Prof. Dr. Florian Frank

  • Organisation: Department Mathematik
  • Abteilung: Professur für Angewandte Mathematik (Mathematische Modellierung)
  • Telefonnummer: +49 9131 85-67214
  • Faxnummer: +49 9131 85-67225
  • E-Mail:
  • Webseite:
  • Adresse:
    Cauerstraße 11
    91058 Erlangen
    Raum 04.338

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  • 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.

  • 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.

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