Time-space fractional governing equations of one-dimensional unsteady open channel flow process: Numerical solution and exploration

Date

2017-07-01

Author

Ercan, Ali
Kavvas, M. Levent

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Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics, and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time-space fractional governing equations of 1-dimensional unsteady/non-uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint-Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint-Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional-order differentiation framework have the capability of modelling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may possibly shed light on understanding the theory of the anomalous transport processes and observed heavy-tailed distributions of particle displacements in transport processes.

Subject Keywords

fractional differentiation, nonlocal processes, numerical solution, open channel flow, time-space fractional governing equations, ADVECTION-DISPERSION EQUATION, SAINT-VENANT EQUATIONS, HURST PHENOMENON, DIFFUSION-EQUATIONS, CALCULUS, MODELS, TURBULENCE, TRANSPORT, MEDIA

URI

https://hdl.handle.net/11511/100527

Journal

HYDROLOGICAL PROCESSES

DOI

https://doi.org/10.1002/hyp.11240

Collections

Department of Civil Engineering, Article

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Citation Formats

A. Ercan and M. L. Kavvas, “Time-space fractional governing equations of one-dimensional unsteady open channel flow process: Numerical solution and exploration,” HYDROLOGICAL PROCESSES, vol. 31, no. 16, pp. 2961–2971, 2017, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100527.