Flexible and efficient discretizations of multilayer models with variable density

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