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 Structural Engineering and Mechanics   Volume 81, Number 4, February25 2022 , pages 523-527 DOI: https://doi.org/10.12989/sem.2022.81.4.523 Numerical simulation of the flow in pipes with numerical models Hongjie Gao, Xinyu Li, Abdolreza Hooshmandi Nezhad and Amir Behshad Abstract The objective of this study is to simulate the flow in pipes with various boundary conditions. Free-pressure fluid model, is used in the pipe based on Navier-Stokes equation. The models are solved by using the numerical method. A problem called "stability of pipes" is used in order to compare frequency and critical fluid velocity. When the initial conditions of problem satisfied the instability conditions, the free-pressure model could accurately predict discontinuities in the solution field. Employing nonlinear strains-displacements, stress-strain energy method the governing equations were derived using Hamilton's principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The results of this paper are analyzed by hyperbolic numerical method. Results show that the level of numerical diffusion in the solution field and the range of well-posedness are two important criteria for selecting the two-fluid models. The solutions for predicting the flow variables is approximately equal to the two-pressure model 2. Therefore, the predicted pressure changes profile in the twopressure model is more consistent with actual physics. Therefore, in numerical modeling of gas-liquid two-phase flows in the vertical pipe, the present model can be applied. Key Words fluid flow; Navier-Stokes equation; numerical simulation; pipes Address Hongjie Gao: Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China Xinyu Li: Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China; State Key Laboratory of Hydroscience and Hydraulic Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China Abdolreza Hooshmandi Nezhad: Department of Civil Engineering, Jasb Branch, Islamic Azad University, Jasb, Iran Amir Behshad: Faculty of Technology and Mining, Yasouj University, Choram 75761-59836, Iran

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