A Structure Preserving Finite Volume Scheme for the Navier-Stokes-Korteweg Equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912820275183616 |
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| author | Giesselmann, Jan Öffner, Philipp Sauerborn, Robert |
| author_facet | Giesselmann, Jan Öffner, Philipp Sauerborn, Robert |
| contents | We present a semi-discrete finite volume scheme for the local NavierStokes-Korteweg and Euler-Korteweg systems. Our scheme is applicable for equidistant Cartesian meshes in one and two space dimensions. In contrast to other works, which employ, for example, hyperbolic approximations of the equations or auxiliary-variable approaches leading to extended systems, our scheme operates directly on the original system. We prove that it conserves mass and momentum and is energy stable. Numerical experiments complement our theoretical findings, showing that the scheme is convergent of order one if employed with explicit or implicit time discretisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Structure Preserving Finite Volume Scheme for the Navier-Stokes-Korteweg Equations Giesselmann, Jan Öffner, Philipp Sauerborn, Robert Numerical Analysis 65M08, 65M12 We present a semi-discrete finite volume scheme for the local NavierStokes-Korteweg and Euler-Korteweg systems. Our scheme is applicable for equidistant Cartesian meshes in one and two space dimensions. In contrast to other works, which employ, for example, hyperbolic approximations of the equations or auxiliary-variable approaches leading to extended systems, our scheme operates directly on the original system. We prove that it conserves mass and momentum and is energy stable. Numerical experiments complement our theoretical findings, showing that the scheme is convergent of order one if employed with explicit or implicit time discretisation. |
| title | A Structure Preserving Finite Volume Scheme for the Navier-Stokes-Korteweg Equations |
| topic | Numerical Analysis 65M08, 65M12 |
| url | https://arxiv.org/abs/2601.08498 |