Identification of multi-scale coherent eddy structures in a homogeneous isotropic turbulence

Kareem, Waleed Abdel; Izawa, Seiichiro; Xiong, Ao Kui; Fukunishi, Yu

doi:10.1504/pcfd.2006.010965

Cited by 12 publications

(6 citation statements)

References 10 publications

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“…where A and φ are the amplitude and the random phase, respectively [17]. The forcing amplitude is chosen as 10 −4 with a low cutoff wave-number (0…”

Section: Forcing Methodsmentioning

confidence: 99%

“…For isotropic turbulence, Refs. [17,18] applied the forcing method to the SRT for simulating box turbulence with resolutions of 128 3 and 256 3 , respectively. There are several techniques for forcing the lattice Boltzmann equation, the first technique is depending on shifting the velocity field based on the Newtonian 2 nd law, the second techniques is depending on adding the force at the collision term as a special term where it was previously proposed in [18].…”

Section: Introductionmentioning

confidence: 99%

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Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

Kareem

IZAWA

Fukunishi

2023

Preprint

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The single relaxation time (SRT) and the revised matrix (RM) lattice Boltzmann models are compared for simulations of three dimensional forced isotropic turbulence with resolutions of 1283 and 2563, respectively. Guo et al.[1] forcing technique with the same forcing parameters and conditions is used to investigate the ability and stability of the two models for simulations of forced turbulence. Some new aspects and results have been confirmed such as the superiority of the MRT model to simulate forced turbulence in comparison with the SRT model. To overcome the stability shortage problem of the lattice Boltzmann models, it is proposed to apply the Courant-Friedichs-Lewy condition (CFL) [2] by multiplying the velocity input with the CFL coefficient which is less than unity and by dividing the output velocity data by the same CFL coeffi-cent. The initial velocity field is chosen as u(x, 0) = 0 and the force is injected at low wave-numbers with a fixed forcing amplitude of 10−4 for all cases. The single relaxation time is set to τ = 0.503 in all SRT simulations. Results show that the obtained turbulent velocity fields yield universal characteristics as proven in previous theoretical, experimental and numerical studies. The Taylor Reynolds number for the simulations are found as : Rλ(SRT) = 62 and Rλ(M RT) = 65 for the resolution of 1283 and Rλ(SRT) = 107 and Rλ(M RT) = 82 for the case of 2563, respectively. To test the weak incompressibility for the SRT model in comparison to the MRT model, the probability distribution function (PDF) of the density ρ is depicted and it is found that ρ is almost unity at all timesteps for the MRT case, while a clear disturbance about unity is observed for the SRT case. Time variation’s statistics such as the Taylor Reynolds number Rλ, the Taylor microscale λ, the Kolmogrov microscale η and energy spectra are calculated and depicted for all cases. One of the disadvantages of the MRT case is the simulations time which is found about twice the SRT simulations time, where about 80 hours are needed for simulating 12000 timesteps in the 2563 case in comparison to 42 hours for the SRT model using the same hardware resources.

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“…where A and φ are the amplitude and the random phase, respectively [17]. The forcing amplitude is chosen as 10 −4 with a low cutoff wave-number (0…”

Section: Forcing Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

Kareem

IZAWA

Fukunishi

2023

Preprint

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“…function F that appeared in the last term in the equation. All the parameters and definitions of the functions introduced in the above LBE can be found in references [8,9], respectively. Also, the force code will be discussed and some parts will be introduced.…”

Section: The Forcing Function and Fortran Codementioning

confidence: 99%

“…Many studies have been presented to study the forcing of the lattice Boltzmann method such as Luo [1], Shan and Chen [2], Guo et al [3], Succi [4], Cosgrove et al [5], Siggia and Patterson [6], Mohseni et al [7]. Generating the velocity field of isotropic turbulence using the forcing function was introduced by Abdel Kareem et al [8] where extracting of multiscale vortical structures was investigated with resolution of 128 3 and the function is also used to resolution of 256 3 by comparing the lattice D3Q15 and D3Q19 models [9]. It was shown that the D3Q19 model is more stable than the D3Q15 model.…”

Section: Introductionmentioning

confidence: 99%

A constant force function for the lattice Boltzmann equation in isotropic turbulence

Kareem

2021

Frontiers in Scientific Research and Technology

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A constant force function for the lattice Boltzmann method is introduced and parts of the programming code are presented. Adding force to the lattice Boltzmann equation is a challenging issue because the nature of the forcing techniques and the nature of the lattice Boltzmann equation (LBE) itself. The LBE is a difference equation and it is coded in the physical space, however, the forcing is usually done in the Fourier space at low wave-numbers. This paper discusses the force function and its coding to be readable by the LBE without losing of any physical meaning of the engineering problem.

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“…The extracted coherent and incoherent parts using the fourth order (PDEs) from a turbulent flow field were studied by Abdel Kareem [8]. Also, Abdel Kareem et al [9] identified the coherent vortices of various scales from a turbulent flow field obtained by a direct numerical simulation (DNS using sharp cutoff filters before the vortex-identifying method. Perona and Malik introduced nonlinear noise removal algorithm [10], which at first was used in image processing and restoration.…”

Section: Introductionmentioning

confidence: 99%

Joint Probability Distribution Functions for the Filtered Velocity Gradient Invariants in Homogeneous Isotropic Turbulence

Kareem¹,

Aty²,

Asker³

2018

TOMEJ

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Background: Turbulent flow is characterized by vortices with different scales. Extraction of various scales and filtering the turbulent field into coherent and incoherent parts are important processes that improve our understanding of turbulent characteristics. Objective: Joint probability distribution functions (JPDFs) for the filtered velocity gradient invariants are extensively studied for different scales as well as for the coherent and incoherent parts of each scale. Methods: The Fourier decomposition and the anisotropic diffusion model are used in the investigation. The extraction process is performed by employing the Fourier decomposition at different cutoff wavenumbers for the velocity field and three distinct scales (large, medium and fine scale) are identified. The velocity gradient invariants such as the second invariant Q and the third invariant R for the different scales are extracted. Then other important invariants such as the rate of rotation tensor QW and the rate of deformation QS are also identified for each scale. The anisotropic diffusion model is used to extract the coherent and incoherent parts of each invariant at each scale. Then the JPDFs of the coherent and incoherent invariants are compared. The scale decomposition and the filtering process are applied for turbulent flow fields that are simulated using the lattice Boltzmann method with resolution of 1283. Results: Results show that the (R-Q) space has a universal topological pear-like shape for the different scales as well as their coherent field. However, the (R-Q)-space for the incoherent fields are found different and no general shape can be observed. The (Qw-QS)-space results show self-similar shapes for coherent fields and for the incoherent fields no specific shape can be observed since the noise distributed as separated points everywhere. Conclusion: Two different methods for extraction and filtering of forced isotropic turbulence and the JPDFs of the velocity gradient invariants are studied. Some universal characteristics for the coherent parts were found. However, for the incoherent parts, no universal JPDFs were found.

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Identification of multi-scale coherent eddy structures in a homogeneous isotropic turbulence

Cited by 12 publications

References 10 publications

Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

A constant force function for the lattice Boltzmann equation in isotropic turbulence

Joint Probability Distribution Functions for the Filtered Velocity Gradient Invariants in Homogeneous Isotropic Turbulence

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