Barotropic-Baroclinic Splitting for Multilayer Shallow Water Models with Exchanges

TL;DR

This paper introduces an exact operator splitting method for multilayer shallow water models that efficiently separates barotropic and baroclinic processes, ensuring energy conservation and improved computational performance.

Contribution

It presents a novel barotropic-baroclinic splitting scheme that preserves energy, satisfies stability principles, and enhances efficiency in multilayer shallow water simulations.

Findings

Preserves total energy conservation.

Maintains discrete maximum principle and entropy inequality.

Reduces computational cost in low Froude number simulations.

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.