# On a relation between the volume of fluid, level-set and phase field interface models

On a relation between the volume of fluid, level-set and phase field interface models •The relation between the sharp and diffusive interface models is established. •A statistical model of the non-flat interface is introduced. •The new Lagrangian scheme for advection of the level-set functions is derived. •The second-order convergence rates of the advected interface shape and curvature are obtained using the second order accurate discretization. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Multiphase Flow Elsevier

# On a relation between the volume of fluid, level-set and phase field interface models

International Journal of Multiphase Flow, Volume 97 – Dec 1, 2017

## On a relation between the volume of fluid, level-set and phase field interface models

Article history: This paper discusses a relation between the re-initialization equation of the level-set functions derived Received 22 December 2016 by Wacławczyk [ J. Comput. Phys. , 299 (2015)] and the condition for the phase equilibrium provided by the Revised 25 July 2017 stationary solution to the modiﬁed Allen-Cahn equation [ Acta Metall. , 27 (1979)]. As a consequence, the Accepted 3 August 2017 statistical model of the non-ﬂat interface in the state of phase equilibrium is postulated. This new phys- Available online 4 August 2017 ical model of the non-ﬂat interface is introduced based on the statistical picture of the sharp interface disturbed by the ﬁeld of stochastic forces, it yields the relation between the sharp and diffusive interface Keywords: Statistical interface model models. Furthermore, the new techniques required for the accurate solution of the model equations are Volume of ﬂuid method proposed. First it is shown, the constrained interpolation improves re-initialization of the level-set func- Conservative level-set method tions as it avoids oscillatory numerical errors typical for the second-order accurate interpolation schemes. Phase ﬁeld method Next, the new semi-analytical, second order accurate Lagrangian scheme is put forward to integrate the Multiphase ﬂows advection equation in time avoiding interface curvature oscillations introduced by the second-order accu- rate ﬂux limiters. These techniques provide means to obtain complete, second-order convergence during advection and re-initialization of the interface in the state of phase equilibrium. ©2017 Elsevier Ltd. All rights reserved. 1. Introduction The sharp interface model is the cornerstone of the volume of ﬂuid (VOF) family of numerical methods, see Tryggvason et al. Experiments reveal the macroscopic interface is a region of a ﬁ- (2011) . The key problem there is numerical approximation of the transport equation nite thickness  ∼ k T /σ [ m] ,...

/lp/elsevier/on-a-relation-between-the-volume-of-fluid-level-set-and-phase-field-G9xOReYHEB
Publisher
Elsevier
ISSN
0301-9322
D.O.I.
10.1016/j.ijmultiphaseflow.2017.08.003
Publisher site
See Article on Publisher Site

### Abstract

•The relation between the sharp and diffusive interface models is established. •A statistical model of the non-flat interface is introduced. •The new Lagrangian scheme for advection of the level-set functions is derived. •The second-order convergence rates of the advected interface shape and curvature are obtained using the second order accurate discretization.

### Journal

International Journal of Multiphase FlowElsevier

Published: Dec 1, 2017

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