An Interface Tracking Method with Triangle Edge Cuts

TL;DR

This paper presents a novel volume-conserving interface tracking method on unstructured triangle meshes using triangle edge cuts for efficient implicit interface representation and advection without optimization.

Contribution

It introduces a new interface tracking algorithm with a compact representation and volume-preserving advection, improving efficiency and accuracy over existing methods.

Findings

The method accurately tracks interfaces on unstructured meshes.

It conserves volume during advection without complex optimization.

Performance comparisons show advantages over VOF and MOF methods.

Abstract

This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.