Share This Article:

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

Abstract Full-Text HTML XML Download Download as PDF (Size:2200KB) PP. 989-996
DOI: 10.4236/jamp.2015.38121    2,715 Downloads   3,202 Views  
Author(s)    Leave a comment

ABSTRACT

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.

Cite this paper

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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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. http://dx.doi.org/10.1080/00221688909499167
[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. http://dx.doi.org/10.1061/(ASCE)0733-9429(1990)116:8(1013)
[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. http://dx.doi.org/10.4236/eng.2015.75022
[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. http://dx.doi.org/10.1137/1025002
[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. http://dx.doi.org/10.1002/fld.475
[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. http://dx.doi.org/10.1080/00221689509498555
[8] Leveque, R.J. (2002) Finite Volume Methods for Hyperbolic Problems. Cambridge Univ. Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511791253
[9] Graf, W.H. (1998) Fluvial Hydraulics. John Wiley & Sons, Chiche-ster.
[10] Julien, P.Y. (2002) River Mechanics. Cambridge Univ. Press, Cambridge. http://dx.doi.org/10.1017/CBO9781139164016
[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. http://dx.doi.org/10.1016/j.advwatres.2006.01.005
[12] Bhallamudi, S.M. and Chaudhry, M.H. (1991) Numerical Modeling of Aggradation and Degradation in Alluvial Channels. J. Hydr. Engng., 117, 1145-1164. http://dx.doi.org/10.1061/(ASCE)0733-9429(1991)117:9(1145)

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.