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Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces


Smolianski, A (2005). Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces. International Journal for Numerical Methods in Fluids, 48(3):231-269.

Abstract

The present work is devoted to the study of unsteady flows of two immiscible viscous fluids separated by a freely moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits us to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows us to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh-Taylor instability are presented to validate the computational method.

The present work is devoted to the study of unsteady flows of two immiscible viscous fluids separated by a freely moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits us to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows us to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh-Taylor instability are presented to validate the computational method.

Citations

29 citations in Web of Science®
31 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:two-fluid interfacial flow;surface tension;Navier–Stokes equations;free moving boundary;finite element method;operator-splitting;level-set approach
Language:English
Date:2005
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Wiley-Blackwell
ISSN:0271-2091
Publisher DOI:10.1002/fld.823

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