A New Well-Balanced Reconstruction Technique for the Numerical Simulation of Shallow Water Flows with Wet/Dry Fronts and Complex Topography

Zhengtao Zhu,Fengpeng Bai,Ruidong An,Zhonghua Yang

doi:10.3390/w10111661

Abstract

This study develops a new well-balanced scheme for the one-dimensional shallow water system over irregular bed topographies with wet/dry fronts, in a Godunov-type finite volume framework. A new reconstruction technique that includes flooded cells and partially flooded cells and preserves the non-negative values of water depth is proposed. For the wet cell, a modified revised surface gradient method is presented assuming that the bed topography is irregular in the cell. For the case that the cell is partially flooded, this paper proposes a special reconstruction of flow variables that assumes that the bottom function is linear in the cell. The Harten–Lax–van Leer approximate Riemann solver is applied to evaluate the flux at cell faces. The numerical results show good agreement with analytical solutions to a set of test cases and experimental results.

Highlights

Non-linear shallow water equations, which can be derived by integrating the Euler equations in depth, have wide applications to surface flows, such as water flows of rivers, flood plains, practical dam failures, coastal regions and tides
The present paper focuses on one-dimensional shallow water equation [5]:
Paper, we we present present aa new new reconstruction reconstruction technique technique including including flooded flooded cells cells and and partially partially flooded cells that preserves the non-negative values of water depth at the cell interface

Summary

Introduction

Non-linear shallow water equations, which can be derived by integrating the Euler equations in depth, have wide applications to surface flows, such as water flows of rivers, flood plains, practical dam failures, coastal regions and tides. Dam-breaks and floods may have enormous economic and human costs. Numerical solutions to the shallow water equations have been important in simulating floods and dam-break flows [1,2,3,4]. The present paper focuses on one-dimensional shallow water equation [5]: ∂ ∂t " h hu # +. Where h(x, t) is the water depth, u(x, t) is the depth-averaged velocity, g is the gravitational constant, and B(x) is bottom topography.

Methods

Results

Conclusion