Flood control and management by CAPABLE simulator of unsteady flow in river

Document Type : Research Paper

Authors

1 Msc in Hydraulic Structure, Faculty of Agriculture, Tarbiat Modarres University, Tehran, Iran

2 Professor of Water Structures Engineering, Faculty of Agriculture, Tarbiat Modarres University, Tehran, Iran

3 Assistant Professor of Water Structures Engineering, Faculty of Agriculture, Tarbiat Modarres University, Tehran, Iran

Abstract

Flood flow importance enforces we to simulate its components exactly. In this study, saint-venant equations in conservative form are usedto simulate one-dimensional rapidly varied flow in the river. Upstream methods of Godunov family in finite volume frame work are used to numerical solution. According to Flow conditions in the river, the equations used are included in the source term of the bed slope, friction slope, change within width, and lateral flows. These factors grant high performance to the model. The method is based on solving a series of Riemann problems. HLL and Roe Riemann solver is used to approximate the flux. To improve the accuracy of the order of one to two MUSCL algorithms is used. To evaluate the performance of the proposed numerical algorithms, model results are compared with Analytical Solution and experimental data. At the end, sensitivity of effective parameters in numerical results have been measured. According to the results, both algorithms provide solutions with high precision and optimum results and they have a great ability to simulate one-dimensional flow in different hydraulic conditions in the river.

Keywords


 1. ضیاء  ع (1387) الگوریتم عددی ساده و کارآمد برای مدلسازی شکست سد. دانشگاه تهران، تهران، پایان‌نامۀ دکتری.
2 . Ahmad M F and Mamat M and Rizki S and Mohd I and Abdullah I (2011) The Development of Numerical Method or Shock Waves and Wave Propagation on Irregular Bathymetry. Applied Mathematical Sciences. 5(6): 293-308.
3 . Akbari G and Firoozi B (2010) Implicit and Explicit Numerical Solution of Saint-Venent Equations for Simulating Flood Wave in Natural Rivers. 5th National Congress on Civil Engineering,  Iran.
4 . Aldrighetti E (2007) Computational hydraulic techniques for the Saint Venant Equations in arbitrarily shaped geometry. degliStudi University, Trento, Ph.D. Dissertation.
5 . Benkhaldoun F and Seaid M (2010) A simple finite volume method for the shallow water equations. journal of Computational and Applied Mathematics, 234(1):  58-72.
6 . Brufau P and Ghilardi P and Savi F (2001) 1D Mathematical modelling of debris flow. journal of Hydraulic Research. 38(6): 435-446.
7 . Capart H and Eldho T I and Huang S Y and Young D L and Zech Y (2003) Treatment of Natural Geometry in Finite Volume River Flow Computations. journal of Hydraulic Engineering. 129(5): 385-393.
8 . Chaudhry M H (2008) Open-Channel Flow. 2th ed. Springer, Carolina, 523 p.
9 . Crossley A J (1999) Accurate and efficient numerical solution for Saint Venant equations of open channel. Nottingham University, Nottingham, Ph.D. Dissertation.
10 . Garcia-Navarro P and Vazques-Cendon  M  E (2000) On numerical treatment of the source terms in the shallow water equations. Computers and Fluids, 29(8): 951–979.
11 . Guinot V and Delenne C (2012) MUSCL schemes for the shallow water sensitivity equations with passive scalar transport. Computers and Fluids, 59 (1): 11-30.
12 . Korichi Kh and Hazzab A (2010) Application of Shock Capturing Method for Free Surface Flow Simulation. Jordan Journal of Civil Engineering, 4(4): 310-320.
13 . Lai W and Khan A A (2012) Discontinuous Galerkin method for 1D shallow water flows in natural rivers. Engineering Applications of Computational Fluid Mechanics, 6(1): 74-86.
14 . Lencina I V (2007) Comparison between 1D and 2D models to analyze the dam break wave using the FEM method and the shallow water equations. Royal Institute of Technology, Sweden, Master’s Dissertation.
15 . Leon  A S (2007) Improved Modeling of Unsteady Free Surface, Pressurized and Mixed Flows in Storm-sewer Systems. Illinois University, Urbana-Champaign, Ph.D. Dissertation.
16 . Leveque R J (2002) Finite-Volume Methods for Hyperbolic Problems. Cambridge University Press, New York, 580 p.
17 . Liang D and Falconer R and Lin B (2006) Comparison between TVD-Mac Cormack and ADI-type solvers of the shallow water equations. Advances in Water Resources, 29(12): 1833-1845.
18 . Liang Q and Marche F (2009) Numerical resolution of well-balanced shallow water equations with complex source terms. Advances in Water Resources, 32(6): 873–884.
19 . Mohapatra P K and Bhallamudi S M (1996) Computation of a dam-break flood wave in channel transitions. Advances in Water Resources, 19(3): 181-187
20 . Sanders B F (2001) High Resolution and Non-Oscillatory Solution of the St.Venant Equations in Non-Rectangular and Non-Prismatic Channels. journal of Hydraulic Research, 39(3): 236-244.
21 . Song L and Zhou J and Guo  j and Liu  Y (2011) A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain. Advances in Water Resources, 34(7): 915–932.
22 . Toro E F (2001) Shock Capturing Methods for Free Surface Shallow Flows. Wiley, Chichester, 326 p.
23 . Toro E F (2009) Riemann Solvers and Numerical Methods for Fluid Dynamics. 3thed. springer, verlag berlin Heidelberg, 724 p.
24 . Zhou  J G and Causon D M and Mingham C G and Ingram D M (2001) Surface gradient method for treatment of source terms in the shallow-water equations. Computer and Physics, 168(1): 1-25.
25 . Zia A and Banihashemi M A (2008) Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds. International journal for Numerical Methods in Fluids, 56(11): 2021-2043.