Multi-material interface reconstruction on generalized polyhedral meshes

We describe multi-material (more than two materials) interface reconstruction methods for 3D meshes of generalized polyhedra. The basic information used in interface reconstruction is the volume fraction of each material in mixed cells, that is, those containing multiple materials. All methods subdivide a mixed cell into a set of pure non-overlapping sub-cells, each containing just one material that have the reference volume fraction. We describe three methods. The first two methods represent an extension of standard piece-wise linear interface construction (PLIC) methods to 3D and use information only about volume fractions. The first method is first-order accurate and is based on the discrete gradient of the volume fraction as an estimate of the normal to the interface. The second method is planarity-preserving (second-order accurate) and is an extension to 3D of the least squares volume-of-fluid interface reconstruction algorithm (LVIRA, see [E. Puckett, A volume-of-fluid interface tracking algorithm with applications to computing shock wave refraction, in: H. Dwyer (Ed.), Proceedings of the Fourth International Symposium on Computational Fluid Dynamics, 1991, pp. 933–938; J.E. Pilliod, E.G. Puckett, Second-order accurate volume-of-fluid algorithms for tracking material interfaces, Journal of Computational Physics 199 (2004) 465–502] for the 2D case). The third method is an extension to 3D of the so-called moment-of-fluid (MoF) method [V. Dyadechko, M. Shashkov, Moment-of-fluid interface reconstruction, Tech. Rep. LA-UR-05-7571, Los Alamos National Laboratory, 2005. Also available as http://cnls.lanl.gov/~shashkov/; V. Dyadechko, M. Shashkov, Multi-material interface reconstruction from the moment data, Tech. Rep. LA-UR-06-5846, Los Alamos National Laboratory, 2006. Also available as http://cnls.lanl.gov/~shashkov/]. The MoF method is also second-order accurate. This method uses information not only about volume fractions but also about the position of the centroids of each material. In contrast to standard PLIC methods, the MoF method uses only information from the cell where reconstruction is performed; no information from neighboring cells is needed. Also, the MoF method provides automatic ordering of the materials during interface reconstruction. Optimal ordering is based on comparing the positions of the reference centroids and actual centroids of the reconstructed pure sub-cells. The performance of the methods is demonstrated with numerical examples.