Document Type : Original Research Paper

Authors

• M.H. Afshar ¹
• H. Arzani ²

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.

Keywords

• Minimum discrete squares
• No network
• The Peacock Equations
• shallow water equation

Main Subjects

• Architecture