An Extended Discontinuous Galerkin Framework for Multiphase Flows

  • Thomas Utz
  • Christina Kallendorf
  • Florian Kummer
  • Björn Müller
  • Martin OberlackEmail author
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)


We present a framework for handling cut cells in a high order discontinuous Galerkin (DG) context. To describe the boundary between fluid phases, we use a level-set formulation. When the interface cuts a computational cell, we discretize the resulting sub-cells with the same DG method as used on standard cells. This requires a suitable quadrature procedure. Within this framework, we present a solver for the two-phase Navier-Stokes equation, a reinitialization procedure for the level-set and a solver for transport-processes on the surface.



This work is supported by the ‘Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt. The work of T. Utz and C. Kallendorf is supported by the German Science Foundation (DFG) within the Priority Program (SPP) 1506 “Transport Processes at Fluidic Interfaces”. The work of F. Kummer is supported by the German DFG through Research Fellowship KU 2719/1-1. The work of B. Müller is supported by the German Research Foundation (DFG) through Research Grant WA 2610/2-1.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Thomas Utz
    • 1
  • Christina Kallendorf
    • 1
  • Florian Kummer
    • 1
  • Björn Müller
    • 1
  • Martin Oberlack
    • 1
    Email author
  1. 1.Institute of Fluid DynamicsTechnische Universität DarmstadtDarmstadtGermany

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