Conservative and skew-symmetric forms of the incompressible Navier-Stokes equations in sigma-coordinates
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917431720542208 |
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| author | Jung, Jaeyoung Giometto, Marco |
| author_facet | Jung, Jaeyoung Giometto, Marco |
| contents | This study derives conservative and skew-symmetric formulations of the incompressible flow equations in a terrain-following sigma-coordinate system that preserve key structural properties of the Cartesian formulation. Unlike conventional formulations based on the direct application of the sigma-transformation to Cartesian equations, in which metric-induced terms disrupt the intrinsic structure of the governing equations, the proposed formulations are designed to avoid these structural inconsistencies. A conservative form is derived in a manner consistent with general conservation laws, and its modified eigenstructure is analyzed relative to the Cartesian counterpart. A skew-symmetric formulation is then derived by introducing a new set of variables, yielding a form that is energy-conserving for the Euler equations and energy-bounded for the Navier-Stokes equations. Finally, we discuss characteristic-based boundary conditions to ensure energy boundedness of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22060 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conservative and skew-symmetric forms of the incompressible Navier-Stokes equations in sigma-coordinates Jung, Jaeyoung Giometto, Marco Fluid Dynamics This study derives conservative and skew-symmetric formulations of the incompressible flow equations in a terrain-following sigma-coordinate system that preserve key structural properties of the Cartesian formulation. Unlike conventional formulations based on the direct application of the sigma-transformation to Cartesian equations, in which metric-induced terms disrupt the intrinsic structure of the governing equations, the proposed formulations are designed to avoid these structural inconsistencies. A conservative form is derived in a manner consistent with general conservation laws, and its modified eigenstructure is analyzed relative to the Cartesian counterpart. A skew-symmetric formulation is then derived by introducing a new set of variables, yielding a form that is energy-conserving for the Euler equations and energy-bounded for the Navier-Stokes equations. Finally, we discuss characteristic-based boundary conditions to ensure energy boundedness of the system. |
| title | Conservative and skew-symmetric forms of the incompressible Navier-Stokes equations in sigma-coordinates |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2604.22060 |