Computing interface curvature from volume fractions: a machine learning approach

Research output: Contribution to journalArticleAcademicpeer-review

1 Downloads (Pure)

Abstract

The volume of fluid (VOF) method is widely used to simulate the flow of immiscible fluids. It uses a discrete and sharp volume fractions field to represent the fluid-fluid interface on a Eulerian grid. The most challenging part of the VOF method is the accurate computation of the local interface curvature which is essential for evaluation of the surface tension force at the interface. In this paper, a machine learning approach is used to develop a model which predicts the local interface curvature from neighbouring volume fractions. A novel data generation methodology is devised which generates well-balanced randomized data sets comprising of spherical interface patches of different configurations/orientations. A two-layer feed-forward neural network with different network parameters is trained on these data sets and the developed models are tested for different shapes i.e. ellipsoid, 3D wave and Gaussian. The best model is selected on the basis of specific criteria and subsequently compared with conventional curvature computation methods (convolution and height function) to check the nature and grid convergence of the model. The model is also coupled with a multiphase flow solver to evaluate its performance using standard test cases: i) stationary bubble, ii) oscillating bubble and iii) rising bubble under gravity. Our results demonstrate that machine learning is a feasible approach for fairly accurate curvature computation. It easily outperforms the convolution method and even matches the accuracy of the height function method for some test cases.

Original languageEnglish
Article number104263
Number of pages15
JournalComputers and Fluids
Volume193
DOIs
Publication statusPublished - 30 Oct 2019

Fingerprint

Learning systems
Volume fraction
Fluids
Convolution
Multiphase flow
Feedforward neural networks
Surface tension
Flow of fluids
Gravitation

Keywords

  • Curvature computation
  • Grace diagram
  • Machine learning
  • Multiphase flow
  • Neural network
  • Volume of fluid

Cite this

@article{efa8b4c61106460fb23cf2bad6a91fee,
title = "Computing interface curvature from volume fractions: a machine learning approach",
abstract = "The volume of fluid (VOF) method is widely used to simulate the flow of immiscible fluids. It uses a discrete and sharp volume fractions field to represent the fluid-fluid interface on a Eulerian grid. The most challenging part of the VOF method is the accurate computation of the local interface curvature which is essential for evaluation of the surface tension force at the interface. In this paper, a machine learning approach is used to develop a model which predicts the local interface curvature from neighbouring volume fractions. A novel data generation methodology is devised which generates well-balanced randomized data sets comprising of spherical interface patches of different configurations/orientations. A two-layer feed-forward neural network with different network parameters is trained on these data sets and the developed models are tested for different shapes i.e. ellipsoid, 3D wave and Gaussian. The best model is selected on the basis of specific criteria and subsequently compared with conventional curvature computation methods (convolution and height function) to check the nature and grid convergence of the model. The model is also coupled with a multiphase flow solver to evaluate its performance using standard test cases: i) stationary bubble, ii) oscillating bubble and iii) rising bubble under gravity. Our results demonstrate that machine learning is a feasible approach for fairly accurate curvature computation. It easily outperforms the convolution method and even matches the accuracy of the height function method for some test cases.",
keywords = "Curvature computation, Grace diagram, Machine learning, Multiphase flow, Neural network, Volume of fluid",
author = "H.V. Patel and A. Panda and J.A.M. Kuipers and E.A.J.F. Peters",
year = "2019",
month = "10",
day = "30",
doi = "10.1016/j.compfluid.2019.104263",
language = "English",
volume = "193",
journal = "Computers & Fluids",
issn = "0045-7930",
publisher = "Elsevier",

}

TY - JOUR

T1 - Computing interface curvature from volume fractions

T2 - a machine learning approach

AU - Patel, H.V.

AU - Panda, A.

AU - Kuipers, J.A.M.

AU - Peters, E.A.J.F.

PY - 2019/10/30

Y1 - 2019/10/30

N2 - The volume of fluid (VOF) method is widely used to simulate the flow of immiscible fluids. It uses a discrete and sharp volume fractions field to represent the fluid-fluid interface on a Eulerian grid. The most challenging part of the VOF method is the accurate computation of the local interface curvature which is essential for evaluation of the surface tension force at the interface. In this paper, a machine learning approach is used to develop a model which predicts the local interface curvature from neighbouring volume fractions. A novel data generation methodology is devised which generates well-balanced randomized data sets comprising of spherical interface patches of different configurations/orientations. A two-layer feed-forward neural network with different network parameters is trained on these data sets and the developed models are tested for different shapes i.e. ellipsoid, 3D wave and Gaussian. The best model is selected on the basis of specific criteria and subsequently compared with conventional curvature computation methods (convolution and height function) to check the nature and grid convergence of the model. The model is also coupled with a multiphase flow solver to evaluate its performance using standard test cases: i) stationary bubble, ii) oscillating bubble and iii) rising bubble under gravity. Our results demonstrate that machine learning is a feasible approach for fairly accurate curvature computation. It easily outperforms the convolution method and even matches the accuracy of the height function method for some test cases.

AB - The volume of fluid (VOF) method is widely used to simulate the flow of immiscible fluids. It uses a discrete and sharp volume fractions field to represent the fluid-fluid interface on a Eulerian grid. The most challenging part of the VOF method is the accurate computation of the local interface curvature which is essential for evaluation of the surface tension force at the interface. In this paper, a machine learning approach is used to develop a model which predicts the local interface curvature from neighbouring volume fractions. A novel data generation methodology is devised which generates well-balanced randomized data sets comprising of spherical interface patches of different configurations/orientations. A two-layer feed-forward neural network with different network parameters is trained on these data sets and the developed models are tested for different shapes i.e. ellipsoid, 3D wave and Gaussian. The best model is selected on the basis of specific criteria and subsequently compared with conventional curvature computation methods (convolution and height function) to check the nature and grid convergence of the model. The model is also coupled with a multiphase flow solver to evaluate its performance using standard test cases: i) stationary bubble, ii) oscillating bubble and iii) rising bubble under gravity. Our results demonstrate that machine learning is a feasible approach for fairly accurate curvature computation. It easily outperforms the convolution method and even matches the accuracy of the height function method for some test cases.

KW - Curvature computation

KW - Grace diagram

KW - Machine learning

KW - Multiphase flow

KW - Neural network

KW - Volume of fluid

UR - http://www.scopus.com/inward/record.url?scp=85072269289&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2019.104263

DO - 10.1016/j.compfluid.2019.104263

M3 - Article

AN - SCOPUS:85072269289

VL - 193

JO - Computers & Fluids

JF - Computers & Fluids

SN - 0045-7930

M1 - 104263

ER -