Efficient threematerial PLIC interface positioning on unstructured polyhedral meshes
Abstract
This paper introduces an efficient algorithm for the sequential positioning (or nested dissection) of two planar interfaces in an arbitrary polyhedron, such that, after each truncation, the respectively remaining polyhedron admits a prescribed volume. This task, among others, is frequently encountered in the numerical simulation of threephase flows when resorting to the geometric VolumeofFluid method. For twophase flows, the recent work of Kromer & Bothe (doi.org/10.1016/j.jcp.2021.110776) addresses the positioning of a single plane by combining an implicit bracketing of the sought position with up to thirdorder derivatives of the volume fraction. An analogous application of their highly efficient rootfinding scheme to threematerial configurations requires computing the volume of a twice truncated arbitrary polyhedron. The present manuscript achieves this by recursive application of the Gaussian divergence theorem in appropriate form, which allows to compute the volume as a sum of quantities associated to the faces of the original polyhedron. With a suitable choice of the coordinate origin, accounting for the sequential character of the truncation, the volume parametrization becomes comoving with respect to the planes. This eliminates the necessity to establish topological connectivity and tetrahedron decomposition after each truncation. After a detailed mathematical description of the concept, we conduct a series of carefully designed numerical experiments to assess the performance in terms of polyhedron truncations. The high efficiency of the twophase positioning persists for sequential application, thereby being robust with respect to input data and possible intersection topologies. In comparison to an existing decompositionbased approach, the number of truncations was reduced by up to an order of magnitude.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 DOI:
 10.48550/arXiv.2105.08972
 arXiv:
 arXiv:2105.08972
 Bibcode:
 2021arXiv210508972K
 Keywords:

 Mathematics  Numerical Analysis;
 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Physics  Computational Physics