Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912634026065920 |
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| author | Kaiser, Michael Wolfgang Fries, Thomas-Peter |
| author_facet | Kaiser, Michael Wolfgang Fries, Thomas-Peter |
| contents | A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by all level sets of a scalar function, bounded by the three-dimensional bulk domain. This bulk domain is discretized with hexahedral finite elements which do not necessarily conform with the level sets but with the boundary. The resulting numerical method is a hybrid between conforming and non-conforming finite element methods. Taylor-Hood elements or equal-order element pairs for velocity and pressure, together with stabilization techniques, are applied to fulfil the inf-sup conditions resulting from the mixed-type formulation of the governing equations. Numerical studies confirm good agreement with independently obtained solutions on selected, individual surfaces. Furthermore, higher-order convergence rates are obtained for sufficiently smooth solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces Kaiser, Michael Wolfgang Fries, Thomas-Peter Computational Engineering, Finance, and Science A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by all level sets of a scalar function, bounded by the three-dimensional bulk domain. This bulk domain is discretized with hexahedral finite elements which do not necessarily conform with the level sets but with the boundary. The resulting numerical method is a hybrid between conforming and non-conforming finite element methods. Taylor-Hood elements or equal-order element pairs for velocity and pressure, together with stabilization techniques, are applied to fulfil the inf-sup conditions resulting from the mixed-type formulation of the governing equations. Numerical studies confirm good agreement with independently obtained solutions on selected, individual surfaces. Furthermore, higher-order convergence rates are obtained for sufficiently smooth solutions. |
| title | Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2502.09355 |