Flexible and efficient discretizations of multilayer models with variable density

TL;DR

This paper extends semi-implicit discretization methods from multilayer shallow water models to variable density models with Boussinesq approximation, enhancing flexibility and efficiency through variable layer counts and stability analysis.

Contribution

It introduces a flexible multilayer discretization approach for variable density models, including stability analysis and numerical validation, expanding previous methods for barotropic cases.

Findings

Effective semi-implicit discretization for variable density models

Enhanced flexibility with variable layer numbers

Numerical experiments confirm approach efficiency

Abstract

We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore, also for the variable density equations, a variable number of layers can be used, so as to achieve greater flexibility and efficiency of the resulting multilayer approach. An analysis of the linearized system, which allows to derive linear stability parameters in simple configurations, and the resulting spatially semi-discretized equations are presented. A number of numerical experiments demonstrate the effectiveness of the proposed approach.