PD Dr. Florian Frank
PD Dr. Florian Frank
Forschungsinteressen
- High-performance computing (HPC)
- Digital rock, flow and transport in porous media
- Phase-field modeling, chemical engineering, separation science
- Discontinuous Galerkin and finite volume methods, physics preservation
Akademische Ausbildung und Abschlüsse
04/2022 | Privatdozent (Lehrbefugnis für das Fach Mathematik, FAU) |
10/2019 | Dr. habil. (Lehrbefähigung für das Fach Mathematik, FAU) |
11/2013 | Dr. rer. nat. (Promotion in Angewandter Mathematik, FAU, Prof. Dr. P. Knabner) |
10/2008–11/2013 | Promotionsstudium in Angewandter Mathematik, FAU |
10/2008 | Diplom-Mathematiker Univ., FAU |
10/2002–10/2008 | Studiengang Diplom-Mathematik, Nebenfach Informatik, FAU |
06/2002 | Zeugnis der allgemeinen Hochschulreife, Bayern (Abitur) |
09/1992–06/2002 | Gymnasium Lichtenfels, naturwissenschaftlicher Zweig |
Universitäre Beschäftigungsverhältnisse
10/2021-03/2022 | Universitätsprofessor (W2, Vertretung), Angewandte Mathematik (Wissenschaftliches Rechnen), FAU |
10/2018-09/2021 | Universitätsprofessor (W2, Vertretung), Angewandte Mathematik (Mathematische Modellierung), FAU |
03/2018–09/2018 | Universitätsprofessor (W3, Vertretung), Angewandte Mathematik, FAU |
08/2017–02/2018 | Senior Postdoctoral Research Associate am CAAM Department, Rice University |
08/2014–07/2017 | Postdoctoral Research Associate am CAAM Department, Rice University |
12/2013–06/2014 | Postdoktorand am Lehrstuhl für Angewandte Mathematik 1, FAU |
11/2008–11/2013 | Wissenschaftlicher Mitarbeiter am Lehrstuhl für Angewandte Mathematik 1, FAU |
04/2010–12/2011 | Wissenschaftlicher Mitarbeiter am Lehrstuhl für Hydrogeologie, Universität Jena |
11/2008–10/2009 | Wissenschaftlicher Mitarbeiter am Lehrstuhl für Hydrogeologie, Universität Jena |
Auszeichnungen und Preise
10/2020 | Emmy-Noether-Preis für die Habilitation, Naturwissenschaftliche Fakultät, FAU |
05/2017 | Auszeichnung und Beförderung zum Senior Postdoctoral Research Associate, George R. Brown School of Engineering, Rice University, Houston, TX, USA |
Reviewer und Gutachter für internationale Zeitschriften
Advances in Water Resources |
Applied Mathematical Modelling |
Chemical Engineering Science |
Computational Geosciences |
Computer Methods in Applied Mechanics and Engineering |
Computer Physics Communications |
Computers and Mathematics with Applications |
Journal of Colloid and Interface Science |
Journal of Computational Methods in Sciences and Engineering |
Journal of Computational Physics |
Numerical Algorithms |
SIAM Journal of Applied Mathematics |
SPE Journal (Society of Petroleum Engineers) |
Redaktionsleitung
Gasteditor der Spezialausgabe „Recent Advances in Numerical Modeling and Simulation of Fluid Flow and Heat Transfer in Porous Media“ der Zeitschrift Computational Geosciences. |
Gasteditor der Spezialausgabe „Advanced Modeling and Simulation of Flow in Subsurface Reservoirs with Fractures and Wells for a Sustainable Industry“ der Zeitschrift Oil & Gas Science and Technology — Revue d’IFP Energies nouvelles. |
Veranstaltungen (als Privatdozent)
WS 2023/2024 | Projektseminar Mathematische Modellierung |
WS 2022/2023 | Seminar Iterative Lösungsverfahren für lineare und nichtlineare Gleichungssysteme (mit C. Pflaum, interdisziplinär mit Informatik und CE) |
Veranstaltungen (als Professor)
WS 2021/2022 | Vorlesung und Übung zu Mathematik für Ingenieure C3 (Informatik) |
SS 2021 | Vorlesung, Übung und Tutorium zu Diskretisierung und numerische Optimierung |
SS 2021 | Programmierkurs Matlab/Octave für Integrated Life Sciences |
SS 2021 | Seminar Mathematische Modellierung und Datenanalyse (mit M. Burger, D. Tenbrinck) |
WS 2020/2021 | Vorlesung, Übung und Tutorium zu Einführung in die Numerische Mathematik |
WS 2020/2021 | Programmierkurs Matlab/Octave zu Einführung in die Numerische Mathematik |
WS 2020/2021 | Seminar zu Diskretisierung und numerische Optimierung |
SS 2020 | Vorlesung, Übung und Tutorium zu Diskretisierung und numerische Optimierung |
SS 2020 | Kurs Modeling, Simulation, and Optimization, Practical Course (in English) |
WS 2019/2020 | Vorlesung, Übung und Tutorium zu Einführung in die Numerische Mathematik |
WS 2019/2020 | Programmierkurs Matlab/Octave zu Einführung in die Numerische Mathematik |
SS 2019 | Vorlesung und Übung zu Numerics of Partial Differential Equations II (in English) |
SS 2019 | Kurs Modeling, Simulation, and Optimization, Practical Course (in English) |
SS 2019 | Seminar Modellierung und Simulation |
SS 2019 | Programmierkurs Matlab/Octave für Integrated Life Sciences |
WS 2018/2019 | Vorlesung und Übung zu Numerics of Partial Differential Equations I (in English) |
WS 2018/2019 | Seminar Diskretisierung und Numerische Optimierung |
SS 2018 | Vorlesung und Übung zu Differentialgleichungsmodelle |
SS 2018 | Kurs Modeling, Simulation, and Optimization, Practical Course (in English) |
SS 2018 | Seminar Numerik nichtlinearer Gleichungssysteme |
Veranstaltungen (als wissenschaftlicher Mitarbeiter)
SS 2014 | Organisation und Leitung des Kurses (Vorlesung, Übung): Finite Element Programming (in English, P. Knabner) |
SS 2014 | Organisation und Leitung des Kurses (Vorlesung, Übung): Einführung in Matlab/Octave (P. Knabner) |
WS 2013/2014 | Betreuung des Seminars Angewandte Mathematik: Fließ- und Transportprozesse |
WS 2013/2014 | Mitarbeit im Programmierpraktikum zur Vorlesung Computational Biology (in English, R. Böckmann/V. Aizinger) |
SS 2013 | Organisation und Leitung des Kurses (Vorlesung, Übung) Einführung in Matlab/Octave (P. Knabner) |
SS 2013 | Mitarbeit im Kurs Wiederholungskurs zu Mathematik für Ingenieure I (V. Aizinger) |
WS 2012/2013 | Organisation und Betreuung der Übung zu Einführung in die Numerische Mathematik (P. Knabner) |
SS 2012 | Organisation und Leitung des Kurses (Vorlesung, Übung) Einführung in Matlab/Octave (G. Grün) |
WS 2011/2012 | Organisation der Übung zu Einführung in die Numerische Mathematik (N. Marheineke) |
SS 2011 | Organisation und Leitung des Kurses (Vorlesung, Übung) Tutorium zur Einführung in die Numerische Mathematik (N. Marheineke) |
SS 2011 | Organisation und Betreuung der Übung zu Numerik II für Ingenieure (N. Marheineke) |
WS 2010/2011 | Organisation und Betreuung der Übung zu Numerik I für Ingenieure (N. Marheineke) |
SS 2010 | Organisation der Übung zu Numerische Mathematik II (G. Grün) |
WS 2009/2010 | Organisation und Leitung des Kurses Rechnergestützte Mathematik zur Linearen Algebra (P. Knabner) |
SS 2009 | Betreuung der Übung zu Numerics of Partial Differential Equations II (P. Knabner) |
WS 2008/2009 | Betreuung der Übung zu Numerics of Partial Differential Equations I (P. Knabner) |
Veranstaltungen (als studentische Hilfskraft)
SS 2006 | Betreuung der Übung zu Numerik II (M. Bause) |
WS 2005/2006 | Betreuung der Übung zu Numerik I (M. Bause) |
Betreuung und Begutachtung
seit 07/2021 | Betreuer und Gutacher der Masterarbeit „Fast and robust numerical solutions of density gradient theory equations for arbitrary components“ von Herrn Paul Maidl (Computational and Applied Mathematics) |
06/2021–08/2021 | Betreuer und Gutacher der Bachelorarbeit „Localization of a discrete preconditon operator for Stokes Schur complements“ von Herrn Fabian Woller (Mathematik) |
05/2020–10/2020 | Betreuer und Gutacher der Masterarbeit „High-performance preconditioning of the Stokes equation in complex domains“ von Herrn Andreas Meier (Computational and Applied Mathematics) |
10/2019–03/2020 | Betreuer und Gutacher der Masterarbeit „Analysis and implementation of an enriched Galerkin scheme for the shallow-water equations“ von Herrn Moritz Hauck (Mathematik) |
06/2019–12/2019 | Betreuer und Gutacher der Bachelorarbeit „Slope-Limitierung für die Enriched-Galerkin-Diskretisierung der Advektionsgleichung“ von Herrn Lukas Weigand (Technomathematik) |
05/2019–11/2019 | Betreuer und Gutacher der Bachelorarbeit „Ein Finite-Volumen-Verfahren auf unstrukturierten Gittern für die Cahn-Hilliard-Gleichung“ von Herrn Paul Maidl (Mathematik) |
06/2018–10/2018 | Betreuer und Gutacher der Bachelorarbeit „Stabilization techniques for the finite element method applied on advection-dominated problems“ von Herrn Moritz Hauck (Mathematik) |
06/2018–10/2018 | Betreuer und Gutacher der Bachelorarbeit „Jacobian-free Newton–Krylov methods applied to the Cahn–Hilliard equation with degenerate mobility“ von Herrn Tim Roith (Mathematik) |
06/2018–09/2018 | Betreuer und Gutacher der Bachelorarbeit „Simulation of reactive transport in saturated porous media with porosity changes through mineral dissolution and precipitation“ von Herrn Andreas Meier (Mathematik) |
07/2018 | Zweitgutachter der Masterarbeit „A hybridizable discontinuous Galerkin scheme with different orders of approximation spaces capable of dealing with jump conditions: analysis and implementation} von Markus Musch (Mathematik, Betreuer: P. Knabner) |
02/2014–05/2014 | Kobetreuer der Bachelorarbeit „Mutual Coupling of PDE Systems: Unsaturated Flow and Mineral Reactions with Porosity Changes“ von Jens Oberlander (Mathematik, Betreuer: P. Knabner) |
02/2012–08/2012 | Kobetreuer der Masterarbeit „Mathematical Modeling and Simulation of a Microfluidic Reactor“ von Beatriz Pérez-Pardo (Computational Engineering, Betreuer: P. Knabner) |
Achieving Convergence in Multiphase Multicomponent Density Gradient Theory Calculations through Regularization
In: Industrial & Engineering Chemistry Research (2024)
ISSN: 0888-5885
DOI: 10.1021/acs.iecr.4c01669
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Correction to: Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS (Computational Geosciences, (2023), 10.1007/s10596-022-10184-0)
In: Computational Geosciences (2023)
ISSN: 1420-0597
DOI: 10.1007/s10596-023-10196-4
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Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS
In: Computational Geosciences (2023)
ISSN: 1420-0597
DOI: 10.1007/s10596-022-10184-0
URL: https://link.springer.com/article/10.1007/s10596-022-10184-0
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Estimating relative diffusion from 3D micro-CT images using CNNs
In: Artificial Intelligence in Geosciences 4 (2023), S. 199-208
ISSN: 2666-5441
DOI: 10.1016/j.aiig.2023.11.001
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Schur preconditioning of the Stokes equations in channel-dominated domains
In: Computer Methods in Applied Mechanics and Engineering 398 (2022)
ISSN: 0045-7825
DOI: 10.1016/j.cma.2022.115264
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A diffuse interface model for cell blebbing including membrane-cortex coupling with linker dynamics
In: SIAM Journal on Applied Mathematics 3 (2022), S. 1091-1112
ISSN: 0036-1399
DOI: 10.1137/21m1433642
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Editorial: Advanced modeling and simulation of flow in subsurface reservoirs with fractures and wells for a sustainable industry
In: Oil & Gas Science and Technology-Revue De L Institut Francais Du Petrole 76 (2021)
ISSN: 1294-4475
DOI: 10.2516/ogst/2021008
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Numerical benchmark study for flow in highly heterogeneous aquifers
In: Advances in Water Resources (2020), S. 103558
ISSN: 0309-1708
DOI: 10.1016/j.advwatres.2020.103558
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Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn–Hilliard equation
In: Computer Methods in Applied Mechanics and Engineering 359 (2020)
ISSN: 0045-7825
DOI: 10.1016/j.cma.2019.112665
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Enriched Galerkin method for the shallow-water equations
In: GEM - International Journal on Geomathematics 11 (2020), Art.Nr.: 31
ISSN: 1869-2672
DOI: 10.1007/s13137-020-00167-7
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An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media
In: Journal of Computational Physics 400 (2020), Art.Nr.: 108948
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2019.108948
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FESTUNG 1.0: Overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods
In: Computers & Mathematics with Applications (2020)
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2020.08.018
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FESTUNG: A MATLAB / GNU Octave Toolbox for the Discontinuous Galerkin Method. Part IV: Generic Problem Framework and Model-Coupling Interface
In: Communications in Computational Physics 28 (2020), S. 827-876
ISSN: 1815-2406
DOI: 10.4208/cicp.OA-2019-0132
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An interior penalty discontinuous Galerkin approach for 3D incompressible Navier–Stokes equation for permeability estimation of porous media
In: Journal of Computational Physics 396 (2019), S. 669-686
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2019.06.052
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Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation
In: Numerical Methods For Partial Differential Equations (2019)
ISSN: 0749-159X
DOI: 10.1002/num.22362
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A distributed parallel direct simulator for pore-scale two-phase flow on digital rock images using a finite difference implementation of the phase-field method
In: Journal of Petroleum Science and Engineering 166 (2018), S. 806–824
ISSN: 0920-4105
DOI: 10.1016/j.petrol.2017.11.022
URL: https://www.sciencedirect.com/science/article/abs/pii/S0920410517309051?via=ihub
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Direct numerical simulation of flow on pore-scale images using the phase-field method
In: Spe Journal 23 (2018), S. 1–18
ISSN: 1086-055X
DOI: 10.2118/182607-PA
URL: https://www.onepetro.org/journal-paper/SPE-182607-PA
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A finite volume/discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging
In: Computational Geosciences 22 (2018), S. 543–563
ISSN: 1420-0597
DOI: 10.1007/s10596-017-9709-1
URL: https://link.springer.com/article/10.1007/s10596-017-9709-1
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An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods
In: Journal of Colloid and Interface Science 523 (2018), S. 282–291
ISSN: 0021-9797
DOI: 10.1016/j.jcis.2018.02.075
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Mass-conserved density gradient theory model for nucleation process
In: Industrial & Engineering Chemistry Research (2018)
ISSN: 0888-5885
DOI: 10.1021/acs.iecr.8b03389
URL: https://pubs.acs.org/doi/10.1021/acs.iecr.8b03389
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Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system
In: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique 51 (2017), S. 1883-1902
ISSN: 0764-583X
DOI: 10.1051/m2an/2017002
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_FrankKn_ConvergenceAnalysisOfBDFDarcyNernstPlanckPoissonSystem
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Stabilized density gradient theory algorithm for modeling interfacial properties of pure and mixed systems
In: Fluid Phase Equilibria 435 (2017), S. 118–130
ISSN: 0378-3812
DOI: 10.1016/j.fluid.2016.11.024
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Inexact hierarchical scale separation: a two-scale approach for linear systems from discontinuous Galerkin discretizations
In: Computers & Mathematics with Applications 74 (2017), S. 1769–1778
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2017.06.025
URL: https://www.sciencedirect.com/science/article/pii/S0898122117303735?via=ihub
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A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition
In: Computational Geosciences 20 (2016), S. 881–908
ISSN: 1420-0597
DOI: 10.1007/s10596-015-9551-2
URL: https://link.springer.com/article/10.1007/s10596-015-9551-2
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FESTUNG: A MATLAB /GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting
In: Computers & Mathematics with Applications 72 (2016), S. 1896-1925
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2016.08.006
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_ReuterAizingerWielandFrankKn_FestungAMatLabGnuPartII
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Strong solvability up to clogging of an effective diffusion-precipitation model in an evolving porous medium
In: European Journal of Applied Mathematics (2016), S. 1-29
ISSN: 0956-7925
DOI: 10.1017/S0956792516000164
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_SchulzRayFrankMahatoKn_StrongSolvUpToCloggingInAnEvolvingPM
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FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator
In: Computers & Mathematics with Applications 70 (2015), S. 11 - 46
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2015.04.013
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_FrankReuterAizingerKn_FestungAMatlabGnuPartIDiffusionOperator
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FV upwind stabilization of FE discretizations for advection-diffusion problems
7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7 (Berlin, 15-06-2014 - 20-06-2014)
In: Fuhrmann Jürgen, Ohlberger Mario, Rohde Christian (Hrsg.): Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects 2014
DOI: 10.1007/978-3-319-05684-5_16
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_BrunnerFrankKn_FVUpwindStabOfFEForAdvancedDiffProblems
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Multiscale Modeling of Colloid and Fluid Dynamics in Porous Media Including an Evolving Microstructure
In: Transport in Porous Media 95 (2012), S. 669-696
ISSN: 0169-3913
DOI: 10.1007/s11242-012-0068-z
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_RayNoordenFrankKn_MultiscaleModelOfColloidAndFluidDynInPMinclAnEvolvMicrostr
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Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems
In: Computing and Visualization in Science 14 (2011), S. 385-400
ISSN: 1432-9360
DOI: 10.1007/s00791-013-0189-0
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_FrankRayKn_NumericalInvestiOfHomogeStokNernPlanPoissSystmes
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Entwicklung, Zuverlässigkeit und Effizienz reaktiver Mehrkomponententransportmodelle
In: KORA - Synopse "Systemanalyse, Modellierung und Prognose der Wirkungen natürlicher Schadstoffminderungsprozesse - eine rezente Synopse", 2008, S. 195-233 (Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner, Bd.5)
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Parallel mesh loading and partitioning for large-scale simulation
(Drittmittelfinanzierte Einzelförderung)
Laufzeit: seit 01-01-2021
Mittelgeber: Bayerisches Staatsministerium für Wissenschaft und Kunst (StMWK) (seit 2018)
URL: https://www.konwihr.de/ -
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,
- the attachment and detachment of colloids under consideration air-water interface of the soil,
- the transformation of the pore space and the thus induced coupling to the fluid transport in soil, and
- 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.
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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 / VerbundprojektThe 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.