scholarly journals On the existence of local strong solutions to chemotaxis–shallow water system with large data and vacuum

2016 ◽  
Vol 261 (12) ◽  
pp. 6758-6789 ◽  
Author(s):  
Jiahang Che ◽  
Li Chen ◽  
Ben Duan ◽  
Zhen Luo
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Strong Solutions ◽  
Large Data ◽  
Shallow Water System ◽  
Local Strong Solutions

scholarly journals Blowup Phenomena for a Modified Dullin-Gottwald-Holm Shallow Water System

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Panpan Zhai ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Strong Solutions ◽  
Integral Form ◽  
Two Component ◽  
Shallow Water System

We discuss blowup phenomena for a modified two-component Dullin-Gottwald-Holm shallow water system. In this paper, some new blowup criteria of strong solutions involving the density and suitable integral form of the momentum are established.

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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