1. Book: Numerical Methods for Two-phase Incompressible Flows
    S. Groß, A. Reusken,
    Numerical Methods for Two-phase Incompressible Flows,
    First edition 2011,
    Springer Series in Computational Mathematics, Vol. 40,
    ISBN 978-3-642-19685-0

  2. L. Zhang:
    Numerical methods for mass transfer in falling films and two-phase flows with moving contact lines,
    doctoral thesis, IGPM, RWTH Aachen, 2017.
  3. P. Esser:
    Parallel higher order methods for solving twophase flows (in German),
    doctoral thesis, IGPM, RWTH Aachen, 2016.
  4. Y. Zhang:
    Numerical simulation of two-phase flows with complex interfaces,
    doctoral thesis, IGPM, RWTH Aachen, 2015.
  5. C. Lehrenfeld:
    On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems,
    doctoral thesis, IGPM, RWTH Aachen, 2015.
  6. E. Loch:
    The level set method for capturing interfaces with applications in two-phase flow problems,
    doctoral thesis, IGPM, RWTH Aachen, 2013.
  7. O. Fortmeier:
    Parallel re-initialization of level set functions and load balancing for two-phase flow simulations,
    doctoral thesis, IGPM, RWTH Aachen, 2009.
  8. T. H. Nguyen:
    Numerical methods for mass transport equations in two-phase incompressible flows,
    doctoral thesis, IGPM, RWTH Aachen, 2009.
  9. S. Groß:
    Numerical methods for three-dimensional incompressible two-phase flow problems,
    doctoral thesis, IGPM, RWTH Aachen, 2008.
  10. DROPS-Package: User's guide
    March 19, 2008.


  1. J. Grande :
    Red-Green Refinement of Simplicial Meshes in D Dimensions ,
    IGPM report 436, RWTH Aachen (2015)
  2. A. Reusken, X. Xu, L. Zhang :
    Finite Element Methods for a Class of Continuum Models for Immiscible Flows with Moving Contact Lines ,
    IGPM report 432, RWTH Aachen (2015)
  3. S. Groß, T. Ludescher, M. Olshanskii, A. Reusken :
    Robust Preconditioning for XFEM Applied to Time-Dependent Stokes Problems ,
    IGPM report 424, RWTH Aachen (2015)
  4. M. Kirchhart, S. Groß, A. Reusken :
    Analysis of an XFEM Discretization for Stokes Interface Problems ,
    IGPM report 420, RWTH Aachen (2015)
  5. J. Grande :
    Analysis of Highly Accurate Finite Element Based Algorithms For Computing Distances To Level Sets ,
    IGPM report 419, RWTH Aachen (2015)
  6. C. Lehrenfeld, A. Reusken :
    Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport ,
    IGPM report 413, RWTH Aachen (2014)
  7. C. Lehrenfeld, A. Reusken :
    Optimal preconditioners for Nitsche-XFEM discretizations of interface problems ,
    IGPM report 406, RWTH Aachen (2014)
  8. J. Grande, A. Reusken :
    A Higher Order Finite Element Method for Partial Differential Equations on Surfaces ,
    IGPM report 403, RWTH Aachen (2014)
  9. S. Groß, M. A. Olshanskii, A. Reusken :
    A Trace Finite Element Method for a Class of Coupled Bulk-Interface Transport Problemes ,
    IGPM report 398, RWTH Aachen (2014)
  10. J. Adelsberger, P. Esser, M. Griebel, S. Groß, M. Klitz, A. Rüttgers :
    3D Incompressible Two-Phase Flow Benchmark Computations for Rising Droplets ,
    IGPM report 393, RWTH Aachen (2014)
  11. A. Reusken :
    Analysis of trace Finite Element Methods for surface partial differential equations,
    IGPM report 387, RWTH Aachen (2014)
  12. J. Grande, M.A. Olshanskii, A. Reusken :
    A space-time FEM for PDEs on evolving surfaces,
    IGPM report 386, RWTH Aachen (2014)
  13. J. Grande :
    Finite Element Discretization Error Analysis of a General Interfacial Stress Functional ,
    IGPM report 380, RWTH Aachen (2014)
  14. O. Fortmeier, H.M. Bücker, B.O. Fagginger Auer, R.H. Bisseling :
    A New Metric Enabling an Exact Hypergraph Model for the Communication Volume in Distributed-memory Parallel Applications ,
    Parallel Computing, Vol. 39, No. 8, 319-335 (August 2013), voted into the list of top 25 hottest articles by ScienceDirect
  15. P. Esser, J. Grande :
    An Accurate and Robust Finite Element Level Set Redistancing Method ,
    IGPM report 379, RWTH Aachen (2013)
  16. C. Lehrenfeld :
    The Nitsche XFEM-DG Space-Time Method and its Implementation in Three Space Dimensions ,
    IGPM report 377, RWTH Aachen (2013)
  17. M.A. Olshanskii, A. Reusken :
    Error analysis of a space-time finite element method for solving PDEs on evolving surfaces,
    IGPM report 376, RWTH Aachen (2013)
  18. H. Marschall, S. Boden, C. Lehrenfeld, C.J. Falconi, U. Hampel, A. Reusken, M. Wörner, D. Bothe :
    Validation of interface capturing and tracking techniques with different surface tension treatments against a Taylor bubble benchmark problem,
    Computers & Fluids, Volume 102, Pages 336–352, October 2014
  19. M.A. Olshanskii, A. Reusken, X. Xu :
    An Eulerian space-time finite element method for diffusion problems on evolving surfaces,
    IGPM report 362, RWTH Aachen (2013)
  20. J. Grande :
    Eulerian Finite Element Methods for Parabolic Equations on Moving Surfaces,
    IGPM report 360, RWTH Aachen (2013)
  21. E. Loch :
    Analysis of a Discontinuous Galerkin Method Applied to the Level Set Equation ,
    IGPM report 354, RWTH Aachen (2012)
  22. M.A. Olshanskii, A. Reusken, X. Xu :
    On surface meshes induced by level set functions,
    Comp. Vis. Science 15, 53-60 (2012)
  23. A. Reusken:
    A finite element level set redistancing method based on gradient recovery,
    SIAM J. Numer. Analysis 51, 2723-2745 (2013)
  24. S. Gross, A. Reusken:
    Numerical simulation of continuum models for fluid-fluid interface dynamics,
    Eur. Phys. J. Special Topics 222, 211-239 (2013)
  25. A. Reusken, Y. Zhang:
    Numerical simulation of incompressible two-phase flows with a Boussinesq-Scriven surface stress tensor,
    Numerical Methods in Fluids (2013), doi: 10.1002/fld.3835
  26. C. Lehrenfeld. A. Reusken:
    Analysis of a DG-XFEM discretization for a class of two-phase mass transport problems,
    SIAM J. Numer. Anal. 51, No. 2, 958-983 (2013)
  27. M.A. Olshanskii, A. Reusken, X. Xu :
    A stabilized finite element method for advection-diffusion equations on surfaces,
    IMA J. Numer. Anal. (2013), doi:10.1093/imanum/drt016
  28. M.A. Olshanskii, A. Reusken, X. Xu :
    A volume mesh finite element method for PDEs on surfaces,
    IGPM report 342 , RWTH Aachen 2012. In: Proceedings of the ECCOMAS 2012 conference (2012)
  29. A. Reusken :
    Finite element techniques for the numerical simulation of two-phase incompressible flows,
    Proceedings of 6th International Berlin Workshop on Transport Phenomena with Moving Boundaries, VDI Fortschritt Bericht Nr. 929, 162-177 (2012)
  30. P. Bandi, S. Gross, M. Karalashvili, A. Mhamdi, H. Pirnay, L. Zhang, W. Marquardt, M. Modigell, A. Reusken :
    Experimental identification of effective mass transport models in falling films,
    Proceedings of 6th International Berlin Workshop on Transport Phenomena with Moving Boundaries, VDI Fortschritt Bericht Nr. 929, 276-297 (2012)
  31. C. Lehrenfeld. A. Reusken:
    Nitsche-XFEM with streamline diffusion stabilization for a two-phase mass transport problem,
    SIAM J. Sci. Comp. 34, 2740-(2012)
  32. A. Reusken, E. Loch:
    On the accuracy of the level set SUPG method for approximating interfaces,
    IGPM report 319, RWTH Aachen (2011)
  33. A. Reusken, P.Esser:
    Analysis of time discretization methods for a Stokes equations with a nonsmooth forcing term,
    IGPM report 327, RWTH Aachen (2011). Revision submitted to Numerische Mathematik.
  34. O. Fortmeier, H. Martin Bücker:
    Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids.
    Journal of Computational Physics, 230(12) (2011), pp. 4437-4453, DOI: 10.1016/
  35. H. M. Bücker, O. Fortmeier, M. Petera:
    Solving a parameter estimation problem in a three-dimensional conical tube on a parallel and distributed software infrastructure.
    Journal of Computational Science, 2(2) (2011), pp. 95-104, DOI: 10.1016/j.jocs.2011.01.002.
  36. O. Fortmeier, H. M. Bücker:
    A parallel strategy for a level set simulation of droplets moving in a liquid medium.
    In Proc. of the Int. Conf. on High Performance Computing for Computational Science, VECPAR’10, pp. 200–209. Springer (2011), DOI: 10.1007/978-3-642-19328-6_20.
  37. M. Karalashvili, S. Groß, A. Mhamdi, A. Reusken, W. Marquardt:
    Identification of transport coefficient models in convection-diffusion equations
    SIAM J. Sci. Comp., 33(1) (2011), pp. 303-327, DOI: 10.1137/09077360X.
  38. H. M. Bücker, J. Willkomm, S. Groß, O. Fortmeier:
    Discrete and Continuous Adjoint Approaches to Estimate Boundary Heat Fluxes in Falling Films *
    Optimization Methods and Software, 26(1) (2011), pp. 105-125, DOI: 10.1080/10556780903341711.
  39. E. Bertakis, S. Gross, J. Grande, O. Fortmeier, A. Reusken, A. Pfennig:
    Validated simulation of droplet sedimentation with finite-element and level-set methods
    Chem. Eng. Science 65 (2010), pp. 2037-2051.
  40. P. Esser, J. Grande, A. Reusken:
    An extended finite element method applied to levitated droplet problems
    Int. J. for Numer. Meth. in Engineering 84(7) (2010), pp. 757-773. DOI: 10.1002/nme.2913
  41. M. A. Olshanskii, A. Reusken:
    A Finite Element Method for Surface PDES: Matrix Properties
    Numer. Math. 114 (2009), pp. 491-520 .
  42. M. A. Olshanskii, A. Reusken, J. Grande:
    An Eulerian Finite Element Method for Elliptic Equations on Moving Surfaces
    SIAM J. Numer. Anal. 47 (2009), pp. 3339-3358.
  43. A. Reusken, T. H. Nguyen:
    Nitsche's method for a transport problem in two-phase incompressible flows
    J. Fourier Analysis and Applications 15 (2009), pp. 663-683.
  44. M. Karalashvili, S. Gross, A. Mhamdi, A. Reusken, W. Marquardt:
    Incremental Identification of Transport Coefficients in Convection-Diffusion Systems
    SIAM J. Sci. Comp., 30(6) (2008), pp. 3249-3269
  45. A. Reusken:
    Analysis of an extended pressure finite element space for two-phase incompressible flows
    Comp. Visual. Sci., 11 (2008), pp. 293-305.
  46. M. Larin, A. Reusken:
    A comparative study of efficient iterative solvers for generalized Stokes equations
    Numer. Lin. Algebra Appl., 15 (2008), pp. 13-34.
  47. S. Groß, A. Reusken:
    Mathematik für Tropfen ist alles andere als trocken.
    In: RWTH-Themen 2/2007, Computational Engineering Science - Ein neues Ingenieurprofil. pp. 14-17.
  48. S. Groß, A. Reusken:
    Finite element discretization error analysis of a surface tension force in two-phase incompressible flows
    SIAM J. Numer. Anal., 45 (2007), pp. 1679-1700.
  49. S. Groß, A. Reusken:
    An extended pressure finite element space for two-phase incompressible flows with surface tension
    J. Comp. Phys., 45 (2007), pp. 40-58.
  50. S. Groß, V. Reichelt, A. Reusken:
    A Finite Element Based Level Set Method for Two-phase Incompressible Flows
    Comp. Visual. Sci., 9 (2006), pp. 239-257.
  51. M. A. Olshanskii, J. Peters, A. Reusken:
    Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations
    Numer. Math., 105 (2006), pp.159-191.
  52. M. A. Olshanskii, A. Reusken:
    Analysis of a Stokes interface problem
    Numer. Math., 103 (2006), pp.129-149.
  53. S. Groß, M. Soemers, A. Mhamdi, F. Al Sibai, A. Reusken, W. Marquardt, U. Renz:
    Identification of boundary heat fluxes in a falling film experiment using high resolution temperature measurements *
    International Journal of Heat and Mass Transfer, 48 (2005), pp. 5549-5562.
  54. S. Groß, A. Reusken:
    Parallel multilevel tetrahedral grid refinement
    SIAM J. Sci. Comp., 26 (2005), pp. 1261-1288.
  55. J. Peters, V. Reichelt, A. Reusken:
    Fast Iterative Solvers for Discrete Stokes Equations
    SIAM J. Sci. Comp., 27 (2005), pp.646-666.
  56. M. A. Olshanskii, A. Reusken:
    Navier-Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem
    SIAM J. Sci. Comput., 23 (2002), pp.1683-1706.
  57. S. Groß, J. Peters, V. Reichelt, A. Reusken:
    The DROPS Package for Numerical Simulations of Incompressible Flows Using Parallel Adaptive Multigrid Techniques
    IGPM-Report 211, RWTH Aachen, 2002.
  58. A. Reusken, V. Reichelt:
    Mit Gittern auf der Spur von Tropfen
    TerraTech, Zeitschrift für Altlasten und Bodenschutz, 6 (2001), pp. 35-37.
  59. M. A. Olshanskii, A. Reusken:
    On the convergence of a multigrid method for linear reaction-diffusion problems
    Computing, 65 (2000), pp.193-202.


Two-phase incompressible flows: modeling aspects and methods for numerical simulation
June 25th - 27th, 2007, Aachen, Germany.


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Sven Groß ✉, last update: February 9th, 2011