On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas

2007 ◽  
Vol 227 (1) ◽  
pp. 574-601 ◽  
Author(s):  
José M. Gallardo ◽  
Carlos Parés ◽  
Manuel Castro
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
High Order ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Dry Areas

scholarly journals A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

2018 ◽  
Vol 40 ◽  
pp. 05032
Author(s):  
Minh H. Le ◽  
Virgile Dubos ◽  
Marina Oukacine ◽  
Nicole Goutal
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Simple Wave ◽  
Water Model ◽  
Strong Interactions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Rigid Vegetation ◽  
Vertical Cylinders

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

A Characteristic-Based Finite Volume Scheme for Shallow Water Equations

2009 ◽  
Vol 21 (4) ◽  
pp. 531-540 ◽  
Author(s):  
Yan Guo ◽  
Ru-xun Liu ◽  
Ya-li Duan ◽  
Yuan Li
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Finite Volume Scheme ◽  
Volume Scheme
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