Picard iterations for a finite element shallow water equation model

2005 ◽  
Vol 10 (3-4) ◽  
pp. 316-341 ◽  
Author(s):  
Julia C. Muccino ◽  
Hao Luo
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Shallow Water Equation ◽  
Equation Model ◽  
Picard Iterations

scholarly journals An improved shallow water equation model for water animation

2017 ◽  
Author(s):  
Mingjing Ai ◽  
Anding Du ◽  
Han Xu ◽  
Jianwei Niu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Equation Model

A NUMERICAL STUDY OF DAM-BREAK FLOW AND SEDIMENT TRANSPORT FROM A QUAKE LAKE

2011 ◽  
Vol 05 (05) ◽  
pp. 401-428 ◽  
Author(s):  
PENGZHI LIN ◽  
YINNA WU ◽  
JUNLI BAI ◽  
QUANHONG LIN
Keyword(s):  
Sediment Transport ◽  
Shallow Water ◽  
High Speed ◽  
Numerical Study ◽  
Shallow Water Equation ◽  
Equation Model ◽  
Dam Break ◽  
Bed Morphology ◽  
Dam Break Flow ◽  
Quake Lake

Dam-break flows are simulated numerically by a two-dimensional shallow-water-equation model that combines a hydrodynamic module and a sediment transport module. The model is verified by available analytical solutions and experimental data. It is demonstrated that the model is a reliable tool for the simulation of various transient shallow water flows and the associated sediment transport and bed morphology on complex topography. The validated model is then applied to investigate the potential dam-break flows from Tangjiashan Quake Lake resulting from Wenchuan Earthquake in 2008. The dam-break flow evolution is simulated by using the model in order to provide the flooding patterns (e.g., arrival time and flood height) downstream. Furthermore, the sediment transport and bed morphology simulation is performed locally to study the bed variation under the high-speed dam-break flow.

A Finite Element Solution of the Unidimensional Shallow-Water Equation

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Triki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Shallow Water ◽  
Rectangular Channel ◽  
Shallow Water Equation ◽  
The Finite Element Method ◽  
Time Step ◽  
Text Book ◽  
Element Method

Based on the finite element method, the numerical solution of the shallow-water equation for one-dimensional (1D) unsteady flows was established. To respect the stability criteria, the time step of the method was dependent on the space step and flow velocity. This method was used to avoid the restriction due to the wave celerity variation in the computational analysis when using the method of characteristics. Furthermore, boundary conditions are deduced directly from the scheme without using characteristics equations. For the numerical solution, a general-purpose computer program, based on the finite element method (FEM), is coded in fortran to analyze the dynamic response of the open channel flow. This program is able to handle rectangular, triangular, or trapezoidal sections. Some examples solved with the finite element method are reported herein. The first involves routing a discharge hydrograph down a rectangular channel. The second example consists of routing a sudden shutoff of all flow at the downstream end of a rectangular channel. The third one deals with routing a discharge hydrograph down a trapezoidal channel. These examples are taken from the quoted literature text book. Numerical results agree well with those obtained by these authors and show that the proposed method is consistent, accurate, and highly stable in capturing discontinuities propagation in free surface flows.

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