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Veröffentlichungen

Projekte

  • Grenzflächen, komplexe Strukturen und singuläre Limiten in der Kontinuumsmechanik
    (Drittmittelfinanzierte Gruppenförderung – Gesamtprojekt)
    Laufzeit: 01-04-2018 - 30-09-2022
    Mittelgeber: DFG / Graduiertenkolleg (GRK)
  • 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)
    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)
    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
    (Drittmittelfinanzierte Einzelförderung)
    Laufzeit: 01-01-2007 - 31-12-2011
    Mittelgeber: 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.
  • 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)
    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
    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)
    Titel des Gesamtprojektes: Identifikation, Optimierung und Steuerung für technische Anwendungen
    Laufzeit: 01-06-2006 - 30-04-2010
    Mittelgeber: 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.

  • 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 - 31-12-2008
    Mittelgeber: 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.
  • 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/
    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 - 31-12-2004
    Mittelgeber: 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.