Prof. Dr. Florian Frank

Veröffentlichungen

2019

• Liu C., Frank F., Rivière B.:
  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

2018

• Alpak FO., Samardžić A., Frank F.:
  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
• Frank F., Liu C., Alpak FO., Berg S., Rivière B.:
  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
• Frank F., Liu C., Alpak FO., Rivière B.:
  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
• Frank F., Liu C., Scanziani A., Alpak FO., Rivière B.:
  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
• Mu X., Frank F., Rivière B., Alpak FO., Chapman WG.:
  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

2017

• Frank F., Knabner P.:
  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
• Mu X., Frank F., Alpak FO., Chapman WG.:
  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
• Thiele C., Araya-Polo M., Alpak FO., Rivière B., Frank F.:
  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

2016

• Alpak FO., Rivière B., Frank F.:
  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
• Reuter B., Aizinger V., Wieland M., Frank F., Knabner P.:
  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: http://www.sciencedirect.com/science/article/pii/S0898122116304606
• Schulz R., Ray N., Frank F., Mahato H., Knabner P.:
  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

2015

• Frank F., Reuter B., Aizinger V., Knabner P.:
  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: http://www.sciencedirect.com/science/article/pii/S0898122115001820

2014

• Brunner F., Frank F., Knabner P.:
  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)
  DOI: 10.1007/978-3-319-05684-5_16

2012

• Ray N., van Noorden T., Frank F., Knabner P.:
  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

2011

• Frank F., Ray N., Knabner P.:
  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

2008

• Knabner P., Frank F., Hoffmann J., Kräutle S., Oßmann S., Prechtel A.:
  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)

Projekte

• 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)
  Abstract

  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.

  →Mehr Informationen
• 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
  Abstract

  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.
  →Mehr Informationen