A Comparison of Numerical Schemes for Simulating Reflected Wave on Dry and Enclosed Domains

Abstract

This paper is to investigate the capability of six numerical schemes to simulate reflected wave over a dry and closed domain with and without building, namely: (a) two proposed 2D numerical models solving the conservation form of 2D Shallow Water Equations (2D-SWEs) by Finite Volume Method (FVM) with Roe and HLLC schemes are invoked to approximate Reimann solver; (b) three options of shallow models in the commercial software Flow 3D based on a non-conservation form of 2D-SWEs and (c) the Flow 3D with turbulence modules. By analyzing flooding maps, the area of the reflected wave, and water level profiles on a dry and closed domain, two proposed models give reasonable solutions, while three options of the shallow module of Flow 3D originate result less accurately when initial wave celerity (c0) is small. The accuracy level will be increased if c0 value increases. The 3D model presented the best performance of the complex flow pattern in the dry and enclosed domain in both cases without and with building.

1. Introduction

2. Materials and Methods

2.1. 2D Shallow Water Equations

2.2. Flow 3D Model

2.2.1. 3D Navier-Stokes Equations

2.2.2. Shallow Models in Flow 3D

2.3. Computational Domain

2.4. Sensitivity Analysis

2.5. Mesh Convergence Analysis

3. Results and Discussion

3.1. Dam Break Wave in Dry and Enclosed Domain without Building

3.2. Dam Break Wave in Dry and Enclose Domain with Presence of Building

3.3. The Influence of Initial Wave Celerity on Dam Break Wave on Dry and Enclosed Domain

4. Conclusions

References

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► See detail:   A Comparison of Numerical Schemes for Simulating Reflected Wave on Dry and Enclosed Domains

Le Thi Thu Hien^1,* and Nguyen Van Chien²

1 Faculty of Water Resources Engineering, Thuyloi University, Ha Noi 116705, Vietnam
2 Hydraulic Construction Institute, Ha Noi 116705, Vietnam; chiennv131@wru.vn
* Correspondence: lethuhien.thuyluc@tlu.edu.vn; Tel.: +84-985-520-058

Water 2023, 15, 2781                                                                                                 https://www.mdpi.com/journal/water