A conservative level set method for two phase flow

  • Authors:

  • Elin Olsson;Gunilla Kreiss

  • Affiliations:

  • Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Lindstedsvagen 3, 100 44 Stockholm, Sweden;Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Lindstedsvagen 3, 100 44 Stockholm, Sweden

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

A conservative method of level set type for moving interfaces in divergence free velocity fields is presented. The interface is represented implicitly by the 0.5 level set of a function @F being a smeared out Heaviside function, i.e., a function being zero on one side of the interface and one on the other. In a transition layer of finite, constant thickness @F goes smoothly from zero to one. The interface is moved implicitly by the advection of @F, which is split into two steps. First @F is advected using a standard numerical method. Then an intermediate step is performed to make sure that the smooth profile of @F and the thickness of the transition layer is preserved. Both these steps are performed using conservative second order approximations and thus conserving @!@F. In this way good conservation of the area bounded by the 0.5 contour of @F is obtained. Numerical tests shows up to second order accuracy and very good conservation of the area bounded by the interface. The method was also coupled to a Navier-Stokes solver for incompressible two phase flow with surface tension. Results with and without topological changes are presented.