# A two-layer approach for Coupling 1D/2D Shallow Water Flow Models

## TL;DR

This paper introduces a vertical coupling method for 1D/2D shallow water models that improves simulation accuracy and flexibility by modeling the channel as two layers, enabling better flow structure recovery and adaptability.

## Contribution

The paper proposes a novel vertical coupling approach that treats the channel as two layers, allowing dynamic switching and improved flow structure preservation over existing methods.

## Key findings

- The VCM recovers 2D channel flow structure without efficiency loss.
- The method is well-balanced and preserves conservation properties.
- It adapts to different flow situations effectively.

## Abstract

In this paper, we propose a novel approach for coupling 2D/1D shallow water flow models. Efficiently coupling these models is vital for simulating the flow and flooding of open channels. Currently, existing methods couple the models either at the channel lateral boundaries (lateral methods) or at the location, along the channel flow direction, where the two sub-domains intersect (frontal methods). We classify these methods as horizontal methods since the coupling points are on the horizontal plane. The limitations of these methods include their inability to recover the 2D channel flow structure during flooding without losing efficiency, and their inability to switch between lateral and frontal methods, based on the problem. Here, we propose a new paradigm which is to think of the channel flow as a two layer flow. This leads to the vertical coupling method (VCM) which is able to recover 2D channel flow structure without losing efficiency, switch types depending on the flow and is a superset of some existing methods. The VCM is based on a user chosen elevation above which the user considers the channel to be full. From this elevation, all other flow quantities are defined including the two layers. The flows in the lower and upper layers are assumed to be 1D and 2D respectively, and the appropriate flow models with exchange terms are derived. The 2D shallow water flow model is retained for the floodplains. Finite volume methods (FVM) are formulated for the flood model; the FVM with the operator splitting approach are also formulated to solve and couple the two layer channel flow models. We show that the resulting method (i) is well-balanced (ii) preserves the "no-numerical" flooding property (iii) preserves conservation properties and (iv) adapts to the flow situation.