scholarly journals Modelling the pollutants transport in the “air-water” system of a shallow water

2021 ◽  
Vol 1029 ◽  
pp. 012080
Author(s):  
T V Lyashchenko ◽  
I A Lyapunova ◽  
A E Chistyakov ◽  
A V Nikitina ◽  
A A Filina ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Pollutants Transport

scholarly journals CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY

2010 ◽  
Vol 20 (07) ◽  
pp. 1049-1087 ◽  
Author(s):  
BORIS HASPOT
Keyword(s):  
Shallow Water ◽  
Existence Of Solutions ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Water System ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Viscosity Coefficients ◽  
Global Existence Of Solutions ◽  
Dependent Viscosity

In this paper, we consider the compressible Navier–Stokes equation with density-dependent viscosity coefficients and a term of capillarity introduced formally by van der Waals in Ref. 51. This model includes at the same time the barotropic Navier–Stokes equations with variable viscosity coefficients, shallow-water system and the model introduced by Rohde in Ref. 46. We first study the well-posedness of the model in critical regularity spaces with respect to the scaling of the associated equations. In a functional setting as close as possible to the physical energy spaces, we prove global existence of solutions close to a stable equilibrium, and local in time existence of solutions with general initial data. Uniqueness is also obtained.

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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