Development of a two-dimensional flow model using a time-splitting scheme and regular rectangular mesh

Document Type : Original Article

Authors

1 Department of Water Sciences and Engineering, Faculty of Agriculture, Razi University, Kermanshah, Iran.

2 Department of Civil Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran.

Abstract

Objective: In this study, a two-dimensional numerical model is presented to simulate the flow in open channels. The governing equations of the flow are depth-averaged Navier-Stokes equations, which are separated and solved using the finite volume method and the time-splitting scheme. One of the advantages of the time-splitting method is the ability to solve the different terms of the equations separately using the best numerical scheme. Another advantage of this method is its simplicity and ease of understanding, because in all stages the equations are solved in one dimension.
 
Method: Generating the mesh is one of the most important initial operations for solving the governing equations. in this research, a regular rectangular grid was used. The water level variable was defined at the center of the cell and the velocity and discharge were defined at the boundaries of each cell. In order to solve the governing equations of the flow in this model, each time step is divided into several stages. Initially, the advection terms of the equation of motion were solved based on the Fromm scheme and its output was considered for the diffusion term. The diffusion term in the momentum equation was solved implicitly using the TDMA algorithm. Then, the friction term in the flow equation was separated and solved explicitly, and then the water level was calculated by simultaneously solving the continuity equation and the remaining terms of the momentum equations.
 
Results: In order to verify the validity of the two-dimensional model, The longitudinal profile of gradually varying flow in a rectangular channel, hydraulic jump, sudden channel opening, and asymmetric dam failure were considered for evaluating the model. The output results of the numerical model show that the developed model is capable of simulating the flow for different conditions with appropriate accuracy.
 
Conclusions: The time splitting algorithms with staggered grid approach are used to handle the coupling of water depth and velocity parameter. In this case, water level variable was defined at the center of the cell and the velocity and discharge were defined at the boundaries of each cell. The proposed model has been tested in several experimental cases of flow. The simulated water depth and velocity in time and space are in good agreement with the measured data

Keywords

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References

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Advanced Technologies in Water Efficiency
Volume 5, Issue 2
June 2025
Pages 94-115

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History

  • Receive Date: 17 January 2025
  • Revise Date: 01 March 2025
  • Accept Date: 13 April 2025

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