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Development and Application of Two-Dimensional Numerical Model on Shallow Water Flows Using Finite Volume Method

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DOI: 10.4236/jamp.2015.38121    2,715 Downloads   3,202 Views  
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This present study develops a 2-D numerical scheme to simulate the velocity and depth on the actual terrain by using shallow water equations. The computational approach uses the HLL scheme as a basic building block, treats the bottom slope by lateralizing the momentum flux, then refines the scheme using the Strang splitting to deal with the frictional source term. Besides, a decoupled algorithm is also adopted to compute the aggradation and degradation of bed-level elevation by using the Manning-Strickler formula and Exner’s relationship. The main purpose is to set up the window interface of 2-D numerical model and increase the realization of engineers on these characteristics of hydraulic treatment and maintenance.

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Peng, S. and Tang, C. (2015) Development and Application of Two-Dimensional Numerical Model on Shallow Water Flows Using Finite Volume Method. Journal of Applied Mathematics and Physics, 3, 989-996. doi: 10.4236/jamp.2015.38121.

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The authors declare no conflicts of interest.


[1] Fennema, R.J. and Chaudhry, M.H. (1989) Implicit Methods for Two-Dimensional Unsteady Free-Surface Flows. Jour. of Hydraulic Research, International Assoc. for Hydraulic Research, 27, 321-332.
[2] Fennema, R.J. and Chaudhry, M.H. (1990) Explicit Methods for Two-Dimensional Unsteady Free-Surface Flows. Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., 116, 1013-1034.
[3] Chaudhry, M.H. (1993) Open-Channel Flow. Prentice-Hall, Inc., Englewood Cliffs.
[4] Jonsson, P., Jonsén, P., Andreasson, P., Lundstr?m, T. and Hellstr?m, J. (2015) Modelling Dam Break Evolution over a Wet Bed with Smoothed Particle Hydrodynamics: A Parameter Study. Engineering, 7, 248-260.
[5] Harten, A., Lax, P.D. and van Leer, B. (1983) On Upstream Difference and Godunov-Type Schemes for Hyperbolic Conservation Laws. SIAM Review, 25, 35-61.
[6] Fraccarollo, L., Capart, H. and Zech, Y. (2003) A Godunov Method for the Computation of Erosional Shallow Water Transients. Int. J. Numer. Meth. Fluids, 41, 951-976.
[7] Fraccarollo, L. and Toro, E.F. (1995) Experimental and Numerical Assessment of the Shallow Water Model for Two- Dimensional Dam-Break Type Problems. J. Hydr. Res., 33, 843-864.
[8] Leveque, R.J. (2002) Finite Volume Methods for Hyperbolic Problems. Cambridge Univ. Press, Cambridge.
[9] Graf, W.H. (1998) Fluvial Hydraulics. John Wiley & Sons, Chiche-ster.
[10] Julien, P.Y. (2002) River Mechanics. Cambridge Univ. Press, Cambridge.
[11] Liang, D., Falconer, R.A. and Lin, B. (2006) Comparison between TVD-MacCormack and ADI-Type Solvers of the Shallow Water Equations. Advances in Water Resources, 29, 1833-1845.
[12] Bhallamudi, S.M. and Chaudhry, M.H. (1991) Numerical Modeling of Aggradation and Degradation in Alluvial Channels. J. Hydr. Engng., 117, 1145-1164.

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