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

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] ,...
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Publisher
Elsevier
Copyright
Copyright © 2017 Elsevier Ltd
ISSN
0301-9322
D.O.I.
10.1016/j.ijmultiphaseflow.2017.08.003
Publisher site
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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

References

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