scholarly journals Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

2009 ◽  
Vol 198 (33-36) ◽  
pp. 2520-2538 ◽  
Author(s):  
M.J. Castro Dı´az ◽  
E.D. Fernández-Nieto ◽  
A.M. Ferreiro ◽  
C. Parés
Keyword(s):  
Sediment Transport ◽  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Unstructured Meshes ◽  
Second Order ◽  
Two Dimensional ◽  
Transport Models ◽  
Finite Volume Approach

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.

Dam-break computations by a finite volume on dry regions

2021 ◽  
Author(s):  
Farid Boushaba ◽  
Salah Daoudi ◽  
Ahmed Yachouti ◽  
Youssef Regad
Keyword(s):  
Finite Elements ◽  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Equation Model ◽  
Second Order ◽  
Dam Break ◽  
Conservative Form ◽  
Volume Method

Abstract This paper presents numerical solvers, based on the finite volume method. This scheme solves dam break problems on the dry bottom in 2D configuration. The difficulty of the simulation of this type of problem lies in the propagation of shocks on the dry bottom. The equation model used is the shallow water equations written in conservative form. The scheme used is second order in space and time. The method is modified to treat dry bottoms. The validity of the method is demonstrated over the dam break example. A comparison with finite elements shows the weakness and robustness of each method.

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