A Semi-Discrete Optimal Transport Scheme for the 3D Incompressible Semi-Geostrophic Equations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917265014784000 |
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| author | Lavier, Théo |
| author_facet | Lavier, Théo |
| contents | We describe a mesh-free three-dimensional numerical scheme for solving the incompressible semi-geostrophic equations based on semi-discrete optimal transport techniques. These results generalise previous two-dimensional implementations. The optimal transport methods we adopt are known for their structural preservation and energy conservation qualities and achieve an excellent level of efficiency and numerical energy-conservation. We use this scheme to generate numerical simulations of an important cyclone benchmark problem. To our knowledge, this is the first fully three-dimensional simulation of the semi-geostrophic equations, evidencing semi-discrete optimal transport as a novel, robust numerical tool for meteorological and oceanographic modelling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Semi-Discrete Optimal Transport Scheme for the 3D Incompressible Semi-Geostrophic Equations Lavier, Théo Numerical Analysis We describe a mesh-free three-dimensional numerical scheme for solving the incompressible semi-geostrophic equations based on semi-discrete optimal transport techniques. These results generalise previous two-dimensional implementations. The optimal transport methods we adopt are known for their structural preservation and energy conservation qualities and achieve an excellent level of efficiency and numerical energy-conservation. We use this scheme to generate numerical simulations of an important cyclone benchmark problem. To our knowledge, this is the first fully three-dimensional simulation of the semi-geostrophic equations, evidencing semi-discrete optimal transport as a novel, robust numerical tool for meteorological and oceanographic modelling. |
| title | A Semi-Discrete Optimal Transport Scheme for the 3D Incompressible Semi-Geostrophic Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.00575 |