A volume-preserving reference map method for the level set representation

Maxime Theillard

doi:10.1016/j.jcp.2021.110478

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A volume-preserving reference map method for the level set representation

2021-10-01

Maxime Theillard *

DOI：10.1016/j.jcp.2021.110478

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Abstract

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This paper presents an implicit interface representation, where the geometry is captured by a level set function and its deformations are reconstructed from diffeomorphism between the warped and original geometries (the reference map). A key advantage of this representation is that it provides a local estimation of numerical local mass losses. Using this metric, we design a novel projection for the reference map on the space of volume preserving diffeomorphisms which results in enhanced, but inexact, mass conservation. In the limit of small deviations from this space, the projection is shown to be uniquely defined, and the correction can be computed as the solution of a Poisson problem. The method is analyzed and validated in two and three spatial dimensions. Both the theoretical and computational results show it excels at correcting the mass loss due to inaccuracy in the advection process or the velocity field. While this error reduction does not manifest for analytical problems, it is evident for practical applications such as the simulation of multiphase flows over long time intervals and offers improved computational exploration capabilities. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Keywords:

Interfacial problems

Level set

Reference map

Mass conservation

Volume-preserving

Two-phase flows

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