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Title: Interfacial gauge methods for incompressible fluid dynamics

Abstract

Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.

Authors:
 [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Mathematics Group
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1379359
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Science Advances
Additional Journal Information:
Journal Volume: 2; Journal Issue: 6; Journal ID: ISSN 2375-2548
Publisher:
AAAS
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING

Citation Formats

Saye, R. Interfacial gauge methods for incompressible fluid dynamics. United States: N. p., 2016. Web. doi:10.1126/sciadv.1501869.
Saye, R. Interfacial gauge methods for incompressible fluid dynamics. United States. doi:10.1126/sciadv.1501869.
Saye, R. Fri . "Interfacial gauge methods for incompressible fluid dynamics". United States. doi:10.1126/sciadv.1501869. https://www.osti.gov/servlets/purl/1379359.
@article{osti_1379359,
title = {Interfacial gauge methods for incompressible fluid dynamics},
author = {Saye, R.},
abstractNote = {Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.},
doi = {10.1126/sciadv.1501869},
journal = {Science Advances},
number = 6,
volume = 2,
place = {United States},
year = {2016},
month = {6}
}

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