Application of a fractional-step method to incompressible Navier-Stokes equations

Kim, John; Moin, Parviz

doi:10.1016/0021-9991(85)90148-2

Cited by 2,699 publications

(1,741 citation statements)

References 15 publications

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“…The numerical code uses a relatively classical fractional-step method (Kim & Moin 1985;Perot 1993) to solve the incompressible Navier-Stokes equations expressed in primitive variables. It is discussed in detail in Simens (2008) and Simens et al (2009), which also contain examples of applications to other problems.…”

Section: The Numerical Simulationmentioning

confidence: 99%

Turbulent boundary layers and channels at moderate Reynolds numbers

et al. 2010

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The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/S =0.3-0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reg «2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

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Section: The Numerical Simulationmentioning

confidence: 99%

Turbulent boundary layers and channels at moderate Reynolds numbers

et al. 2010

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“…Furthermore, the effect of surface roughness is included by reconstructing the irregularities of the terrain surface in high resolution. The computational algorithm and the time marching method are based on a fractional-step (FS) method 17) and the Euler explicit method, respectively. The Poisson's equation for pressure is solved by the successive over-relaxation (SOR) method.…”

Section: Summary Of the Riam-compact Natural Terrain Version Softwarementioning

confidence: 99%

Wind Turbine Control Based on Computational Fluid Dynamics (CFD) and Its Economic Effects

Uchida¹

2018

Preprint

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At the Atsumi Wind Farm in Aichi Prefecture, Japan, damage to wind turbines occurred frequently due to terrain-induced turbulence. In the present study, numerical analyses of terraininduced turbulence were conducted by reproducing the topography in the vicinity of the wind turbine sites in high resolution and using RIAM-COMPACT natural terrain version, which is based on large eddy simulation (LES). The results of the diagnoses indicated that, in the case of south-easterly wind, terrain-induced turbulence is generated at a small terrain feature located upstream of Wind Turbine (WT) #2, which serves as the origin of the turbulence. At the Atsumi Wind Farm, a combination of the series of wind diagnoses and on-site operation experience led to a decision to adopt an "automatic shutdown program" for WTs #1 and #2. Here, "automatic shutdown program" refers to the automatic suspension of wind turbine operation upon the wind speed and direction meeting the conditions associated with significant effects of terrain-induced turbulence at a wind turbine site. The adoption of the "automatic shutdown program" has successfully resulted in a large reduction in the number of occurrences of wind turbine damage, thus, creating major positive economic effects. 1) a reduction in the repair costs by 9.322 million yen per year per wind turbine, 2) an increase in the availability factor by 8.05%, and 3) an increase in the capacity factor by 1.7%.

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“…Both convective and di↵usive fluxes are approximated by second-order central di↵erences. A second-order-accurate semi-implicit fractional-step procedure (Kim & Moin 1985) is used for the temporal discretization. The Crank-Nicolson scheme is used for the wall-normal di↵usive terms, and the Adams-Bashforth scheme for all the other terms.…”

Section: Problem Formulationmentioning

confidence: 99%

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures

Omidyeganeh

Piomelli

2013

J. Fluid Mech.

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This is the accepted version of the paper.This version of the publication may differ from the final published version. We performed large-eddy simulations of the flow over a series of three-dimensional (3D) dunes at laboratory scale. The bedform three-dimensionality was imposed by shifting a standard two-dimensional (2D) dune shape in the streamwise direction according to a sine wave. The turbulence statistics were discussed in Part 1 of this article [M. Omidyeganeh, U. Piomelli, J. Fluid Mech. 721, pp. 454-483, (2013)]. Coherent flow structures and their statistics are discussed concentrating on two cases with the same crestline amplitudes and wavelengths but di↵erent crestline alignments: in-phase and staggered. The present paper shows that the induced large-scale mean streamwise vortices are the primary factor that alters the features of the instantaneous flow structures. Wall turbulence is insensitive to the crestline alignment; alternating high-and low-speed streaks appear in the internal boundary layer developing on the stoss side, whereas over the node plane (the plane normal to the spanwise direction at the node of the crestline), they are inclined towards the lobe plane (the plane normal to the spanwise direction at the most downstream point of the crestline) due to the mean spanwise pressure gradient. Spanwise vortices (rollers) generated by Kelvin-Helmholtz instability in the separated shear-layer appear regularly over the lobe with much larger length scale than those over the saddle (the plane normal to the spanwise direction at the most upstream point of the crestline). Rollers over the lobe may extend to the saddle plane and a↵ect the reattachment features; their shedding is more frequent than in 2D geometries. Vortices shed from the separated shear-layer in the lobe plane undergo a three-dimensional instability while advected downstream, and rise toward the free surface. They develop into a horseshoe shape (similar to the 2D case) and a↵ect the whole channel depth, whereas those generated near the saddle are advected downstream and toward the bed. When the tip of such a horseshoe reaches the free surface, the ejection of flow at the surface causes "boils" (upwelling events on the surface). Strong boil events are observed on the surface of the lobe planes of 3D dunes more frequently than in the saddle planes. They also appear more frequently than in the corresponding 2D geometry. The crestline alignment of the dune alters the dynamics of the flow structures, in that they appear in the lobe plane and are advected towards the saddle plane of the next dune, where they are dissipated. Boil events occur at a higher frequency in the staggered alignment, but with less intensity than in the in-phase alignment. Permanent repository link

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Application of a fractional-step method to incompressible Navier-Stokes equations

Cited by 2,699 publications

References 15 publications

Turbulent boundary layers and channels at moderate Reynolds numbers

Turbulent boundary layers and channels at moderate Reynolds numbers

Wind Turbine Control Based on Computational Fluid Dynamics (CFD) and Its Economic Effects

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures

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