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Projects

Below you find a list of projects of all members of the chair of Applied Mathematics 1. Further information on projects is given on the pages of the individual researchers.

  • Maschinelles Lernen bei korrelativer MR und Hochdurchsatz-NanoCT

    (Third Party Funds Single)

    Term: 01-04-2020 - 31-03-2023
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
  • Mechanistische, integrative Mehrskalenmodellierung der Umwandlung von Bodenmikroaggregaten

    (Third Party Funds Single)

    Term: 01-04-2020 - 31-08-2024
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Multiscale modeling with evolving microstructure: An approach to
    emergence in the rhizosphere via effective soil functions

    (Third Party Funds Group – Sub project)

    Overall project: DFG Priority Programme 2089 “Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”
    Term: 01-02-2019 - 31-01-2022
    Funding source: DFG / Schwerpunktprogramm (SPP)
    URL: https://www.ufz.de/spp-rhizosphere/index.php?en=46495

    The self-organization of the aggregates in the rhizosphere by various
    attracting forces influenced by geochemistry, and microbiology shall
    be studied by a novel, comprehensive model. This model should
    account for processes on the microscale (single roots, pore scale),
    and then be upscaled to the root system scale (macroscale) by
    mathematical homogenization. This goal exceeds the functional range
    of existing models for aggregation and needs the introduction of an
    explicit phase of mucilage, and attachment properties of root hairs in
    the rhizosheath. The project aims at the development of a mechanistic modeling approach that allows for dynamic structural reorganization of the rhizosphere at the single root scale and couples this evolving microscale model to the root system scale including the inference of soil functions. This means that we do not assume a static rhizosphere but develop a tool that is capable to dynamically track this zone on the basis of the underlying spatiotemporal aggregegate formation and geochemical patterns. The collaboration with experimental groups – analyzing CT images in various moisture and growth conditions - the Central Experiment will allow to derive the properties of the mucilage phase, the pore structure and thus the
    influence of root hairs on aggregation mechanisms.

  • PPP Frankreich 2019 Phase I

    (Third Party Funds Single)

    Term: 01-01-2019 - 31-12-2020
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)
  • Integriertes und an Raum-Zeit-Messungsskalen angepasstes Global Random Walk - Modell für reaktiven Transport im Grundwasser

    (Third Party Funds Single)

    Term: 01-10-2018 - 30-09-2021
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Nonlocal Methods for Arbitrary Data Sources

    (Third Party Funds Group – Sub project)

    Overall project: Nonlocal Methods for Arbitrary Data Sources
    Term: 01-10-2018 - 28-02-2022
    Funding source: EU - 8. Rahmenprogramm - Horizon 2020
  • Implementation of vector operations for SBCL

    (Third Party Funds Single)

    Term: 10-07-2018 - 31-03-2019
    Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)
    Ziel des Projekts ist es, AVX2 Vektoroperationen für die Common LispImplementierung SBCL verfügbar zu machen.  SBCL ist derpopulärste und am weitesten Entwickelte freie Compiler für CommonLisp.  Die Verbesserungen aus diesem Projekt machen es möglichCommon Lisp Programme zu schreiben, deren Ausführungsgeschwindigkeitmit C++ und Fortran Programmen auf Augenhöhe liegt.  Dadurchergeben sich interessante Möglichkeiten der Metaprogrammierung imwissenschaftlichen Rechnen.
  • Interfaces, complex structures, and singular limits in continuum mechanics

    (Third Party Funds Group – Overall project)

    Term: 01-04-2018 - 30-09-2022
    Funding source: DFG / Graduiertenkolleg (GRK)
  • Free boundary propagation and noise: analysis and numerics of stochastic degenerate parabolic equations

    (Third Party Funds Single)

    Term: 01-04-2018 - 31-03-2020
    Funding source: Deutsche Forschungsgemeinschaft (DFG), DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    URL: https://www1.am.uni-erlangen.de/~gruen/

    The porous-medium equation and the thin-film equation are prominent examples of nonnegativity preserving degenerate parabolic equations which give rise to free boundary problems with the free boundary at time t > 0 defined as the boundary of the solution’s support at that time.
    As they are supposed to describe the spreading of gas in a porous-medium or the spreading of a viscous droplet on a horizontal surface, respectively, mathematical results on the propagation of free boundaries become relevant in applications. In contrast to, e.g., the heat equation, where solutions to initial value problems with compactly supported nonnegative initial data
    instantaneously become globally positive, finite propagation and waiting time phenomena are characteristic features of degenerate parabolic equations.
    In this project, stochastic partial differential equations shall be studied which arise from the aforementioned degenerate parabolic equations by adding multiplicative noise in form of source terms or of convective terms. The scope is to investigate the impact of noise on the propagation of free boundaries, including in particular necessary and sufficient conditions for the occurrence
    of waiting time phenomena and results on the size of waiting times. Technically, the project relies both on rigorous mathematical analysis and on numerical simulation.

  • Innovationsfonds 2017: Urkunden und Buchgutscheine für gute Leistungen in Anfängervorlesungen

    (FAU Funds)

    Term: 01-07-2017 - 30-09-2020
    Um den Vorlesungs- und Prüfungsbetrieb persönlicher zu gestalten, wird bei sehr guten Leistungen in meinen Anfängervorlesungen "Mathematik für Ingenieure" ein wenig symbolisches Lob in der Form von Urkunden und auch ein wenig finanzielles Lob in der Form von Buchgutscheinen ausgeteilt.
  • Verbundvorhaben proMT Teilprojekt 2: Modellreduktion zur prognostischen online MR-Thermometrie

    (Third Party Funds Group – Sub project)

    Overall project: Verbundvorhaben proMT Teilprojekt 2: Modellreduktion zur prognostischen online MR-Thermometrie
    Term: 01-12-2016 - 30-11-2019
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
  • "Verbundprojekt MED4D: Dynamische Medizinische Bildgebung: Modellierung und Analyse medizinischer Daten für verbesserte Diagnose, Überwachung und Arzneimittelentwicklung"

    (Non-FAU Project)

    Term: 01-12-2016 - 30-11-2019
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
  • Mathematische Schlüsselqualifikation für Energienetze im Wandel – Teilprojekt FAU

    (Third Party Funds Group – Sub project)

    Overall project: Mathematische Schlüsselqualifikation für Energienetze im Wandel – Teilprojekt FAU
    Term: 01-10-2016 - 30-04-2020
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
  • Analyse und Anwendung reduzierter Modelle

    (Third Party Funds Group – Sub project)

    Overall project: MathEnergy — Mathematische Schlüsseltechniken für Energienetze im Wandel
    Term: 01-04-2016 - 30-04-2020
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)

    Das Kernziel dieses mathematisch orientierten Teilvorhabens ist die Methodenentwicklung und Analyse reduzierter Modelle bzw. Modellhierarchien und ihrer Anwendung zur dynamischen Zustandsschätzung in einer modellprädiktiven Regelung.

  • Mechanistic modelling of the formation and consolidation of soil microaggregates

    (Third Party Funds Group – Sub project)

    Overall project: DFG RU 2179 “MAD Soil - Microaggregates: Formation and turnover of the structural building blocks of soils”
    Term: 01-01-2016 - 31-12-2018
    Funding source: Deutsche Forschungsgemeinschaft (DFG)
  • German-Norwegian collaborative research support scheme

    (Third Party Funds Single)

    Term: 01-01-2016 - 31-12-2017
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)

    Homogenisierung reaktiven Transports in variablen Mikrostrukturen

  • Modellreduktion zur prognostischen online MR-Thermometrie

    (Third Party Funds Group – Sub project)

    Overall project: proMT — Prognostische modellbasierte online MR-Thermometrie bei minimalinvasiver Thermoablation zur Behandlung von Lebertumoren
    Term: 01-01-2016 - 31-12-2019
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)

    In Hinblick auf die angestrebte prognostische Online-Simulationsfähigkeit zielt dieses Teilprojekt auf die Entwicklung und Analyse reduzierter Modelle mittels Techniken der Modellordnungsreduktion (MOR). Die Kombination von MOR und Space-Mapping lässt eine weitere Steigerung der Performance erhoffen, die für die konkrete Anwendung der MR-Thermometrie qualitativ und quantitativ bewertet wird.

  • Scientific Computing for Improved Detection and Therapy of Sepsis

    (Non-FAU Project)

    Term: 15-10-2015 - 15-10-2018
    Funding source: andere Förderorganisation
    URL: http://scidatos.de/
  • Verteiltes Höchstleistungsrechnen in Common Lisp

    (Third Party Funds Single)

    Term: 01-10-2015 - 31-03-2016
    Funding source: Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst (StMWFK) (bis 09/2013)

    The Message Passing Interface\cite{mpi-standard} (MPI) is the de facto
    standard for distributed programming on all modern compute clusters and
    supercomputers. It features a large number of communication patterns with
    virtually no overhead. Our work on bringing MPI functionality to Common
    Lisp resulted in vast improvements to the message passing library CL-MPI
    and the development of severaly new approaches to distributed computing.
     

  • DAAD Exchange Service: PPP Finnland 2017: Bayesian Inverse Problems in Banach Space

    (Non-FAU Project)

    Term: 25-01-2015 - 31-12-2017
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)
  • Simulation hochdynamischer Spinnprozesse unter Turbulenzeinfluss

    (Third Party Funds Single)

    Term: 01-04-2014 - 30-04-2018
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

    Das Vorhaben zielt auf die Simulation hochdynamischer Spinnprozesse unter Turbulenzeinfluss. Es orientiert sich dabei an der Herausforderung, den Meltblowing-Prozess in seiner komplexen Abhängigkeit von der umgebenden turbulenten heißen Luftströmung abzubilden. Infolge der hohen Geschwindigkeiten treten sehr große Dehnungen auf. Die gesponnenen Fasern weisen einen Durchmesser von unter 0.5 Mikrometern auf. Für das Multiskalenproblem wird auf Basis von asymptotischen viskosen Cosserat-Modellen für die Faserjets sowie Wechselwirkungsmodellen mit der Luftströmung ein neuartiges Verfahren zur Turbulenzrekonstruktion mit zu entwickelnden effizienten Strategien zur Handhabung der extrem großen Jetdehnungen kombiniert. Das Vorhaben nähert sich der Zielsetzung schrittweise, indem eine Reihe bereits eigenständig technisch interessanter Entwicklungsszenarien mit entsprechenden Simulationsaufgaben betrachtet wird: viskose Jets mit großen Dehnungen im Rotationsspinnprozess, elastische Filamente unter Turbulenzeinwirkung im Spunbond-Prozess, elastische Filamente mit Temperatureinfluss im Spunbond-Prozess sowie letztlich viskose Jets mit großen Dehnungen unter Einwirkung von Turbulenz und Temperatur im Meltblowing-Prozess. Diese Szenarien beruhen auf realen Anlagendaten industrieller Partner, die Modelle und Algorithmen werden mit vorhandenen Messdaten verglichen.

  • TP C02: Hierarchische PDAE-Surrogate-Modellierung und stabile PDAE-Diskretisierung zur Simulation großer instationärer Gasnetzwerke

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-04-2014 - 30-04-2018
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    This subproject focuses on the development and analysis of models and methods for a stable and fast simulation of huge transient gasnetworks, which will also be used for an efficient parameter optimization and control of the network. The main aspects are the development of a numerical discretization in space and time that is adjusted to the topology of the network as well as a hierarchical modelling of several elements (pipes, compressors ect.) and subnet-structures.For the complete network as a coupled system of nonlinear partial differential equations and algebraic equations (PDAE) we consider approximations by a spatial semi-discretization. We strive for a determination and classification of topology depending critera for the index of the time dependend differential algebraic system. Topology- and controldepending spatial discretizations will be determinded, that lead to DAEs of index 1, in order to diminish the influence of perturbations for the DAE system best possible. Moreover we want to establish a perturbationanalysis as well as existence and uniquness results for die PDAE-model. Here, the time and pressure/flow-depending control-states that can change the variable structure (dynamic as well as static) for certain points in time and for certain states of the network will be a major challange.As a method, we focus on a Galerkin-Approach in space followed by a discretization in time of the resulting DAE with implicit or semi-implicit methods respectively, such that the algebraic constraints hold for the current point in time. Continuationmethods and space-mapping techniques are used for the initialisation to guarantee good convergence behaviour. Furthermore, to satisfy the control requirements of the systems and to enable the handling of huge networks, this subproject aims at the enhancement of the simulation speed. It is planed to detect characteristic subnetstructures and derive parameter dependen transient surrogate models with suitable error estimators by applying model order reduction methods. These input-ouput models as dynamic systems of ODEs will be coupled with die complete PDAE model in one model hierarchy.
  • Variational Methods for Dynamic Inverse Problems in the Life Sciences

    (Non-FAU Project)

    Term: 01-03-2014 - 28-02-2019
    Funding source: Europäische Union (EU)
  • Simulation hochdynamischer Spinnprozesse unter Turbulenzeinfluss

    (Third Party Funds Single)

    Term: since 01-02-2014
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Das Vorhaben zielt auf die Simulation hochdynamischer Spinnprozesse unter Turbulenzeinfluss. Es orientiert sich dabei an der Herausforderung, den Meltblowing-Prozess in seiner komplexen Abhängigkeit von der umgebenden turbulenten heißen Luftströmung abzubilden. Infolge der hohen Geschwindigkeiten treten sehr große Dehnungen auf. Die gesponnenen Fasern weisen einen Durchmesser von unter 0.5 Mikrometern auf. Für das Multiskalenproblem wird auf Basis von asymptotischen viskosen Cosserat-Modellen für die Faserjets sowie Wechselwirkungsmodellen mit der Luftströmung ein neuartiges Verfahren zur Turbulenzrekonstruktion mit zu entwickelnden effizienten Strategien zur Handhabung der extrem großen Jetdehnungen kombiniert. Das Vorhaben nähert sich der Zielsetzung schrittweise, indem eine Reihe bereits eigenständig technisch interessanter Entwicklungsszenarien mit entsprechenden Simulationsaufgaben betrachtet wird: viskose Jets mit großen Dehnungen im Rotationsspinnprozess, elastische Filamente unter Turbulenzeinwirkung im Spunbond-Prozess, elastische Filamente mit Temperatureinfluss im Spunbond-Prozess sowie letztlich viskose Jets mit großen Dehnungen unter Einwirkung von Turbulenz und Temperatur im Meltblowing-Prozess. Diese Szenarien beruhen auf realen Anlagendaten industrieller Partner, die Modelle und Algorithmen werden mit vorhandenen Messdaten verglichen.
  • Implementation and optimization of stencil operations on staggered hierarchical meshes

    (Third Party Funds Single)

    Term: 01-06-2013 - 01-10-2014
    Funding source: Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst (StMWFK) (bis 09/2013)
    URL: http://www.konwihr.uni-erlangen.de/projekte/multicore-software-initiative/stencils-on-staggered-hierarchical-meshes.shtml

    We optimized and parallelized a framework which compiles stencil operations defined by abstract operators into code, which performs the corresponding stencil update. Therefore, we are now able to formulate solvers for a large number of application problems (flow simulation, image analysis, ...) in an abstract way, and then solve efficiently on structured meshes.

  • Diffuse interface models for transport processes at fluidic interfaces

    (Third Party Funds Group – Sub project)

    Overall project: SPP 1506: Fluide Grenzflächen
    Term: 01-06-2013 - 31-10-2017
    Funding source: DFG / Schwerpunktprogramm (SPP)

    In recent years, diffuse interface models turned out to be a promising approach to describe fundamental features of two-phase flow like droplet break-up or coalescence. In the second funding period, novel thermodynamical consistent phase-field models for species transport in two-phase flow shall be derived with an emphasis on soluble surfactants. Additional phenomena -- ranging from microscale effects like molecule orientation over thermal effects to electrostatic interactions -- shall be included as well. On this basis, new sharp-interface models shall be derived by formal asymptotic analysis.
    For selected diffuse-interface models, existence of solutions and stability of fluidic interfaces will be investigated by rigorous mathematical analysis. Stable numerical schemes shall be formulated and implemented in two and three space dimensions. By numerical simulations, partially guided by the "Leitmassnahme" Taylor-flow, the models shall be validated and further improved. By numerical analysis, convergence shall be established for the prototypical problem of species transport in two-phase flow with general mass densities.

  • Mathematische Modellierung und Numerische Simulation von Stahlwalzprozessen

    (Third Party Funds Single)

    Term: 01-01-2013 - 31-12-2014
    Funding source: Siemens AG
  • MPFA and MHFE methods for flow and transport in porous media

    (Third Party Funds Single)

    Term: 01-01-2012 - 31-12-2013
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)

    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.

  • Diffuse interface models for transport processes at fluidic interfaces

    (Third Party Funds Group – Sub project)

    Overall project: SPP 1506: Fluide Grenzflächen
    Term: 01-04-2010 - 30-04-2013
    Funding source: DFG / Schwerpunktprogramm (SPP)

    Topological transitions like droplet coalescence or droplet break-up are fundamental features of two-phase flows. In recent years, diffuse interface models turned out to be a promising approach to describe such phenomena. Species transport across fluidic interfaces and the effects exerted by soluble and insoluble surfactants are additional issues of still increasing technological importance. For those phenomena, novel thermodynamically consistent diffuse interface models shall be developed taking in particular general densities into account. Based on rigorous mathematical analysis, existence and qualitative behaviour of solutions will be investigated, this way enhancing the understanding of the fundamental model properties. Starting from energy and entropy inequalities, stable and convergent numerical schemes shall be formulated and implemented in two and three spatial dimensions. By numerical simulations, the models shall be validated and further improved.

  • Fronts and Interfaces in Science and Technology

    (Third Party Funds Group – Sub project)

    Overall project: Fronts and Interfaces in Science and Technology
    Term: 01-02-2010 - 31-12-2013
    Funding source: EU - 7. RP / People / Initial Training Networks (ITN)

    With this network, the universities of Bath, Eindhoven, Erlangen, Haifa (Technion), Madrid (Complutense), Paris (Orsay), Rome (La Sapienza), Zürich and the industrial partners EGIS and SIEMENS AG foster a joint training platform for PhD-students working on analysis and control of interfacial phenomena. Applications range from image processing over reaction-diffusion systems to complex multi-phase flow.
    FAU is involved in three projects, guided by Proff. Grün, Knabner, and Leugering. The first one is concerned with the effects electric fields have on two-phase flow with electrolyte solutions. The goal is to derive thermodynamically consistent diffuse-interface models for general mass densities and ion distributions and to prove existence and regularity of solutions.
    The second one is a tandem project with Prof. Peletier (TU Eindhoven) devoted to contaminant flow in porous media. There is experimental evidence that attachment to colloids strongly enhances contaminant transport. Derivation and analysis of appropriate multi-scale models are in the focus of this project.
    Prof. Leugering's project -- jointly with Prof. Coron (University Pierre et Marie Curie, Paris) -- is devoted to optimal control and stabilization of flow of gas, water, and traffic in networked pipe- and road-systems. It focusses on reachability and stabilizability properties under constraints both in states and controls and on the derivation of appropriate sensitivities for a numerical treatment of optimal controls for systems of realistic size.

  • Development of filtration systems for air cleaning from nanoparticles, organic admixtures and bacteria with the help of numerical simulations

    (Third Party Funds Single)

    Term: 01-10-2009 - 30-09-2011
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)

    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.

  • Efficient Numerical Methods for Large Partial Differential Complementarity Systems arising in Multispecies Reactive Transport with Minerals in Porous Media

    (Third Party Funds Single)

    Term: 01-01-2007 - 31-12-2011
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    The project focuses on the accurate and efficient numerical treatment of time-dependent reactive transport problems with many species (in porous media) in 2 or 3 space dimensions with local complementarity conditions as essential ingredient. The problem takes the form of a differential algebraic set of equations and complementarity constraints, consisting of time dependent (possibly convection-dominated) semilinear partial differential equations (PDEs), nonlinear ordinary differential equations, nonlinear algebraic equalities, and inequalities. Taking a typical species number of 10 to 20 and of nodal degrees of freedom of 104 to 106, also for an appropriate (e.g., local mass conservative) discretization, the solution of the emerging finite dimensional complementarity system is a formidable task, whose efficient algorithmic treatment is the main topic of the project. Algorithms of semismooth Newton type are the principal choice. Aims are the investigation and improvement of the algorithms w.r.t. efficiency and robustness, and comparing them to other (e.g., interiorpoint-) methods. The algorithms to be developed are supposed to heavily take advantage of knowledge about the substructuring of the problem. The emerging methods and software, also for parallel computers, is supposed to handle several large real world problems, not yet treatable satisfactorily.
  • The Influence of Colloids on Water Flow and Solute Transport in Soils: Side Effect or Key Process?

    (Third Party Funds Single)

    Term: 01-11-2006 - 31-12-2009
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

    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.

  • Identifizierung nichtlinearer Koeffizientenfunktionen des reaktiven Transports durch poröse Medien unter Verwendung rekursiver und formfreier Ansätze

    (Third Party Funds Group – Sub project)

    Overall project: Identifikation, Optimierung und Steuerung für technische Anwendungen
    Term: 01-06-2006 - 30-04-2010
    Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)

    In dem Internationalen Doktorandenkolleg wird vor dem Hintergrund konkreter Anwendungsprobleme der Bogen von der mathematischen Modellierung über die mathematische Analyse und die Entwicklung numerischer Methoden bis hin zum Wissenschaftlichen Rechnen und der Implementierung von Software auf Hoch- und Höchstleistungsrechnern gespannt. Dies geschieht auf den Gebieten der Identifikation, Optimierung und Steuerung komplexer technischer, medizinischer, naturwissenschaftlicher und wirtschaftswissenschaftlicher Systeme.

    Identifikation, Optimierung und Steuerung haben eine große Bedeutung für die technologische Entwicklung. Die Fokussierung auf dieses Gebiet ist deshalb das besondere Merkmal dieses mathematisch orientierten Netzwerkes. Im nordbayerischen Raum bieten sich wegen der dort gegebenen Konzentration international anerkannter Wissenschaftler in diesem Forschungsumfeld die besten Voraussetzungen. Das Ziel des Doktorandenkollegs ist es, den Schritt von der modellbasierten Simulation zum modellgestützten optimalen Design und Steuerung zu vollziehen. Dieser Schritt wird erst durch die Verzahnung der rasanten Entwicklung mathematischer Methoden der Optimierung und der Numerik und mit Hilfe von Hochleistungsrechnern möglich.

    Eine stärkere Einbindung von Ingenieurprojekten in der zweiten Phase des Kollegs wird die Integration der erarbeiteten Konzepte und Algorithmen in konkrete Anwendungsbereiche ermöglichen. Darüber hinaus lassen spezifische Betreuungs- und Lehrkonzepte die fachübergreifende Zusammenarbeit fruchtbar werden.

  • Modelling of the reactive transport of contaminants in the (un-)saturated zone for the prognosis of natural attenuation

    (Third Party Funds Group – Sub project)

    Overall project: Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Böden und Grundwässer (BMBF Förderschwerpunkt KORA)
    Term: 01-04-2004 - 31-03-2007
    Funding source: BMBF / Verbundprojekt

    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.

  • Development of a simulation tool for the prognosis of the spreading and the degradation of contaminants in the saturated and vadose zone

    (Third Party Funds Group – Sub project)

    Overall project: Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens
    Term: 01-06-2001 - 31-05-2003
    Funding source: Bayerisches Staatsministerium für Umwelt und Gesundheit (StMUG) (bis 09/2013)
    URL: https://www.altlasten-bayern.de/projekte/verbundvorhaben-na/

    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.

  • Quantification of Contaminant Sources and Transport Prognosis in Aquifers

    (Third Party Funds Group – Sub project)

    Overall project: BMBF Förderschwerpunkt Sickerwasserprognose
    Term: 01-01-2001 - 31-12-2003
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)

    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.