Streamfunction-vorticity formulation for incompressible viscid and inviscid flows on general surfaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912786599116800 |
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| author | Brüers, Tim Lehrenfeld, Christoph Wardetzky, Max |
| author_facet | Brüers, Tim Lehrenfeld, Christoph Wardetzky, Max |
| contents | This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a fundamental role in the dynamics. By relying only on scalar and finite-dimensional quantities, our formulation ensures that the resulting methods give exactly tangential and incompressible velocity fields, while also being pressure robust. Compared to traditional methods based on velocity-pressure formulations, where one can only guarantee these structural properties by increasing the computational costs, this is a key advantage. We rigorously validate our formulation by proving its equivalence to the well understood velocity-pressure formulation under reasonable regularity assumptions. Furthermore, we demonstrate the applicability of the approach with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Streamfunction-vorticity formulation for incompressible viscid and inviscid flows on general surfaces Brüers, Tim Lehrenfeld, Christoph Wardetzky, Max Numerical Analysis This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a fundamental role in the dynamics. By relying only on scalar and finite-dimensional quantities, our formulation ensures that the resulting methods give exactly tangential and incompressible velocity fields, while also being pressure robust. Compared to traditional methods based on velocity-pressure formulations, where one can only guarantee these structural properties by increasing the computational costs, this is a key advantage. We rigorously validate our formulation by proving its equivalence to the well understood velocity-pressure formulation under reasonable regularity assumptions. Furthermore, we demonstrate the applicability of the approach with numerical examples. |
| title | Streamfunction-vorticity formulation for incompressible viscid and inviscid flows on general surfaces |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.20763 |