An Eulerian label advection method for conservative volume-based tracking of bubbles/droplets
Name
2023-08 ELA_Paper_Final.pdf
Description
Accepted version
Size
6.77 MB
Format
Adobe PDF
Checksum (MD5)
8eb087de8244c576a29078655cbbdfe0
Author(s)
Gaylo, Declan B.
Hendrickson, Kelli
Yue, Dick K.P.
Date Issued
December 2022
Journal
Journal of Computational Physics
Publisher
Elsevier BV
Citation
Gaylo, Declan B., Hendrickson, Kelli and Yue, Dick K.P. 2022. "An Eulerian label advection method for conservative volume-based tracking of bubbles/droplets." Journal of Computational Physics, 470.
Version
Author's final manuscript
Abstract
We develop a robust volume-conservative framework for tracking blob evolution in complex two-phase flow that accurately and uniquely obtains the volume transfer among bubbles/droplets (blobs). This new framework is built on a volume-tracking matrix (VTM) that quantifies the volume transfer between any two blobs in two separated instances (snapshots) during the evolution, and an efficient Eulerian label advection (ELA) algorithm that explicitly provides the unique, consistent, volume-conservative VTM. Given a set of blobs defined at a snapshot by, say, a connected-component labeling (CCL) method and the grid-level volume-fraction flux from the conservative Volume of Fluid (cVOF) method, ELA gives the VTM by solving the Eulerian flow of each blob's fluid through time. Due to its grid-level Eulerian nature, ELA is independent of the complexity of the blob-level evolution, including high-arity (tertiary, quaternary, etc.) events and cycles which prevent previous methods from obtaining the VTM. We prove theoretically that ELA is volume-conservative to machine precision, with the same Courant restriction as cVOF. Furthermore, we show that, by allowing a diffusive error, multiplying the VTM obtains volume-conservative tracking over longer intervals without increasing the computational cost of ELA. We verify all these results using extensive simulations of evolving blob populations in flows with prescribed velocity and isotropic homogeneous turbulence (IHT).
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcp.2022.111560
