A Relaxation Scheme for the Two-Layer Shallow Water System

2008 ◽  
pp. 135-144 ◽  
Author(s):  
R. Abgrall ◽  
S. Karni
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Relaxation Scheme ◽  
Shallow Water System

Global well-posedness for the viscous shallow water system with Korteweg type

2017 ◽  
Vol 97 (16) ◽  
pp. 2865-2879
Author(s):  
Jinlu Li ◽  
Zhaoyang Yin
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Well Posedness ◽  
Shallow Water System

Delta Shock Waves in the Shallow Water System

2017 ◽  
Vol 30 (3) ◽  
pp. 1187-1198 ◽  
Author(s):  
C. O. R. Sarrico ◽  
A. Paiva
Keyword(s):  
Shock Waves ◽  
Shallow Water ◽  
Water System ◽  
Delta Shock ◽  
Shallow Water System ◽  
Delta Shock Waves

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

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1661 ◽  
Author(s):  
Zhengtao Zhu ◽  
Zhonghua Yang ◽  
Fengpeng Bai ◽  
Ruidong An
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Reconstruction Technique ◽  
Test Cases ◽  
Bed Topography ◽  
Surface Gradient ◽  
Shallow Water Flows ◽  
Shallow Water System ◽  
The One ◽  
Flow Variables

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.

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