# A hybrid particle volume-of-fluid method for curvature estimation in multiphase flows

## TL;DR

This paper introduces a hybrid particle-based curvature estimation method for multiphase flow simulations, combining particles and height functions to improve accuracy especially for under-resolved interfaces.

## Contribution

A novel hybrid particle and height function method for curvature estimation that outperforms existing techniques in multiphase flow simulations.

## Key findings

- More accurate curvature estimation in under-resolved interfaces.
- Effective in both 2D and 3D multiphase flow benchmarks.
- Enhances simulation capabilities for complex flow phenomena.

## Abstract

We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic fitting that is employed in such cases. The curvature is computed from the equilibrium positions of particles constrained to circular arcs and attracted to the interface. The proposed particle method is combined with the method of height functions at higher resolutions, and it is shown to outperform the current combinations of height functions and parabolic fitting. The algorithm is conceptually simple and straightforward to implement on new and existing software frameworks for multiphase flow simulations thus enhancing their capabilities in challenging flow problems. We evaluate the proposed hybrid method on a number of two- and three-dimensional benchmark flow problems and illustrate its capabilities on simulations of flows involving bubble coalescence and turbulent multiphase flows.