712	RWTH Publication No: 1026871        2026
TITLE	Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges
AUTHORS	Nina Aguillon, Sophie Hörnschemeyer, Jacques Sainte-Marie
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.
KEYWORDS	ensity-stratified flows multilayer models, Saint-Venant equations, splitting, free surface flows, well-balancing, density-stratified flows