Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. I. Development of the Equations

2015 ◽  
Vol 20 (9) ◽  
pp. 04014096 ◽  
Author(s):  
M. L. Kavvas ◽  
A. Ercan
Keyword(s):  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Kinematic Wave ◽  
Governing Equations ◽  
Diffusion Wave ◽  
Time Space

scholarly journals Numerical Solution and Application of Time-Space Fractional Governing Equations of One-Dimensional Unsteady Open Channel Flow Process

2016 ◽  
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Transport Processes ◽  
Governing Equations ◽  
Flow Process ◽  
One Dimensional ◽  
Time Space ◽  
Flow Processes ◽  
Saint Venant Equations

Abstract. 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 one-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 modeling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may shed light into understanding the theory of the anomalous transport processes and observed heavy tailed distributions of particle displacements in transport processes.

Finite element modeling of surge propagation and an application to the Hay River, N.W.T.

1992 ◽  
Vol 19 (3) ◽  
pp. 454-462 ◽  
Author(s):  
F. E. Hicks ◽  
P. M. Steffler ◽  
R. Gerard
Keyword(s):  
Finite Element ◽  
Channel Flow ◽  
Open Channel ◽  
Initial Conditions ◽  
Open Channel Flow ◽  
Kinematic Wave ◽  
Finite Element Scheme ◽  
Flow Problems ◽  
Ice Jam

This paper describes the application of the characteristic-dissipative-Galerkin method to steady and unsteady open channel flow problems. The robust performance of this new finite element scheme is demonstrated in modeling the propagation of ice jam release surges over a 500 km reach of the Hay River in Alberta and Northwest Territories. This demonstration includes the automatic determination of steady flow profiles through supercritical–subcritical transitions, establishing the initial conditions for the unsteady flow analyses. The ice jam releases create a dambreak type of problem which begins as a very dynamic situation then develops into an essentially kinematic wave problem as the disturbance propagated downstream. The characteristic-dissipative-Galerkin scheme provided stable solutions not only for the extremes of dynamic and kinematic wave conditions, but also through the transition between the two. Key words: open channel flow, finite element method, dam break, surge propagation.

scholarly journals Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: theoretical development

2017 ◽  
Author(s):  
Alain Dib ◽  
M. Levent Kavvas
Keyword(s):  
Monte Carlo ◽  
Channel Flow ◽  
Open Channel ◽  
Planck Equation ◽  
Open Channel Flow ◽  
Theoretical Development ◽  
Roughness Coefficient ◽  
Monte Carlo Approach ◽  
Time Space ◽  
Saint Venant Equations

Abstract. The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian–Eulerian Fokker–Planck Equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

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