Asymptotically well-balanced geostrophic reconstruction finite volumes numerical schemes for the 2D rotating NLSWE in spherical coordinates
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| Format: | Preprint |
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2025
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| _version_ | 1866917023686066176 |
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| author | del Pino, Alejandro González Díaz, Manuel Jesús Castro Sánchez, Jorge Macías |
| author_facet | del Pino, Alejandro González Díaz, Manuel Jesús Castro Sánchez, Jorge Macías |
| contents | The dynamics of large-scale geophysical fluids is primarily governed by the balance between the Coriolis force and the pressure gradient.
This phenomenon, known as geostrophic equilibrium, is the basis for the geostrophic model, which has proven to be extremely useful for understanding and forecasting large-scale atmospheric and oceanic dynamics.
In the present work, we develop second- and third-order finite-volume numerical schemes applied to the 2D rotating shallow-water equations in spherical coordinates. These schemes are designed to preserve the geostrophic equilibrium in the limit as the Rossby number tends to zero.
The final goal is to design reliable and efficient forecasting models for simulating meteotsunamis, long-wave events generated in the ocean by atmospheric pressure disturbances. These disturbances produce long waves of small amplitude that gradually amplify as they approach the coast.
The numerical results for various analytical and real-world test cases underscore the importance of maintaining geostrophic equilibrium over time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_16002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically well-balanced geostrophic reconstruction finite volumes numerical schemes for the 2D rotating NLSWE in spherical coordinates del Pino, Alejandro González Díaz, Manuel Jesús Castro Sánchez, Jorge Macías Atmospheric and Oceanic Physics Numerical Analysis Fluid Dynamics 86A15, 65L05, 65M99, 65M08, 65-04 The dynamics of large-scale geophysical fluids is primarily governed by the balance between the Coriolis force and the pressure gradient. This phenomenon, known as geostrophic equilibrium, is the basis for the geostrophic model, which has proven to be extremely useful for understanding and forecasting large-scale atmospheric and oceanic dynamics. In the present work, we develop second- and third-order finite-volume numerical schemes applied to the 2D rotating shallow-water equations in spherical coordinates. These schemes are designed to preserve the geostrophic equilibrium in the limit as the Rossby number tends to zero. The final goal is to design reliable and efficient forecasting models for simulating meteotsunamis, long-wave events generated in the ocean by atmospheric pressure disturbances. These disturbances produce long waves of small amplitude that gradually amplify as they approach the coast. The numerical results for various analytical and real-world test cases underscore the importance of maintaining geostrophic equilibrium over time. |
| title | Asymptotically well-balanced geostrophic reconstruction finite volumes numerical schemes for the 2D rotating NLSWE in spherical coordinates |
| topic | Atmospheric and Oceanic Physics Numerical Analysis Fluid Dynamics 86A15, 65L05, 65M99, 65M08, 65-04 |
| url | https://arxiv.org/abs/2510.16002 |