A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by hydrodynamic forces. However, for the vorticity-velocity form of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2024
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| Online Access: | https://hdl.handle.net/1721.1/155799 |
| _version_ | 1824457899532877824 |
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| author | Ji, Xinjie Gabbard, James van Rees, Wim M. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Ji, Xinjie Gabbard, James van Rees, Wim M. |
| author_sort | Ji, Xinjie |
| collection | MIT |
| description | Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by hydrodynamic forces. However, for the vorticity-velocity form of the Navier-Stokes equations, existing immersed geometry discretizations for two-way coupled problems only achieve first order spatial accuracy near solid boundaries. Here we introduce a sharp-interface approach based on the immersed interface method to handle the one- and two-way coupling between an incompressible flow and one or more rigid bodies using the 2D vorticity-velocity Navier-Stokes equations. Our main contributions are three-fold. First, we develop and analyze a moving boundary treatment for sharp immersed methods that can be applied to PDEs with implicitly defined boundary conditions, such as those commonly imposed on the vorticity field. Second, we develop a two-way coupling methodology for the vorticity-velocity Navier-Stokes equations based on control-volume momentum balance that does not require the pressure field. Third, we show through extensive testing and validation that our resulting flow-body solver reaches second-order accuracy for most practical scenarios, and provides significant efficiency benefits compared to a representative first-order approach. |
| first_indexed | 2024-09-23T08:43:20Z |
| format | Article |
| id | mit-1721.1/155799 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:17:20Z |
| publishDate | 2024 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1557992024-11-21T15:46:09Z A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations Ji, Xinjie Gabbard, James van Rees, Wim M. Massachusetts Institute of Technology. Department of Mechanical Engineering Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by hydrodynamic forces. However, for the vorticity-velocity form of the Navier-Stokes equations, existing immersed geometry discretizations for two-way coupled problems only achieve first order spatial accuracy near solid boundaries. Here we introduce a sharp-interface approach based on the immersed interface method to handle the one- and two-way coupling between an incompressible flow and one or more rigid bodies using the 2D vorticity-velocity Navier-Stokes equations. Our main contributions are three-fold. First, we develop and analyze a moving boundary treatment for sharp immersed methods that can be applied to PDEs with implicitly defined boundary conditions, such as those commonly imposed on the vorticity field. Second, we develop a two-way coupling methodology for the vorticity-velocity Navier-Stokes equations based on control-volume momentum balance that does not require the pressure field. Third, we show through extensive testing and validation that our resulting flow-body solver reaches second-order accuracy for most practical scenarios, and provides significant efficiency benefits compared to a representative first-order approach. 2024-07-29T16:11:29Z 2024-07-29T16:11:29Z 2023-12 2024-07-29T16:05:52Z Article http://purl.org/eprint/type/JournalArticle 0021-9991 https://hdl.handle.net/1721.1/155799 Ji, Xinjie, Gabbard, James and van Rees, Wim M. 2023. "A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations." Journal of Computational Physics, 494. en 10.1016/j.jcp.2023.112513 Journal of Computational Physics Creative Commons Attribution-Noncommercial-ShareAlike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Elsevier BV Author |
| spellingShingle | Ji, Xinjie Gabbard, James van Rees, Wim M. A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations |
| title | A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations |
| title_full | A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations |
| title_fullStr | A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations |
| title_full_unstemmed | A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations |
| title_short | A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations |
| title_sort | sharp immersed method for 2d flow body interactions using the vorticity velocity navier stokes equations |
| url | https://hdl.handle.net/1721.1/155799 |
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