Asymptotically well-balanced geostrophic reconstruction finite volumes numerical schemes for the 2D rotating NLSWE in spherical coordinates

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: del Pino, Alejandro González, Díaz, Manuel Jesús Castro, Sánchez, Jorge Macías
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917023686066176
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
id 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