Document Type : Original Research Paper

Authors

1 Civil Engineering Department, Iran University of Science and Technology,Tehran,Iran

2 Faculty of Engineering, Shahid Rajaee Teacher Training University,Tehran,Iran

Abstract

Analyzing the flow on dams by numerical methods compared to the physical model preparation is the most efficient way to reduce costs and time.
In general the type of method used, flow analysis on overflows in its permanent condition requires solving the category of differential equations involved called Navirastox equations in order to make the free surface of the flow very complex and uneconomical.One type of equation used in overflows is the use of medium depth equation model, or in other words, shallow water equations that result from integrating the Navier-Stokes equations in depth and applying boundary conditions of surface and substrate. Intermediate depth equations, also known as shallow water equations, are mainly used to simulate currents where the velocity value is constant at depth of flow and the pressure distribution at depth is hydrostatic.Due to the complexity of the equations and the lack of a precise answer, different numerical methods have been developed to solve the equations governing the physical phenomena.One of the newest of these methods is the set of methods without a network, which has been introduced in the last two decades to solve differential equations, each of which has its own advantages and disadvantages.
Dissociation of the problem in many non-networked methods leads to integral equations, the solution of which requires numerical integralization and the introduction of gaseous points and related weights along with networking.
In this paper, the least squares method is used to solve shallow water equations.At least discrete squares have been used in the dissection phase of the differential equation to achieve algebraic equations, as well as the minimum weight squares of the data in order to obtain the values ​​of the form functions.The most important advantage of this method should be considered in eliminating the steps of integrating the process of calculating the matrices of the coefficients and also supporting it without networking in the real sense.Correction of the method has been done by numerical analysis of the flow on the overflow of one of the dams of the country and its comparison with the results related to the speed and water level in the physical model.

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###### ##### References
1) Arash Yavari, Ali Kaveh, Shahram Sarkani , Hosein Ali Rahimi Bondarabady Topological aspects of meshless methods and nodal ordering for meshless discritization; Int. J. Numer. Meth. Engng. 52,921-938 (2001).
2) B. Nayroles, G.Touzot and P.Villon; Generalizing the finite element method diffuse approximation and diffuse element; Coput. Mech. 10,307-318 (1992).
3) T. Belytschko, L.Gu and Y.Y.Lu; Fracture and crack growth by element free Galerkin      methods; Model. Simul.Mater. Sci. Engrg.  2,519-534 (1994)
4) T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P.Krysl; Meshless methods : An overview and recent development; Comput. Methods Appl. Mech. Engrg. 139,3-47 (1996).
5) Javier Bonet, Sivakumar Kulasegaram; A simplified approach to enhance the performance of smooth particle hydrodynamics methods; Applied Mathematics and Computation 126,133-155 (2002).
6) Javier Bonet, B. Hassani, L.-T. Lok, S. Kulasegaram; Corrected smooth particle hydrodynamics- a reproducing kernel meshless method for computational mechanics in UK – 5th ACME Annual Conference, (1997).
7) Yunhua. Luo, Ulrich Haussler-Combe; A generalized finite-difference method based on minmizing global residual; Comput. Methods Appl. Mech. Engrg. 191,1421-1438 (2002).
8) E. Onate, S. Idelsohn, O.C. Zienkiewicz, R.L. Taylor, C. Sacco; A stabilized finite point method for analysis of fluid mechanics problems; Comput. Methods Appl. Mech. Engrg. 139,315-346 (1996).
9) E. Onate, S. Idelsohn, O.C. Zienkiewicz, R.L. Taylor; A finite point method in    computational mechanics applications to convective transport and fluid flow; Int. J. Numer. Meth.Engng.Vol.39pp. 3839-3866 (1996).
10) Chongjiang Du; An element free galerki method for simulation of dtationary two dimensional shallow water flows in rivers; Comput. Methods Appl. Mech. Engrg. 182,89-107 (2000).
11) J.K. Chen, J.E. Beraun; A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems; Comput. Methods Appl. Mech. Engrg. 190,225-239 (2000).
12) M. Zerroukat, K. Djidjeli and A. Charafi; Explicit and Implicit Meshless Methods for Linear Advection-Diffusion- type Partial Differential Equation; International Journal for Numerical Methods in Engng. 48,19-35 (2000).
13) I. Boztosun, A. Charafi; An Analysis of the Linear Advection-Diffusion Equation Using Mesh-free and Mesh-depended Methods; Engineering Analysis with Boundary Elements 26,889-895 (2002).
14) Antonio Huerta, and Sonia Fernandez-Mendez; Time accurate consistently stabilized mesh-free methods for convection dominated problems;  Int. J. Numer. Meth. Engng. 56,1225-1242 (2003).
15) Sang-Hoon Park and Sung-Lie Youn; The least-squares meshfree method; Int. J. Numer. Meth. Engng. 52,997-1012 (2001).
16) M. H. Afshar; Linear and quadratic least square finite element method for compressible and incompressible flows; Phd  Thesis, Department of Civil Engineering, University college of Swansea, UK, (1992).
17) H. Arzani, M.H. Afshar, Solving Poisson's equations by the Discrete Least Square meshless method; Paper presented at 28th Boundary Elements and other Mesh Reduction Methods (BEM/MRM28), Skiathos, Greece (2006).
18) M.H. Afshar, H. Arzani; Discrete Least Square meshless method for Solving Partial  Differential Equations; Paper presented at 13th Conference on  Finite Elements for Flow Problem, School of Engineering – University of Wales, Swansea- Wales-UK (2005). 