Efficient sequential PLIC interface positioning for enhanced performance of the three-phase VoF Method

This paper presents an efficient algorithm for the sequential positioning, also called nested dissection, of two planes in an arbitrary polyhedron. Two planar interfaces are positioned such that the first plane truncates a given volume from this arbitrary polyhedron and the next plane truncates a second given volume from the residual polyhedron. This is a relevant task in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid (VoF) method with a Piecewise Linear Interface Calculation (PLIC). An efficient algorithm for this task significantly speeds up the three-phase PLIC algorithm. The present study describes a method based on a recursive application of the Gaussian divergence theorem, where the fact that the truncated polyhedron shares multiple faces with the original polyhedron can be exploited to reduce the computational effort. A careful choice of the coordinate system origin for the volume computation allows for successive positioning of two planes without reestablishing polyhedron connectivity. Combined with a highly efficient root finding, this results in a significant performance gain in the reconstruction of the three-phase interface configurations. The performance of the new method is assessed in a series of carefully designed numerical experiments. Compared to a conventional decomposition-based approach, the number of iterations and, thus, of the required truncations was reduced by up to an order of magnitude. The PLIC positioning run-time was reduced by about 90% in our reference implementation. Integrated into the multi-phase flow solver Free Surface 3D (FS3D), an overall performance gain of about 20% was achieved. Allowing for simple integration into existing numerical schemes, the proposed algorithm is self-contained (example Fortran Module see https://doi.org/10.18419/darus-2488), requiring no external decomposition libraries.