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arXiv · 2601.16709

Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges

Nina Aguillon·Sophie Hörnschemeyer·Jacques Sainte-Marie
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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.

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Nina Aguillon, Sophie Hörnschemeyer, Jacques Sainte-Marie. 2026-01-23. Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges. https://arxiv.org/abs/2601.16709

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