Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. II. Numerical Simulations

Date

2015-09-01

Author

Ercan, Ali
Kavvas, M. Levent

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

101
views

0
downloads

In this study, finite difference numerical methods, first order accurate in time and second order accurate in space, are proposed to solve the governing equations of the one-dimensional unsteady kinematic and diffusion wave open-channel flow processes in fractional time and fractional space, which were derived in the accompanying paper. Advantages of modeling open-channel flow in a fractional time-space framework over integer time-space framework are threefold. First, the nonlocal phenomena in the open-channel flow process in either space or time can be considered by taking the global correlations into consideration. Second, the proposed governing equations of the open-channel flow process in the fractional order differentiation framework are generalization of the governing equations in the integer order differentiation framework. Third, the physics of the observed heavy tailed distributions of particle displacements in transport processes, as reported in the literature, may be explained by a flow field that is governed by the nonlocal (or long-range dependence) phenomena. Numerical examples in this study demonstrate that the proposed finite difference methods are capable of solving the governing equations of the one-dimensional unsteady kinematic and diffusion wave open-channel flow processes in fractional time and fractional space. The numerical examples also show that the proposed governing equations, which were derived in the accompanying paper for the one-dimensional unsteady kinematic and diffusion wave open-channel flow processes in fractional time and fractional space, may provide additional flexibility and understanding to model open-channel flow processes. (C) 2014 American Society of Civil Engineers.

Subject Keywords

Fractional governing equations, Fractional differential equations, Kinematic wave, Diffusion wave, Open channel flow, Numerical solution, Nonlocal phenomena, FINITE-DIFFERENCE APPROXIMATIONS, STABILITY, CALCULUS, MODELS

URI

https://hdl.handle.net/11511/100308

Journal

JOURNAL OF HYDROLOGIC ENGINEERING

DOI

https://doi.org/10.1061/(asce)he.1943-5584.0001081

Collections

Department of Civil Engineering, Article

Suggestions

OpenMETU
Core

Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. I. Development of the Equations Kavvas, M. L.; Ercan, Ali (2015-09-01) In this study the fractional governing equations for diffusion wave and kinematic wave approximations to unsteady open-channel flow in prismatic channels in fractional time-space were developed. The governing fractional equations were developed from the mass and motion conservation equations in order to provide a physical basis to these equations. A fractional form of the resistance formula for open-channel flow was also developed. Detailed dimensional analyses of the derived equations were then performed i...
Fractional Ensemble Average Governing Equations of Transport by Time-Space Nonstationary Stochastic Fractional Advective Velocity and Fractional Dispersion. I: Theory Kavvas, M. L.; Kim, S.; Ercan, Ali (2015-02-01) In this study, starting from a time-space nonstationary general random walk formulation, the pure advection and advection-dispersion forms of the fractional ensemble average governing equations of solute transport by time-space nonstationary stochastic flow fields were developed. In the case of the purely advective fractional ensemble average equation of transport, the advection coefficient is a fractional ensemble average advective flow velocity in fractional time and space that is dependent on both space ...
Space and Time Fractional Governing Equations of Unsteady Overland Flow Kavvas, M. Levent; Ercan, Ali; Tu, Tongbi (2021-07-01) Combining fractional continuity and motion equations, the space and time fractional governing equations of unsteady overland flow were derived. The kinematic and diffusion wave approximations were obtained from the space and time fractional continuity and motion equations of the overland flow process. When the fractional powers of space and time derivatives go to 1, the fractional governing equations become the conventional governing equations of unsteady overland flow, and the conventional equations can be...
Fractional incompressible stars Bayin, Selcuk S.; Krisch, Jean P. (2015-10-01) In this paper we investigate the fractional versions of the stellar structure equations for non radiating spherical objects. Using incompressible fluids as a comparison, we develop models for constant density Newtonian objects with fractional mass distributions and/or stress conditions. To better understand the fractional effects, we discuss effective values for the density and equation of state. The fractional objects are smaller and less massive than integer models. The fractional parameters are related t...
Fractional Ensemble Average Governing Equations of Transport by Time-Space Nonstationary Stochastic Fractional Advective Velocity and Fractional Dispersion. II: Numerical Investigation Kim, Sangdan; Kavvas, M. L.; Ercan, Ali (2015-02-01) In this paper, the second in a series of two, the theory developed in the companion paper is applied to transport by stationary and nonstationary stochastic advective flow fields. A numerical solution method is presented for the resulting fractional ensemble average transport equation (fEATE), which describes the evolution of the ensemble average contaminant concentration (EACC). The derived fEATE is evaluated for three different forms: (1) purely advective form of fEATE, (2) moment form of the fractional e...

Citation Formats

A. Ercan and M. L. Kavvas, “Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. II. Numerical Simulations,” JOURNAL OF HYDROLOGIC ENGINEERING, vol. 20, no. 9, pp. 0–0, 2015, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100308.