PD Dr. Florian Frank
Research interests
- 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
Education and degrees
| 04/2022 | Privatdozent (teaching authorization for mathematics, FAU) |
| 10/2019 | Dr. habil. (teaching qualification for mathematics, FAU) |
| 11/2013 | Dr. rer. nat. (doctorate in applied mathematics, FAU, Prof. Dr. P. Knabner) |
| 10/2008–11/2013 | Doctoral studies in applied mathematics, FAU |
| 10/2008 | Diplom-Mathematiker Univ., FAU |
| 10/2002–10/2008 | Major mathematics (diploma), minor computer science, FAU |
| 06/2002 | General qualification for university entrance, Bavaria (Abitur) |
| 09/1992–06/2002 | Gymnasium Lichtenfels, science track |
Academic employment
| 10/2021–03/2022 | Interim Professor (W2), Applied Mathematics (Scientific Computing), FAU |
| 10/2018–09/2021 | Interim Professor (W2), Applied Mathematics (Mathematical Modeling), FAU |
| 03/2018–09/2018 | Interim Professor (W3), Applied Mathematics, FAU |
| 08/2017–02/2018 | Senior Postdoctoral Research Associate, CAAM Department, Rice University |
| 08/2014–07/2017 | Postdoctoral Research Associate, CAAM Department, Rice University |
| 12/2013–06/2014 | Postdoctoral researcher, Chair of Applied Mathematics 1, FAU |
| 11/2008–11/2013 | Research associate, Chair of Applied Mathematics 1, FAU |
| 04/2010–12/2011 | Research associate, Chair of Hydrogeology, University of Jena |
| 11/2008–10/2009 | Research associate, Chair of Hydrogeology, University of Jena |
Awards and honors
| 10/2020 | Emmy Noether Award for the habilitation, Faculty of Sciences, FAU |
| 05/2017 | Award and promotion to Senior Postdoctoral Research Associate, George R. Brown School of Engineering, Rice University, Houston, TX, USA |
Reviewer for international journals
| 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) |
Editorial activities
| Guest editor of the special issue “Recent Advances in Numerical Modeling and Simulation of Fluid Flow and Heat Transfer in Porous Media” of the journal Computational Geosciences. |
| Guest editor of the special issue “Advanced Modeling and Simulation of Flow in Subsurface Reservoirs with Fractures and Wells for a Sustainable Industry” of the journal Oil & Gas Science and Technology — Revue d’IFP Energies nouvelles. |
Courses (as Privatdozent)
| SS 2026 | Lecture Differential Equation Models |
| WS 2024/2025 | Project seminar Mathematical Modeling |
| WS 2023/2024 | Project seminar Mathematical Modeling |
| WS 2022/2023 | Seminar Iterative Solution Methods for Linear and Nonlinear Systems of Equations (with C. Pflaum, interdisciplinary with Computer Science and CE) |
Courses (as professor)
| WS 2021/2022 | Lecture and exercise class on Mathematics for Engineers C3 (Computer Science) |
| SS 2021 | Lecture, exercise class, and tutorial on Discretization and Numerical Optimization |
| SS 2021 | Matlab/Octave programming course for Integrated Life Sciences |
| SS 2021 | Seminar Mathematical Modeling and Data Analysis (with M. Burger, D. Tenbrinck) |
| WS 2020/2021 | Lecture, exercise class, and tutorial on Introduction to Numerical Mathematics |
| WS 2020/2021 | Matlab/Octave programming course for Introduction to Numerical Mathematics |
| WS 2020/2021 | Seminar on Discretization and Numerical Optimization |
| SS 2020 | Lecture, exercise class, and tutorial on Discretization and Numerical Optimization |
| SS 2020 | Course Modeling, Simulation, and Optimization, Practical Course (in English) |
| WS 2019/2020 | Lecture, exercise class, and tutorial on Introduction to Numerical Mathematics |
| WS 2019/2020 | Matlab/Octave programming course for Introduction to Numerical Mathematics |
| SS 2019 | Lecture and exercise class on Numerics of Partial Differential Equations II (in English) |
| SS 2019 | Course Modeling, Simulation, and Optimization, Practical Course (in English) |
| SS 2019 | Seminar Modeling and Simulation |
| SS 2019 | Matlab/Octave programming course for Integrated Life Sciences |
| WS 2018/2019 | Lecture and exercise class on Numerics of Partial Differential Equations I (in English) |
| WS 2018/2019 | Seminar Discretization and Numerical Optimization |
| SS 2018 | Lecture and exercise class on Differential Equation Models |
| SS 2018 | Course Modeling, Simulation, and Optimization, Practical Course (in English) |
| SS 2018 | Seminar Numerics of Nonlinear Systems of Equations |
Courses (as research associate)
| SS 2014 | Organization and teaching of the course (lecture, exercise class): Finite Element Programming (in English, P. Knabner) |
| SS 2014 | Organization and teaching of the course (lecture, exercise class): Introduction to Matlab/Octave (P. Knabner) |
| WS 2013/2014 | Supervision of the seminar Applied Mathematics: Flow and Transport Processes |
| WS 2013/2014 | Contribution to the programming lab for the course Computational Biology (in English, R. Böckmann/V. Aizinger) |
| SS 2013 | Organization and teaching of the course (lecture, exercise class) Introduction to Matlab/Octave (P. Knabner) |
| SS 2013 | Contribution to the course Review Course on Mathematics for Engineers I (V. Aizinger) |
| WS 2012/2013 | Organization and supervision of the exercise class for Introduction to Numerical Mathematics (P. Knabner) |
| SS 2012 | Organization and teaching of the course (lecture, exercise class) Introduction to Matlab/Octave (G. Grün) |
| WS 2011/2012 | Organization of the exercise class for Introduction to Numerical Mathematics (N. Marheineke) |
| SS 2011 | Organization and teaching of the course (lecture, exercise class) Tutorial on Introduction to Numerical Mathematics (N. Marheineke) |
| SS 2011 | Organization and supervision of the exercise class for Numerics II for Engineers (N. Marheineke) |
| WS 2010/2011 | Organization and supervision of the exercise class for Numerics I for Engineers (N. Marheineke) |
| SS 2010 | Organization of the exercise class for Numerical Mathematics II (G. Grün) |
| WS 2009/2010 | Organization and teaching of the course Computer-Aided Mathematics for Linear Algebra (P. Knabner) |
| SS 2009 | Supervision of the exercise class for Numerics of Partial Differential Equations II (P. Knabner) |
| WS 2008/2009 | Supervision of the exercise class for Numerics of Partial Differential Equations I (P. Knabner) |
Courses (as student assistant)
| SS 2006 | Supervision of the exercise class for Numerics II (M. Bause) |
| WS 2005/2006 | Supervision of the exercise class for Numerics I (M. Bause) |
Supervision and assessment
| 07/2021–10/2021 | Advisor and reviewer of the master’s thesis “Fast and robust numerical solutions of density gradient theory equations for arbitrary components” by Paul Maidl (Computational and Applied Mathematics) |
| 06/2021–08/2021 | Advisor and reviewer of the bachelor’s thesis “Localization of a discrete preconditon operator for Stokes Schur complements” by Fabian Woller (Mathematics) |
| 05/2020–10/2020 | Advisor and reviewer of the master’s thesis “High-performance preconditioning of the Stokes equation in complex domains” by Andreas Meier (Computational and Applied Mathematics) |
| 10/2019–03/2020 | Advisor and reviewer of the master’s thesis “Analysis and implementation of an enriched Galerkin scheme for the shallow-water equations” by Moritz Hauck (Mathematics) |
| 06/2019–12/2019 | Advisor and reviewer of the bachelor’s thesis “Slope limiting for the enriched Galerkin discretization of the advection equation” by Lukas Weigand (Industrial Mathematics) |
| 05/2019–11/2019 | Advisor and reviewer of the bachelor’s thesis “A finite volume method on unstructured grids for the Cahn–Hilliard equation” by Paul Maidl (Mathematics) |
| 06/2018–10/2018 | Advisor and reviewer of the bachelor’s thesis “Stabilization techniques for the finite element method applied on advection-dominated problems” by Moritz Hauck (Mathematics) |
| 06/2018–10/2018 | Advisor and reviewer of the bachelor’s thesis “Jacobian-free Newton–Krylov methods applied to the Cahn–Hilliard equation with degenerate mobility” by Tim Roith (Mathematics) |
| 06/2018–09/2018 | Advisor and reviewer of the bachelor’s thesis “Simulation of reactive transport in saturated porous media with porosity changes through mineral dissolution and precipitation” by Andreas Meier (Mathematics) |
| 07/2018 | Second reviewer of the master’s thesis “A hybridizable discontinuous Galerkin scheme with different orders of approximation spaces capable of dealing with jump conditions: analysis and implementation” by Markus Musch (Mathematics, advisor: P. Knabner) |
| 02/2014–05/2014 | Co-advisor of the bachelor’s thesis “Mutual Coupling of PDE Systems: Unsaturated Flow and Mineral Reactions with Porosity Changes” by Jens Oberlander (Mathematics, advisor: P. Knabner) |
| 02/2012–08/2012 | Co-advisor of the master’s thesis “Mathematical Modeling and Simulation of a Microfluidic Reactor” by Beatriz Pérez-Pardo (Computational Engineering, advisor: P. Knabner) |
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Multiscale flow simulations of dilute polymeric solutions with bead-rod chains using Brownian configuration fields
In: Applied Mathematics and Computation 487 (2025), Article No.: 129091
ISSN: 0096-3003
DOI: 10.1016/j.amc.2024.129091
BibTeX: Download
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Thickness and surface estimation of thin porous media based on 3D image data
In: Measurement Science & Technology 35 (2024), Article No.: 056002
ISSN: 0957-0233
DOI: 10.1088/1361-6501/ad2421
BibTeX: Download - , , :
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), p. 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), p. 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), p. 103558
ISSN: 0309-1708
DOI: 10.1016/j.advwatres.2020.103558
BibTeX: Download - , , :
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), Article No.: 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), Article No.: 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), p. 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), p. 669-686
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2019.06.052
BibTeX: Download - , , :
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), p. 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), p. 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), p. 543–563
ISSN: 1420-0597
DOI: 10.1007/s10596-017-9709-1
URL: https://link.springer.com/article/10.1007/s10596-017-9709-1
BibTeX: Download - , , , , :
An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods
In: Journal of Colloid and Interface Science 523 (2018), p. 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), p. 1883-1902
ISSN: 0764-583X
DOI: 10.1051/m2an/2017002
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_FrankKn_ConvergenceAnalysisOfBDFDarcyNernstPlanckPoissonSystem
BibTeX: Download - , , , :
Stabilized density gradient theory algorithm for modeling interfacial properties of pure and mixed systems
In: Fluid Phase Equilibria 435 (2017), p. 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), p. 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), p. 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), p. 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
BibTeX: Download - , , , , :
Strong solvability up to clogging of an effective diffusion-precipitation model in an evolving porous medium
In: European Journal of Applied Mathematics (2016), p. 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), p. 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 (ed.): 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), p. 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), p. 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, p. 195-233 (Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner, Vol.5)
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Term: since 01.01.2021
Funding source: Bayerisches Staatsministerium für Wissenschaft und Kunst (StMWK) (seit 2018)
Project leader:
Funding source: Bayerisches Staatsministerium für Wissenschaft und Kunst (StMWK) (seit 2018)
Project leader:
Term: 01.11.2006 - 31.12.2009
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
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 considerat…
Term: 01.04.2004 - 31.12.2008
Funding source: BMFTR / Verbundprojekt
Project leader: ,
Funding source: BMFTR / Verbundprojekt
Project leader: ,
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 met…
- Google Scholar
- ResearchGate
- ORCID
- DGT Web App (equilibrium density profiles, density gradient theory)