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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.16709 |
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| _version_ | 1866908783458910208 |
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| author | Aguillon, Nina Hörnschemeyer, Sophie Sainte-Marie, Jacques |
| author_facet | Aguillon, Nina Hörnschemeyer, Sophie Sainte-Marie, Jacques |
| contents | This work presents the numerical analysis of a barotropic-baroclinic splitting in a nonlinear multilayer framework with exchanges between the layers in terrain-following coordinates. The splitting is formulated as an exact operator splitting. The barotropic step handles free surface evolution and depth-averaged velocity via a well-balanced one-layer model, while the baroclinic step manages vertical exchanges between layers and adjusts velocities to their mean values. We show that the barotropic-baroclinic splitting preserves total energy conservation and meets both a discrete maximum principle and a discrete entropy inequality. Several numerical experiments are presented showing the gain in computational cost, particularly in low Froude simulations, with no loss of accuracy. The benefits of using a well-balancing strategy in the barotropic step to preserve the geostrophic equilibrium are inherited in the overall scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges Aguillon, Nina Hörnschemeyer, Sophie Sainte-Marie, Jacques Numerical Analysis This work presents the numerical analysis of a barotropic-baroclinic splitting in a nonlinear multilayer framework with exchanges between the layers in terrain-following coordinates. The splitting is formulated as an exact operator splitting. The barotropic step handles free surface evolution and depth-averaged velocity via a well-balanced one-layer model, while the baroclinic step manages vertical exchanges between layers and adjusts velocities to their mean values. We show that the barotropic-baroclinic splitting preserves total energy conservation and meets both a discrete maximum principle and a discrete entropy inequality. Several numerical experiments are presented showing the gain in computational cost, particularly in low Froude simulations, with no loss of accuracy. The benefits of using a well-balancing strategy in the barotropic step to preserve the geostrophic equilibrium are inherited in the overall scheme. |
| title | Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.16709 |