Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges

arXiv (Cornell University)

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.

Authors 3

1. Nina Aguillon

   Centre National de la Recherche Scientifique · Sorbonne Université · Laboratoire Jacques-Louis Lions

   Affiliation as printed

   Sorbonne Université , CNRS , Inria , Laboratoire J.-L. Lions , F-75005 Paris , France

2. Sophie Hörnschemeyer Aachen

   RWTH Aachen University

   Affiliation as printed

   IGPM , RWTH Aachen University , Germany

3. Jacques Sainte-Marie

   Centre National de la Recherche Scientifique · Sorbonne Université · Laboratoire Jacques-Louis Lions

   Affiliation as printed

   Sorbonne Université , CNRS , Inria , Laboratoire J.-L. Lions , F-75005 Paris , France