# On algebraic TVD-VOF methods for tracking material interfaces

## TL;DR

This paper improves algebraic TVD-VOF methods for interface tracking by introducing a CFL-dependent limiter, achieving sharper interfaces with limited numerical diffusion and comparable efficiency to geometrical VOF methods.

## Contribution

It presents a novel CFL-dependent limiter that enhances algebraic TVD-VOF methods, surpassing classical bounds for better interface sharpness.

## Key findings

- Crisp numerical interfaces with limited atomization.
- Larger error compared to geometrical VOF at same resolution.
- Comparable efficiency when considering computational cost.

## Abstract

We revisit simple algebraic VOF methods for advection of material interfaces based of the well established TVD paradigm. We show that greatly improved representation of contact discontinuities is obtained through use of a novel CFL-dependent limiter whereby the classical TVD bounds are exceeded. Perfectly crisp numerical interfaces are obtained with very limited numerical atomization (flotsam and jetsam) as compared to previous SLIC schemes. Comparison of the algorithm with accurate geometrical VOF shows larger error at given mesh resolution, but comparable efficiency when the reduced computational cost is accounted for.