Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges
Abstract
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.
Cite
@article{arxiv.2601.16709,
title = {Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges},
author = {Nina Aguillon and Sophie Hörnschemeyer and Jacques Sainte-Marie},
journal= {arXiv preprint arXiv:2601.16709},
year = {2026}
}