Dr. Felix Jaegle
Dipl.-Math. Christoph Zeiler
Kirill Pichon Gostaf

Prof. Dr. Claus-Dieter Munz

Modeling surface tension is a key ingredient for the simulation of free surface flows. While different methods have been successfully applied in flow solvers based on the incompressible Navier-Stokes equations, methods for the compressible case are still in their beginnings. What makes the description for compressible two-phase fluids complicated is the presence of phase transitions, although their effects occur only locally near the phase boundary.

To overcome this problem, we use different models for the fluid in one phase or at phase boundaries. With a heterogeneous multiscale approach, we model the dynamics of the bulk phases on a macro scale, and the behavior at the phase boundary on the micro scale. On the macro scale common one-phase fluid solver can be used, the challenge is the tracking of the phase boundary and the estimation of the surface tension. Models on the micro scale mainly reduce to Riemann type problems. The method has been demonstrated for one-dimensional cases with spherical symmetry.

In the proposed project, the treatment for surface tension is in a compressible, three-dimensional flow solver that uses a Discontinuous Galerkin- based Level-Set framework to define the location and curvature of the interface on the macro scale. Information from the solution of the micro scale problem is applied in the framework of a Ghost - Fluid type procedure, which will be extended to take the effects of surface tension into account. The evaluation and exploration of different implementation methods is a central part of this project.

The simulations have been implemented and run with the finete element code:

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 _|            _|      _|    _|  _|    _|  _|  _|        _|        _|  
   _|_|        _|      _|_|_|    _|    _|  _|_|          _|        _|  
       _|      _|      _|    _|  _|    _|  _|  _|        _|        _|  
 _|_|_|        _|      _|    _|    _|_|    _|    _|      _|      _|_|_|

 http://twitter.com/Strukti

Additional test cases

small droplet

large droplet

moving droplet

unstable level setsolution