A simple numerical scheme for the 2D shallow-water system

TL;DR

This paper introduces a straightforward numerical scheme for the 2D shallow-water equations, extending 1D methods to 2D while maintaining simplicity, and verifies its effectiveness through various tests and sensitivity analysis.

Contribution

It develops a simple, easily applicable numerical scheme for 2D SWEs based on 1D approaches, integrated into TELEMAC-2D, and validated through multiple flow regime tests.

Findings

Scheme accurately models equilibrium and flow regimes

Effective in transcritical flows with hydraulic jumps

Converges reliably in sensitivity analysis

Abstract

This paper presents a simple numerical scheme for the two dimensional Shallow-Water Equations (SWEs). Inspired by the study of numerical approximation of the one dimensional SWEs Audusse et al. (2015), this paper extends the problem from 1D to 2D with the simplicity of application preserves. The new scheme is implemented into the code TELEMAC-2D [tel2d, 2014] and several tests are made to verify the scheme ability under an equilibrium state at rest and different types of flow regime (i.e., fluvial regime, transcritical flow from fluvial to torrential regime, transcritical flow with a hydraulic jump). The sensitivity analysis is conducted to exam the scheme convergence.