Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids

  • Authors:

  • Xiaofeng Yang;Ashley J. James

  • Affiliations:

  • Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street SE, Minneapolis, MN 55455, USA;Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street SE, Minneapolis, MN 55455, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

In volume of fluid methods for interfacial flow simulations, one essential process is the so-called interface reconstruction, in which an approximate interface is reconstructed from a given discrete volume fraction field. In [J. Comput. Phys. 164 (2000) 228-237], Scardovelli and Zaleski presented analytical relations connecting linear interfaces and volume fractions in rectangular grids. Here, we present analytical relations connecting linear interfaces and volume fractions in triangular and tetrahedral grids. For computing the volume of fluid in an arbitrary polygonal or polyhedral fluid element, we also cite some of the most efficient formulas for polygon area and polyhedron volume computations. Simple test cases show that this analytic method of interface reconstruction is about 18 times faster than an iterative method in two dimensions, and four to six times faster in three dimensions. The results can be in general applied to other fields as well.