scholarly journals Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water

2020 ◽  
Vol 8 (1) ◽  
pp. 19-34
Author(s):  
Bandung Arry Sanjoyo ◽  
Mochamad Hariadi ◽  
Mauridhi Hery Purnomo
Keyword(s):  
Numerical Solution ◽  
Shallow Water ◽  
Shallow Water Equation ◽  
Steady State Solution ◽  
Dam Break ◽  
Stability And Convergence ◽  
Flow Depth ◽  
Stable Algorithm ◽  
Long Time ◽  
Dam Break Flow

Many game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity.  We propose a stable algorithm for visualization of dam-break flow on flat and flat with bumps topography. We choose Lax-Friedrichs scheme as the numerical method for solving the SWE. Then, we investigate the consistency, stability, and convergence of the scheme. Finally, we transform the strategy into a visualization algorithm of SWE and analyze the complexity. The results of this paper are: 1) the Lax-Friedrichs scheme that is consistent and conditionally stable; furthermore, if the stability condition is satisfied, the scheme is convergent; 2) an algorithm to visualize flow depth and velocity which has complexity O(N) in each time iteration. We have applied the algorithm to flat and flat with bumps topography. According to visualization results, the numerical solution is very close to analytical solution in the case of flat topography. In the case of flat with bumps topography, the algorithm can visualize the dam-break flow and after a long time the numerical solution is very close to the analytical steady-state solution. Hence the proposed visualization algorithm is suitable for game applications containing flat with bumps environments.

scholarly journals 1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Szu-Hsien Peng
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equation ◽  
Dam Break ◽  
Flume Experiments ◽  
One Dimensional ◽  
Dam Break Flow ◽  
The One ◽  
Volume Method

The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.

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.

scholarly journals Parallel Algorithms of Well-Balanced and Weighted Average Flux for Shallow Water Model Using CUDA

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nugool Sataporn ◽  
Worasait Suwannik ◽  
Montri Maleewong
Keyword(s):  
Shallow Water ◽  
Weighted Average ◽  
Dam Break ◽  
Global Memory ◽  
Water Model ◽  
Shallow Water Model ◽  
Real World Problem ◽  
Dry Conditions ◽  
Dam Break Flow ◽  
Volume Method

Compute Unified Device Architecture (CUDA) implementations are presented of a well-balanced finite volume method for solving a shallow water model. The CUDA platform allows programs to run parallel on GPU. Four versions of the CUDA algorithm are presented in addition to a CPU implementation. Each version is improved from the previous one. We present the following techniques for optimizing a CUDA program: limiting register usage, changing the global memory access pattern, and using loop unroll. The accuracy of all programs is investigated in 3 test cases: a circular dam break on a dry bed, a circular dam break on a wet bed, and a dam break flow over three humps. The last parallel version shows 3.84x speedup over the first CUDA implementation. We use our program to simulate a real-world problem based on an assumed partial breakage of the Srinakarin Dam located in Kanchanaburi province, Thailand. The simulation shows that the strong interaction between massive water flows and bottom elevations under wet and dry conditions is well captured by the well-balanced scheme, while the optimized parallel program produces a 57.32x speedup over the serial version.

scholarly journals Construction, verification of a software for the 2D dam-break flow and some its applications

2007 ◽  
Vol 29 (4) ◽  
pp. 539-550
Author(s):  
Hoang Van Lai ◽  
Nguyen Thanh Don
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations ◽  
Theoretical Basis ◽  
Dam Break ◽  
River Delta ◽  
Red River ◽  
Test Cases ◽  
Red River Delta ◽  
Dam Break Flow

In this paper the numerical method for the shallow water equations is studied. The paper consists of 3 sections. In the section 1 the theoretical basis and software IMECI-L2DBREAK for simulation of the 2D dam-break or dyke-break flows is outlined. In the section 2 some results in verification of the IMECH_2DBREAK by the test cases proposed in the big European Hydraulics Laboratories are shown. In the last section some applications of IMECH_2DBREAK for the inundation problem in the Red river delta in the Northern of Vietnam are presented.

scholarly journals Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation

2014 ◽  
Vol 12 ◽  
pp. 10-20
Author(s):  
Jiang Bo Zhou ◽  
Jun De Chen ◽  
Wen Bing Zhang
Keyword(s):  
Global Existence ◽  
Shallow Water ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Holm Equation ◽  
Special Cases ◽  
Long Time

We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.

scholarly journals CFD modelling approach for dam break flow studies

2009 ◽  
Vol 6 (6) ◽  
pp. 6759-6793 ◽  
Author(s):  
C. Biscarini ◽  
S. Di Francesco ◽  
P. Manciola
Keyword(s):  
Shallow Water ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Dam Break ◽  
Navier Stokes ◽  
Cfd Modelling ◽  
Wave Celerity ◽  
Dam Break Flow ◽  
Complete Set ◽  
First Time

Abstract. This paper presents numerical simulations of free surface flows induced by a dam break comparing the shallow water approach to fully three-dimensional simulations. The latter are based on the solution of the complete set of Reynolds-Averaged Navier-Stokes (RANS) equations coupled to the Volume of Fluid (VOF) method. The methods assessment and comparison are carried out on a dam break over a flat bed without friction and a dam break over a triangular bottom sill. Experimental and numerical literature data are compared to present results. The results demonstrate that the shallow water approach loses some three-dimensional phenomena, which may have a great impact when evaluating the downstream wave propagation. In particular, water wave celerity and water depth profiles could be underestimated due to the incorrect shallow water idealization that neglects the three-dimensional aspects due to the gravity force, especially during the first time steps of the motion.

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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