  We propose an extension of the discretization approaches for multilayer
shallow water models, aimed at making them more flexible and efficient for
realistic applications to coastal flows. A novel discretization approach is
proposed, in which the number of vertical layers and their distribution are
allowed to change in different regions of the computational domain.
Furthermore, semi-implicit schemes are employed for the time discretization,
leading to a significant efficiency improvement for subcritical regimes. We
show that, in the typical regimes in which the application of multilayer
shallow water models is justified, the resulting discretization does not
introduce any major spurious feature and allows again to reduce substantially
the computational cost in areas with complex bathymetry. As an example of the
potential of the proposed technique, an application to a sediment transport
problem is presented, showing a remarkable improvement with respect to standard
discretization approaches.
