# High-resolution transport of regional level sets for evolving complex interface networks

## TL;DR

This paper introduces a high-resolution regional level-set method that improves the accuracy of simulating complex interface network evolutions while maintaining comparable computational costs to existing methods.

## Contribution

It presents a novel high-resolution transport formulation with local level set construction and reconstruction, enhancing the prediction of complex interface networks.

## Key findings

- Accurate simulation of complex interface network evolutions.
- Comparable computational cost to existing semi-Lagrangian methods.
- Significantly improved prediction accuracy.

## Abstract

In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local level sets and reconstruction of a global regional level sets, (ii) locally transporting the interface network by employing high-order spatial discretization schemes for improved representation of complex topologies. Various numerical test cases of multi-region flow problems, including triple-point advection, single vortex flow, mean curvature flow, normal driven flow and dry foam dynamics, show that the method is accurate and suitable for a wide range of complex interface-network evolutions. Its overall computational cost is comparable to the Semi-Lagrangian regional level-set method while the prediction accuracy is significantly improved. The approach thus offers a \textbf{viable} alternative to previous interface-network level-set method.