Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

TL;DR

This paper introduces a flexible multilayer shallow water model with variable layers and semi-implicit time discretization, significantly improving efficiency and accuracy for coastal flow simulations with complex bathymetry.

Contribution

It presents a novel discretization method allowing variable vertical layers and employs semi-implicit schemes, enhancing computational efficiency for realistic coastal flow modeling.

Findings

Reduces computational cost in complex bathymetry regions

Maintains accuracy without introducing major spurious features

Shows improved results in sediment transport simulations

Abstract

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.