symposium Natürliches Reinigungsvermögen – Natural Attenuation, Landesamt für Umweltschutz, November 10-11, 2003, Augsburg, Germany.
    • „Modeling and Simulation of Reactive Multicomponent Transport: Model Equations and Efficient Solution Concepts“.
       Workshop Porous Media, Zentrum für Angewandte Geowissenschaften, December 2-3, 2004, Blaubeuren, Germany.
    • „Efficient Modified Newton’s Method for Solving Reactive Multicomponent Transport Problems in Porous Media“.
      SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 6-10, 2005, Avignon, France.
    • „Grundlagen und Modellierung der Schadstoffausbreitung im Boden“.
       DECHEMA-Arbeitskreis „Auswirkungen von Stoff- und Energiefreisetzungen“, November 3, 2005, Frankfurt am Main, Germany.
    • „Große Mehrkomponentenprobleme berechenbar machen: Reduktion der Komplexität“.
      2. BMBF Statusseminar KORA, November 22-23, 2005, Frankfurt am Main, Germany.
    • „Grundlagen und Stolpersteine der Modellierung in der Altlastenbearbeitung“.
      BEW-Seminar „Numerische Modelle als Instrument in der Altlastenbearbeitung“, 31. Mai 2006, Duisburg, Germany
    • „Efficient process-preserving modified Newton’s method for solving reactive multicomponent transport problems in porous media“.
       Workshop on simulation, modelling and numerical analysis, September 18-20, 2006, Liberec, Czech Republic.
    • „Efficient process-preserving and adaptive modified Newton’s method for solving reactive multicomponent transport problems in porous media“.
      6th International Congress on Industrial and Applied Mathematics, July 16-20, 2007, Zurich, Switzerland.
    • „Modellierung als Werkzeug zur Prozessidentifikation und -quantifizierung von NA-Prozessen sprengstofftypischer Verbindungen“.
      Abschließendes BMBF-Statusseminar des TV5 „Rüstungsaltlasten“ – KORA, 17.-18. Juni 2008, Berlin.
    • „An adaptive, process-preserving modified Newton’s method to solve reactive multicomponent transport problems efficiently“.
      5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), June 30 – July 5, 2008, Venice, Italy.
    • „Efficient and Reliable Simulation of Reactive Multicomponent Problems“.
      Bio-Geo-Kolloquium Friedrich-Schiller-Universität Jena, December 16, 2008.
    • „Adaptive, Selective Coupling of Multicomponent Transport and Kinetic Reactions“.
      SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 15 – 18, 2009, Leipzig.
    • „Identification of biogeochemical degradation parameters of propylene glycol by complex modelling“.
      Computational Methods in Water Resources XIX, June 17-21, 2012, Urbana-Champaign, Illinois, USA.
    • „Spatio-Temporal Modelling of Cell Cycle Control“.
      SIAM Conference on the Life Sciences, August 7 – 10, 2012, San Diego, California, USA.
    • „Solving Coupled Reactive Multicomponent Problems in Geosciences and Biology“, 30. Mai 2013, Universität Bergen, Norwegen.
    • „Mechanistic Modeling of the Formation and Consolidation of Soil Microaggregates“, SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 29 – July 2, 2015, Stanford, California, USA.
    • „Process-based Modelling of the Formation and Consolidation of Soil Microaggregates“.
      Computational Methods in Water Resources XXI, June 20-24, 2016, Toronto, Canada.
    • „Hybrid Discrete-Continuum Modeling for Transport, Biofilm Development and Solid Restructuring including Electrostatic Effects“.
      General Assembly of the European Geophysical Union, April 23-28, 2017, Vienna, Austria.
    • „Mechanistic Model for Transport, Biofilm Development and Solid Restructuring in Soil Microaggregates“.
      Workshop on Formation, Properties and Function of Soil Microaggregates, October 10-12, 2017, Munich.
    • „Linking Processes to Structure and Structure to Function: Hybrid Discrete-Continuum Modeling forMicroaggregate Formation“.
      General Assembly of the European Geophysical Union, April 8-13, 2018, Vienna, Austria.
    • „Discrete-Continuum Multiscale Model for Evolving Microaggregates in Porous Media“.
      PICO Presentation, General Assembly of the European Geophysical Union, April 8-13, 2018, Vienna, Austria.
    • „Hybrid cellular automata / PDE modeling  for solid restructuring including EPS„, Computational Methods in Water Resources XXII, June 3-7, 2018, St. Malo, France.
    • „Hybrid Cellular Automata / PDE Modeling for Self-organisation of Soil Microaggregate Structures“, SIAM Conference on Mathematical and Computational Issues in the Geosciences, March 11 – 14, 2019, Houston, Texas, USA.
    • „Microaggregation of goethite and illite: Linking mechanistic modeling and laboratory experiments“,

      Online Presentation, General Assembly of the European Geophysical Union, May 4-8, 2020, Vienna, Austria.