A projection method for motion of triple junctions by level sets.
type: Item
instance of: scholarly article
title: A projection method for motion of triple junctions by level sets.
zbMATH Open document ID: 1112.76437
DOI: 10.4171/IFB/61
author: Kurt A. Smith
author: Francisco J. Solis
author: D. L. Chopp
published in: Interfaces and Free Boundaries
publication date: 2002-08-28T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: We develop a projection method to treat the motion of multiple junctions (such as contact lines) in the level set formulation. Multiple junctions are relevant to many fields including fluid dynamics, foams, and semiconductor manufacture. In the level set method an interface is defined as the zero level set of a smooth function. For an \(N\)-phase system the location of all interfaces can be specified by \(N-1\) functions (hence only one level set function is needed for a two-phase system). For \(N>2\) we describe a symmetric projection of the \(N\) level set functions onto an \((N-1)\)-dimensional manifold. This reduction in phase space eliminates unacceptable values of the level set functions (such as cases where more than one is positive at a given point). This prevents the formation of vacuums or overlaps at multiple junctions during interface evolution. Further, this method can be applied to any number of phases and spatial dimensions. We present two- and three-dimensional results showing that the method gives correct equilibrium contact angles and produces accurate dynamics in multi-phase fluids.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 76T30
zbMATH DE Number: 1791240
MaRDI profile type: Publication
OpenAlex ID: W1984835880
description: scientific article; zbMATH DE number 1791240