Manifold death: a Volume of Fluid implementation of controlled topological changes in thin sheets by the signature method

TL;DR

This paper introduces a novel algorithm for controlled topological changes in thin liquid sheets within the Volume of Fluid method, improving the physical accuracy of droplet breakup simulations by inducing perforations before numerical artifacts occur.

Contribution

The authors develop a multiscale algorithm that detects thin structures and induces perforations to simulate breakup, enhancing convergence and physical realism in VOF simulations.

Findings

Improved convergence of droplet size distribution with grid refinement

Enhanced physical accuracy of thin film rupture modeling

Better control over topological changes in fluid simulations

Abstract

A well-known drawback of the Volume-Of-Fluid (VOF) method is that the breakup of thin liquid films or filaments is mainly caused by numerical aspects rather than by physical ones. The rupture of thin films occurs when their thickness reaches the order of the grid size and by refining the grid the breakup events are delayed. When thin filaments rupture, many droplets are generated due to the mass conserving properties of VOF. Thus, the numerical character of the breakup does not allow obtaining the desired convergence of the droplet size distribution under grid refinement. In this work, we present a novel algorithm to detect and perforate thin structures. First, thin films or ligaments are identified by taking quadratic moments of an indicator obtained from the volume fraction. A multiscale approach allows us to choose the critical film thickness independently of the mesh resolution. Then, the breakup is induced by making holes in the films before their thickness reaches the grid size. We show that the method improves the convergence upon grid refinement of the droplets size distribution and of enstrophy.