An eXtended Discontinuous Galerkin method for three-dimensional two-phase flows: Application to large amplitude oscillations of viscous drops

ORAL

Abstract

We are going to present a high-order eXtended Discontinuous Galerkin (XDG) method for transient two-phase flows. The XDG method adapts the local ansatz functions to conform with the position of the interface and provides separate degrees of freedom for each phase [1,2]. This allows a sub-cell accurate approximation of the incompressible Navier-Stokes equations in their sharp-interface formulation. The interface is defined as the zero-set of a signed-distance level-set function.

The numerical investigations focus on nonlinear axisymmetric shape oscillations of a drop in a dynamically nearly inert ambient phase. The initial deformation is given by a Legendre polynomial. We compare the numerical results with the analytical results of the weakly nonlinear theory [3]. The properties to be compared include the droplet aspect ratio over time and mode decomposition of the droplet shape. Further, we present the kinetic and surface energy over time for the numerical simulations.

*Funding of this joint project by the German Research Foundation together with the Austrian Science Fund in the DACH framework is gratefully acknowledged. The work by M. Smuda is in part funded by the Federal Ministry of Education and Research (BMBF) and the state of Hesse as a part of the NHR Program.

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Publication: [1] F. Kummer, Extended discontinuous Galerkin methods for two-phase flows: the spatial discretization, Int. J. Numer. Methods. Eng., 109(2), pp. 259-289, 2017.
[2] M. Smuda, F. Kummer, On a marching level-set method for extended discontinuous Galerkin methods for incompressible two-phase flows: Application to two-dimensional settings, Int. J. Numer. Methods. Eng., 123(1), pp. 197-225, 2022.
[3] D. Zrnić, P. Berglez, G. Brenn, Weakly nonlinear shape oscillations of a Newtonian drop, Phys. Fluids, 34, 043103, 2022

Presenters

  • Martin Smuda

    • Chair of Fluid Dynamics, TU Darmstadt

Authors

  • Martin Smuda

    • Chair of Fluid Dynamics, TU Darmstadt

  • Dino Zrnić

    • Institute of Fluid Mechanics and Heat Transfer, TU Graz

  • Florian Kummer

    • Technische Universitat Darmstadt
    • Chair of Fluid Dynamics, TU Darmstadt

  • Günter Brenn

    • Institute of Fluid Mechanics and Heat Transfer, TU Graz

  • Martin Oberlack

    • TU Darmstadt
    • Chair of Fluid Dynamics, TU Darmstadt
    • Technische Universität Darmstadt, Chair of Fluid Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany
    • Fachgebiet für Strömungsdynamik, Technische Universität Darmstadt