Interfacial gauge methods for incompressible fluid dynamics
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 NavierStokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing highorder accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, highorder results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourthorder spatial accuracy in the maximum norm. Applications are demonstrated with twophase fluid flow displaying finescaled capillary wave dynamics, rigid body fluidstructure interaction, and a fluidjet free surface flow problem exhibiting vortex shedding induced by a type of PlateauRayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.
 Authors:

^{[1]}
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Mathematics Group
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Science Advances
 Additional Journal Information:
 Journal Volume: 2; Journal Issue: 6; Journal ID: ISSN 23752548
 Publisher:
 AAAS
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING
 OSTI Identifier:
 1379359
Saye, R. Interfacial gauge methods for incompressible fluid dynamics. United States: N. p.,
Web. doi:10.1126/sciadv.1501869.
Saye, R. Interfacial gauge methods for incompressible fluid dynamics. United States. doi:10.1126/sciadv.1501869.
Saye, R. 2016.
"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 NavierStokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing highorder accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, highorder results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourthorder spatial accuracy in the maximum norm. Applications are demonstrated with twophase fluid flow displaying finescaled capillary wave dynamics, rigid body fluidstructure interaction, and a fluidjet free surface flow problem exhibiting vortex shedding induced by a type of PlateauRayleigh 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}
}