scholarly journals Simulation of Hydraulic Shock Waves by Hybrid Flux-Splitting Schemes in Finite Volume Method

2005 ◽  
Vol 21 (2) ◽  
pp. 85-101 ◽  
Author(s):  
J.-S. Lai ◽  
G.-F. Lin ◽  
W.-D. Guo
Keyword(s):  
Shock Waves ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Second Order ◽  
Dam Break ◽  
Splitting Scheme ◽  
Hydraulic Shock ◽  
Flux Splitting ◽  
Volume Method ◽  
Order Extension

AbstractIn the framework of the finite volume method, a robust and easily implemented hybrid flux-splitting finite-volume (HFF) scheme is proposed for simulating hydraulic shock waves in shallow water flows. The hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method to estimate the cell-interface fluxes. The scheme is extended to be second-order accurate in space and time using the predictor-corrector approach with monotonic upstream scheme for conservation laws. The proposed HFF scheme and its second-order extension are verified through simulations of the 1D idealized dam-break problem, the 2D oblique hydraulic shock-wave problem, and the 2D dam-break experiments with channel contraction as well as wet/dry beds. Comparisons of the HFF and several well-known first-order upwind schemes are made to evaluate numerical performances. It is demonstrated that the HFF scheme captures the discontinuities accurately and produces no entropy-violating solutions. The HFF scheme and its second-order extension are proven to achieve the numerical benefits combining the efficiency of flux-vector splitting scheme and the accuracy of flux-difference splitting scheme for the simulation of hydraulic shock waves.

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.

scholarly journals A second-order face-centred finite volume method for elliptic problems

2020 ◽  
Vol 358 ◽  
pp. 112655 ◽  
Author(s):  
Luan M. Vieira ◽  
Matteo Giacomini ◽  
Ruben Sevilla ◽  
Antonio Huerta
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Problems ◽  
Second Order ◽  
Volume Method

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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