Combined finite volume–finite element method for shallow water equations

2005 ◽  
Vol 34 (10) ◽  
pp. 1199-1222 ◽  
Author(s):  
Ji-Wen Wang ◽  
Ru-Xun Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Element Method

scholarly journals A FINITE ELEMENT METHOD FOR STORM SURGE AND TIDAL COMPUTATION

1984 ◽  
Vol 1 (19) ◽  
pp. 82 ◽  
Author(s):  
Y. Coeffe ◽  
S. Dal Secco ◽  
P. Esposito ◽  
B. Latteux
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Storm Surge ◽  
Incident Wave ◽  
Shallow Water Equations ◽  
Implicit Scheme ◽  
Wave Condition ◽  
Recent Developments ◽  
Element Method

The paper reports the current progress in developing a finite element method for the shallow water equations. Some recent developments as the implementation of a semi implicit scheme or the use of an incident wave condition are described. Different realistic applications are presented concerning tidal and storm surge simulations.

scholarly journals A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alia Al-Ghosoun ◽  
Ashraf S. Osman ◽  
Mohammed Seaid
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Shallow Water ◽  
Finite Volume ◽  
Second Order ◽  
Static Deformation ◽  
Wave Runup ◽  
Content Type ◽  
Element Method

Purpose The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformation. Second, to develop a robust hybrid finite element/finite volume method for solving free-surface runup flow problems over deformable beds. The authors combine the finite volume for free-surface flows and the finite element method for bed elasticity. Design/methodology/approach The authors propose a new model for wave runup by static deformation on seabeds. The model consists of the depth-averaged shallow water system for the water free-surface coupled to the second-order elastostatic formulation for the bed deformation. At the interface between the water flow and the seabed, transfer conditions are implemented. Here, hydrostatic pressure and friction forces are considered for the elastostatic equations, whereas bathymetric forces are accounted for in the shallow water equations. As numerical solvers, the authors propose a well-balanced finite volume method for the flow system and a stabilized finite element method for elastostatics. Findings The developed coupled depth-averaged shallow water system and second-order solid elastostatic system is well suited for modeling wave runup by deformation on seabeds. The derived coupling conditions at the interface between the water flow and the bed topography resolve well the condition transfer between the two systems. The proposed hybrid finite volume element method is accurate and efficient for this class of models. The novel technique used for wet/dry treatment accurately captures the moving fronts in the computational domain without generating nonphysical oscillations. The presented numerical results demonstrate the high performance of the proposed methods. Originality/value Enhancing modeling and computations for wave runup problems is at an early stage in the literature, and it is a new and exciting area of research. To the best of our knowledge, solving wave runup problems by static deformation on seabeds using a hybrid finite volume element method is presented for the first time. The results of this research study, and the research methodologies, will have an important influence on a range of other scientists carrying out research in related fields.

Edge-based finite element method for shallow water equations

2001 ◽  
Vol 36 (6) ◽  
pp. 659-685 ◽  
Author(s):  
F. L. B. Ribeiro ◽  
A. C. Galeão ◽  
L. Landau
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Edge Based ◽  
Element Method
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