Meshless Local Petrov-Galerkin (MLPG) method for simulation of transient state shallow water flows

Document Type : Original Article

Authors

1 M.Sc. Student, Water Resources Engineering, University of Birjand

2 Associate Professor, Department of Civil Engineering, University of Birjand., Birjand., Iran

3 Assistant Professor of Civil Engineering, University of Birjand

Abstract

The importance of shallow water flow in water engineering has led to the governing equations to be studied in various methods. Numerical techniques like finite element are one of these methods. These methods solve differential equations in simple and complex geometric cases by meshing on the computing domain. Recently, Mesh less methods that need no meshing or re-meshing on the domain are being used to solve differential equations in both simple and complex geometric cases. In this research, shallow water equations were modeled using Mesh less local Petrov- Galerk in with moving least squares approximation function. Then, the convergent in the variable velocity field problem was solved and the model error rate was calculated. it was indicated that the model has a good accuracy, so that the mean error and root mean square error were -0.0326 and 0.15627 respectively..Then, the water flow was calculated from the overflow of Siah Bishe dam and the results of the model were compared with the measured values. Which confirms the accuracy of solving the equations of shallow water using the Petrov- Galerkin method.

Keywords

References

ارزانی،ح. 1385. حل معادلات آب­های کم­عمق به روش بدون شبکه. رساله دکتری، دانشکده مهندسی عمران، دانشگاه علم و صنعت، تهران
رحمانی فیروزجائی،ع.، فرویزی،ف. 1392. حل عددی معادلات آب­های کم­عمق با استفاده از روش بدون شبکه گالرکین. هفتمین کنگره ملی مهندسی عمران، دانشکده مهندسی شهید نیکبخت، 17 و 18 اردیبهشت. زاهدان
محتشمی،ع.، اکبرپور،ا.، ملازاده،م. 1396. مدل­سازی جریان آب زیرزمینی در آبخوان آزاد در حالت ماندگار به روش بدون شبکه محلی پتروو – گالرکین. مجله مهندسی مکانیک مدرس، اردیبهشت 96. 17. 2: 393-403
Atluri,S.N and Zhu,T.L. 2000. The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics, Computational mechanics. 25: 169-179.
Belytschko,T., Lu,Y.Y., Gu,L. 1994. Elements free galerkin methods, International journal for numerical methods in engineering. 30. 2: 229-256.
Darbani,M., Ouahsine,A., Villon,P., Naceur,H., Smaoui,H. 2011. Meshless method for shallow water equations with free surface flow. Applied mathematics and computation.217: 5113-5124.
Gingold,R.A and Monaghan,J.J. 1977. Smoothed particle hydrodynamics:Theory and applications to non-spherical stars, Monthly notices of the royal astronomical Society. 181: 375–389.
Liu,G. 2002. Mesh free methods: Moving beyond the finite element method, Boca raton: CRC press.
Liu,G., Gu,Y.T. 2005. An introduction to meshfree methods and their programming, Published by springer, P.O.BOX17, 3300 AA dordrecht, the netherland.
Nayroles,N., Touzot,G., Villon,P.1992. generalizing   the finite element method: Diffuse approximation and diffuse elements, computaional mechanics.10. 5: 307-318.
RahmaniFiroozjaee,A and Afshar,M.H. 2011. Discrete least squares meshless (DLSM) method for simulation of steady state shallow water flows, scientiaIranica. 18: 835-845.
Rodriguez-Paz,M., Bonet,J. 2005. A corrected smooth particle hydrodynamics formulation of the shallow-water equations. Computers and structures. 83. 1396-1410.
Zhou,X., Hon,Y.C and Cheung,K.F. 2004. A grid-free, Nonlinear shallow-water model with moving boundary. Journal of engineering analysis with boundary elements. 28: 967-973.
Zounemat-Kermani,M and Ghiasi-Tarzi,O. 2016. Using natural element mesh-free numerical method in solving shallow water equations, European journal of environmental and civil engineering. 21: 753-767.
Iranian Journal of Irrigation & Drainage
Volume 12, Issue 3 - Serial Number 69
September and October 2018
Pages 512-524

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