  Simulations involving free surfaces and fluid interfaces are important in
many areas of engineering. There is, however, still a need for improved
simulation methods. Recently, a new efficient geometric VOF method called
isoAdvector for general polyhedral meshes was published. We investigate the
interface reconstruction step of isoAdvector, and demonstrate that especially
for unstructured meshes the applied isosurface based approach can lead to noisy
interface orientations. We then introduce a novel computational interface
reconstruction scheme based on calculation of a reconstructed distance function
(RDF). By iterating over the RDF calculation and interface reconstruction, we
obtain second order convergence of both the interface normal and position
within cells even with a strict $L_{\infty}$ error norm. In 2D this is verified
with reconstruction of a circle on Cartesian meshes and on unstructured
triangular and polygonal prism meshes. In 3D the second order convergence is
verified with reconstruction of a sphere on Cartesian meshes and on
unstructured tetrahedral and polyhedral meshes. The new scheme is combined with
the interface advection step of the isoAdvector algorithm. Significantly
reduced absolute advection errors are obtained, and for CFL number 0.2 and
below we demonstrate second order convergence on all the mentioned mesh types
in 2D and 3D. The implementation of the proposed interface reconstruction
schemes is straightforward and the computational cost is significantly reduced
compared to contemporary methods. The schemes are implemented as an extension
to the Computational Fluid Dynamics (CFD) Open Source software package,
OpenFOAM. The extension module and all test cases presented in this paper are
released as open source.
