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Title: Interfacial gauge methods for incompressible fluid dynamics

Journal Article · · Science Advances
 [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Mathematics Group
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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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1379359
Journal Information:
Science Advances, Vol. 2, Issue 6; ISSN 2375-2548
Publisher:
AAASCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

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A new mixed potential representation for the equations of unsteady, incompressible flow preprint January 2018

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