Modeling the gradually varied flow profile in circular and parabolic channels using the Adomian decomposition method

To design dimensions of channels, examining the depth of water in a gradually varied flow is required. Therefore, it is essential to calculate the profile of gradually varied flow in the channels. The differential equation of the gradually varied flow needs to be solved to determine the flow's...

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Bibliographic Details
Published in:Modeling earth systems and environment 2021-06, Vol.7 (2), p.1207-1216
Main Authors: Shahvand, Nastaran Sheni, Sanayei, Hamed Reza Zarif, Kamgar, Reza
Format: Article
Language:English
Subjects:
Approximation
Channels
Chemistry and Earth Sciences
Computer Science
Decomposition
Differential equations
Dimensions
Earth and Environmental Science
Earth Sciences
Earth System Sciences
Ecosystems
Environment
Exact solutions
Finite difference method
Flow equations
Flow profiles
Gradually-varied flow
Math. Appl. in Environmental Science
Mathematical Applications in the Physical Sciences
Mathematical models
Numerical analysis
Numerical methods
Original Article
Physics
Statistics for Engineering
Varied flow
Water depth
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Summary:To design dimensions of channels, examining the depth of water in a gradually varied flow is required. Therefore, it is essential to calculate the profile of gradually varied flow in the channels. The differential equation of the gradually varied flow needs to be solved to determine the flow's depth along the channel to obtain this profile. Previous researches have been carried out to solve this equation by employing numerical methods. In this paper, however, a semi-analytical solution has been proposed to solve the gradually varied flow equation in the circular and parabolic prismatic channels using Adomian Decomposition Method (ADM). The ADM results have also been compared with the numerical Finite Difference Method (FDM) for some examples about the circular and parabolic channels. The results are then presented for three approximations of four sentences, five sentences, and six sentences in the ADM in each channel. Moreover, each approximation results have been compared with the results of the profiles obtained by the numerical finite difference method. The profiles of the ADM in this study are in good agreement with those obtained by the FDM. The ADM analytical solutions presented in this paper can validate other numerical methods in similar research.
ISSN:2363-6203
2363-6211
DOI:10.1007/s40808-020-00994-5