Extensions of Navier-Stokes-Euler Governing Equations of Fluid Flow to Fractional Time and Multi-Fractional Space
Publication: World Environmental and Water Resources Congress 2024
ABSTRACT
This paper describes the recently developed governing equations of unsteady multi-dimensional incompressible and compressible flow in fractional time and multi-fractional space. When their fractional powers in time and in multi-fractional space are specified to unit integer values, the developed fractional equations of continuity and momentum for incompressible and compressible fluid flow reduce to the conventional Navier-Stokes equations. As such, these fractional governing equations for fluid flow may be interpreted as generalizations of the conventional Navier-Stokes equations. The derived governing equations of fluid flow in fractional differentiation framework herein are nonlocal in time and space. Therefore, they can quantify the effects of initial and boundary conditions better than the conventional Navier-Stokes equations. For the frictionless flow conditions, the corresponding fractional governing equations were also developed as a special case of the fractional governing equations of incompressible flow. When their derivative fractional powers are specified to unit integers, these equations are shown to reduce to the conventional Euler equations. The numerical simulations were also performed to investigate the merits of the proposed fractional governing equations. It is shown that the developed equations are capable of simulating anomalous sub- and super-diffusion due to their nonlocal behavior in time and space.
Get full access to this chapter
View all available purchase options and get full access to this chapter.
REFERENCES
Bird, R. B., W. E. Stewart, and E. Lightfoot. Transport phenomena, 2nd edition. (John Wiley & Sons, Inc., (2002).
Kavvas, M. L., and A. Ercan. Generalizations of incompressible and compressible Navier-Stokes equations to fractional time and multi-fractional space. Nature’s Scientific Reports, Vol. 12, Article No. 19337, (2022).
Zaslavsky, G. M. Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461–580 (2002).
Information & Authors
Information
Published In
History
Published online: May 16, 2024
ASCE Technical Topics:
- Analysis (by type)
- Compression
- Continuity equations
- Continuum mechanics
- Differential equations
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Equations (by type)
- Flow (fluid dynamics)
- Flow duration
- Fluid dynamics
- Fluid flow
- Fluid mechanics
- Hydraulic engineering
- Hydrologic engineering
- Mathematics
- Models (by type)
- Navier-Stokes equations
- Numerical analysis
- Numerical models
- Solid mechanics
- Structural dynamics
- Structural engineering
- Water and water resources
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.