Face-based Volume-of-Fluid interface positioning in arbitrary polyhedra

by   Johannes Kromer, et al.

We introduce a fast and robust algorithm for finding a plane Γ with given normal n⃗_Γ, which truncates an arbitrary polyhedron 𝒫 such that the remaining sub-polyhedron admits a given volume α|𝒫|. In the literature, this is commonly referred to as Volume-of-Fluid (VoF) interface positioning problem. The novelty of our work is twofold: firstly, by recursive application of the Gaussian divergence theorem, the volume of a truncated polyhedron can be computed at high efficiency, based on summation over quantities associated to the faces of the polyhedron. One obtains a very convenient piecewise parametrization (within so-called brackets) in terms of the signed distance s to the plane Γ. As an implication, one can restrain from the costly necessity to establish topological connectivity, rendering the present approach most suitable for the application to unstructured computational meshes. Secondly, in the vicinity of the truncation position s, the volume can be expressed exactly, i.e. in terms of a cubic polynomial of the normal distance to the PLIC plane. The local knowledge of derivatives enables to construct a root-finding algorithm that pairs bracketing and higher-order approximation. The performance is assessed by conducting an extensive set of numerical experiments, considering convex and non-convex polyhedra of genus (i.e., number of holes) zero and one in combination with carefully selected volume fractions α (including α≈0 and α≈1) and normal orientations n⃗_Γ. For all configurations we obtain a significant reduction of the number of (computationally costly) truncations required for the positioning: on average, our algorithm requires between one and two polyhedron truncations to find the position of the plane Γ, outperforming existing methods.


page 3

page 5

page 8

page 9

page 11

page 20

page 21

page 28


Efficient three-material PLIC interface positioning on unstructured polyhedral meshes

This paper introduces an efficient algorithm for the sequential position...

A Deep Learning Algorithm for Piecewise Linear Interface Construction (PLIC)

Piecewise Linear Interface Construction (PLIC) is frequently used to geo...

Second-order accurate normal reconstruction from volume fractions on unstructured meshes with arbitrary polyhedral cells

This paper introduces a novel method for the efficient second-order accu...

Third-order accurate initialization of VOF volume fractions on unstructured meshes with arbitrary polyhedral cells

This paper introduces a novel method for the efficient and accurate comp...

a Decision-Tree based Moment-of-Fluid (DTMOF) Method in 3D rectangular hexahedrons

The moment-of-fluid (MOF) method is an extension of the volume-of-fluid ...

NPLIC: A Machine Learning Approach to Piecewise Linear Interface Construction

Volume of fluid (VOF) methods are extensively used to track fluid interf...

The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics

We extend the recently introduced divergence-conforming immersed boundar...

Please sign up or login with your details

Forgot password? Click here to reset