A variational principle in terms of stream function for free-surface flows and its application to the finite element method

Betts, P. L.

doi:10.1016/0045-7930(79)90030-6

Cited by 25 publications

(9 citation statements)

References 6 publications

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“…The numerical results were almost the same as the experimental results, suggesting the insignificant effect of viscosity on the free surface. Ikegawa and Washizu [9] and Bett [10] employed the linear finite element method (FEM) to solve the equations governing the flow field. They confirmed the results of Cassidy [8].…”

Section: Literature Reviewmentioning

confidence: 99%

Numerical Investigation of Cavitation on Spillways. A Case Study: Aydoghmush dam

Barzegari

Foumani

Isari

et al. 2019

NMCE

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Cavitation is among the most complicated and common damages of spillway structures. This phenomenon is controlled by different parameters including the pressure, flow velocity, spillway surface material, operation time, and air flow content. The cavitation index is calculated along the spillway and compared with its critical value using the measured values of the flow's hydraulic parameters. The high cost of experimental models for determining hydraulic parameters, the time required for developing experimental models, and the ever-increasing capabilities of computational fluid mechanics (CFD) models have led to the use of numerical simulation in the flow analyses. The present study employs ANSYS FLUENT to simulate the flow on the spillway of Aydoghmush Dam (Iran), calculate flow parameters, and determine the cavitation index at the flow rates of 35, 800, 1500, and 1850 m 3 /s. The standard k-ε equations were applied to model the turbulent flow, while the volume of fluid (VOF) method was employed to determine the flow's free surface profile. The results showed acceptable consistency between the FLUENT and physical model results. It was also found that cavitation did not occur at any of the flow rates.

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Section: Literature Reviewmentioning

confidence: 99%

Numerical Investigation of Cavitation on Spillways. A Case Study: Aydoghmush dam

Barzegari

Foumani

Isari

et al. 2019

NMCE

View full text Add to dashboard Cite

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“…The application of this method to the free surface flow problems mainly started in 1970s. Chan and Larock (1973), Larock & Taylor (1976), O'Carroll (1976), Betts (1979), Aitchison (1980) and Betts and Assaat (1980) used the FEM principle to solve linear and nonlinear water wave problems without a body. Around the same time, the FEM was also used for the linear wave radiation and diffraction by a floating body.…”

Section: Introductionmentioning

confidence: 98%

A brief summary of finite element method applications to nonlinear wave-structure interactions

Wang

2011

J. Marine. Sci. Appl.

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We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.

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“…Solutions with the finite element method (FEM) began with McCorquodale & Li (1971) for sluice gates. Among many other works that appeared in the literature using FEM, mentioned can be Ikegawa & Washizu (1973), Isaacs (1977), Betts (1979), Khan & Steffler (1996), Sankaranarayanan & Rao (1996) and Braess & Wriggers (2000). As examples of use of the boundary element method (BEM) in the solution of this problem type, mentioned can be Cheng et al (1981), Liggett & Salmon (1981), Jovanovic (1987), Medina et al (1991) and Machane & Canot (1997).…”

Section: Bem Numerical Simulation Of Spillway Flows 1 Introductionmentioning

confidence: 99%

BEM numerical simulation of spillway flows

Mello

2014

Rem: Rev. Esc. Minas

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The study of gravity-free surface flows presents difficulties, such as the nonlinearity of the dynamic boundary condition in the free surface, and also the fact that the location of this surface is not known a priori. Traditionally, this phenomenon has been investigated by physical models, but the progress of computer science and numeric methods has allowed more and more the successful use of mathematical models to simulate this type of flow. This work presents a boundary element method (BEM) numerical simulation of spillway flows with discontinuous linear elements. The solution procedure involves an iterative process in the determination of the free surface. The Newton-Raphson method is adopted together with the use of pseudo-nodes on the free surface and an empiric step factor (or damping factor) which controls the stability and the rate of convergence. An example of WES standard spillway shape is presented. The obtained results are compared with experimental data and they check the efficiency and good precision of the adopted method.

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A variational principle in terms of stream function for free-surface flows and its application to the finite element method

Cited by 25 publications

References 6 publications

Numerical Investigation of Cavitation on Spillways. A Case Study: Aydoghmush dam

Numerical Investigation of Cavitation on Spillways. A Case Study: Aydoghmush dam

A brief summary of finite element method applications to nonlinear wave-structure interactions

BEM numerical simulation of spillway flows

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