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A stable numerical method for the dynamics of fluidic membranes
We develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in Navier–Stokes flow. Local inextensibility of the membrane is ensured by solving a tangential Navier–Stokes equation, taking surface viscosity effects of Boussinesq–Scriven type into accou...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5444514/ https://www.ncbi.nlm.nih.gov/pubmed/28603298 http://dx.doi.org/10.1007/s00211-015-0787-5 |
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author | Barrett, John W. Garcke, Harald Nürnberg, Robert |
author_facet | Barrett, John W. Garcke, Harald Nürnberg, Robert |
author_sort | Barrett, John W. |
collection | PubMed |
description | We develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in Navier–Stokes flow. Local inextensibility of the membrane is ensured by solving a tangential Navier–Stokes equation, taking surface viscosity effects of Boussinesq–Scriven type into account. In our approach the bulk and surface degrees of freedom are discretized independently, which leads to an unfitted finite element approximation of the underlying free boundary problem. Bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by Dziuk (Numer Math 111:55-80, 2008). The obtained numerical scheme can be shown to be stable and to have good mesh properties. Finally, the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions. The numerical results demonstrate the robustness of the method, and it is observed that the conservation properties are fulfilled to a high precision. |
format | Online Article Text |
id | pubmed-5444514 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-54445142017-06-09 A stable numerical method for the dynamics of fluidic membranes Barrett, John W. Garcke, Harald Nürnberg, Robert Numer Math (Heidelb) Article We develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in Navier–Stokes flow. Local inextensibility of the membrane is ensured by solving a tangential Navier–Stokes equation, taking surface viscosity effects of Boussinesq–Scriven type into account. In our approach the bulk and surface degrees of freedom are discretized independently, which leads to an unfitted finite element approximation of the underlying free boundary problem. Bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by Dziuk (Numer Math 111:55-80, 2008). The obtained numerical scheme can be shown to be stable and to have good mesh properties. Finally, the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions. The numerical results demonstrate the robustness of the method, and it is observed that the conservation properties are fulfilled to a high precision. Springer Berlin Heidelberg 2016-02-23 2016 /pmc/articles/PMC5444514/ /pubmed/28603298 http://dx.doi.org/10.1007/s00211-015-0787-5 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Barrett, John W. Garcke, Harald Nürnberg, Robert A stable numerical method for the dynamics of fluidic membranes |
title | A stable numerical method for the dynamics of fluidic membranes |
title_full | A stable numerical method for the dynamics of fluidic membranes |
title_fullStr | A stable numerical method for the dynamics of fluidic membranes |
title_full_unstemmed | A stable numerical method for the dynamics of fluidic membranes |
title_short | A stable numerical method for the dynamics of fluidic membranes |
title_sort | stable numerical method for the dynamics of fluidic membranes |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5444514/ https://www.ncbi.nlm.nih.gov/pubmed/28603298 http://dx.doi.org/10.1007/s00211-015-0787-5 |
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