A multi-moment finite volume formulation for shallow water equations on unstructured mesh

2010 ◽  
Vol 229 (12) ◽  
pp. 4567-4590 ◽  
Author(s):  
Ryosuke Akoh ◽  
Satoshi Ii ◽  
Feng Xiao
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Unstructured Mesh

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 Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Sudi Mungkasi
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Error Indicator ◽  
Triangular Grids ◽  
Volume Method ◽  
Numerical Entropy

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

scholarly journals A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Sheng Bi ◽  
Jianzhong Zhou ◽  
Yi Liu ◽  
Lixiang Song
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Second Order ◽  
Topographic Features ◽  
Shallow Flows ◽  
Local Complex ◽  
Proposed Model ◽  
Volume Method

A second-order accurate, Godunov-type upwind finite volume method on dynamic refinement grids is developed in this paper for solving shallow-water equations. The advantage of this grid system is that no data structure is needed to store the neighbor information, since neighbors are directly specified by simple algebraic relationships. The key ingredient of the scheme is the use of the prebalanced shallow-water equations together with a simple but effective method to track the wet/dry fronts. In addition, a second-order spatial accuracy in space and time is achieved using a two-step unsplit MUSCL-Hancock method and a weighted surface-depth gradient method (WSDM) which considers the local Froude number is proposed for water depths reconstruction. The friction terms are solved by a semi-implicit scheme that can effectively prevent computational instability from small depths and does not invert the direction of velocity components. Several benchmark tests and a dam-break flooding simulation over real topography cases are used for model testing and validation. Results show that the proposed model is accurate and robust and has advantages when it is applied to simulate flow with local complex topographic features or flow conditions and thus has bright prospects of field-scale application.

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