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An Extended Discontinuous Galerkin Framework for Multiphase Flows

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Transport Processes at Fluidic Interfaces

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

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.

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Acknowledgements

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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  1. Institute of Fluid Dynamics, Technische Universität Darmstadt, Otto-Bernd-Straße 2, 64287, Darmstadt, Germany

    Thomas Utz, Christina Kallendorf, Florian Kummer, Björn Müller & Martin Oberlack

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  1. Thomas Utz
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  2. Christina Kallendorf
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  3. Florian Kummer
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  1. Fachbereich Mathematik, Technische Universität Darmstadt , Darmstadt, Germany

    Dieter Bothe

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Arnold Reusken

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Utz, T., Kallendorf, C., Kummer, F., Müller, B., Oberlack, M. (2017). An Extended Discontinuous Galerkin Framework for Multiphase Flows. In: Bothe, D., Reusken, A. (eds) Transport Processes at Fluidic Interfaces. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-56602-3_3

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