scholarly journals A well-balanced upstream flux-splitting finite-volume scheme for shallow-water flow simulations with irregular bed topography

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
Jihn-Sung Lai ◽  
Wen-Dar Guo ◽  
Gwo-Fong Lin ◽  
Yih-Chi Tan
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Finite Volume ◽  
Finite Volume Scheme ◽  
Shallow Water Flow ◽  
Flow Simulations ◽  
Volume Scheme ◽  
Bed Topography ◽  
Flux Splitting ◽  
Irregular Bed Topography

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.

scholarly journals Coupled method for the numerical simulation of 1D shallow water and Exner transport equations in channels with variable cross-section

2018 ◽  
Vol 40 ◽  
pp. 05012
Author(s):  
Sergio Martínez-Aranda ◽  
Javier Murillo ◽  
Pilar García-Navarro
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Cross Section ◽  
Physical Phenomenon ◽  
Mathematical Expression ◽  
Channel Cross Section ◽  
Finite Volume Scheme ◽  
Variable Cross ◽  
Volume Scheme ◽  
Solid Transport

This work is focused on the a numerical finite volume scheme for the resulting coupled shallow water-Exner system in 1D applications with arbitrary geometry. The mathematical expression modeling the the hydrodynamic and morphodynamic components of the physical phenomenon are treated to deal with cross-section shape variations and empirical solid discharge estimations. The resulting coupled system of equations can be rewritten as a nonconservative hyperbolic system with three moving waves and one stationary wave to account for the source terms discretization. But, even for the simplest solid transport models as the Grass law, to find a linearized Jacobian matrix of the system can be a challenge if one considers arbitrary shape channels. Moreover, the bottom channel slope variations depends on the erosion-deposition mechanism considered to update the channel cross-section profile. In this paper a numerical finite volume scheme is proposed, based on an augmented Roe solver (first order accurate in time and space) and dealing with solid transport flux variations caused by the channel geometry changes. Channel crosssection variations lead to the appearance of a new solid flux source term which should be discretized properly. Comparison of the numerical results for several analytical and experimental cases demonstrate the effectiveness, exact wellbalanceness and accuracy of the scheme.

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