Modelling of the decay of isotropic turbulence by the LES

Abdibekov, Ualikhan; Zhakebaev, D. B.

doi:10.1088/1742-6596/318/4/042042

Cited by 4 publications

(2 citation statements)

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“…At the second stage the Poisson equation is solved, which is satisfies the continuity equation with considering the velocity field from the first stage. Obtained the pressure field is used at the third stage for the recallculate of the final velocity field [6].…”

Section: Methodsmentioning

confidence: 99%

Modelling of the turbulent energy decay based on the finite-difference and spectral methods

Abdigaliyeva¹

2016

INT J MATH PHYS

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Abstract:The work deals with the modeling of turbulent energy using finite-difference and spectral methods. Simulation of the turbulent process is based on the filtered three-dimensional unsteady NavierStokes equations, for the closure of the main equation the dynamic model is used. The mathematical model is solved numerically, the equation of motion is solved by a finite-difference method, the equation for pressure is solved by spectral method. Also new algorithm for the numerical solution of the Poisson equation for finding pressure is developed. In the results of simulation, the change of turbulent kinetic energy over the time, the integral length scale, the change of longitudinal-transverse correlation functions are obtained, and longitudinal and transverse one-dimensional spectra are defined.

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Section: Methodsmentioning

confidence: 99%

Modelling of the turbulent energy decay based on the finite-difference and spectral methods

Abdigaliyeva¹

2016

INT J MATH PHYS

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“…The use of large eddy simulation (LES), which resolves relatively large scales of turbulence and either models the dynamics of the small scales or dissipates them implicitly (numerically), has also been used to study isotropic turbulence. Some important LES studies of isotropic turbulence include Langford and Moser, 35 who showed LES formulations for isotropic turbulence, Thornber et al, 36 who used implicit LES to study decaying homogeneous turbulence, Vreman et al, 37 who used a finite volume approach and attempted to quantify compressibility effects, and Abdibekov and Zhakebaev, 38 who studied decaying isotropic turbulence. Also, Hughes et al 39 formulated various LES approaches for decaying, homogeneous isotropic turbulence; Zang et al 40 performed LES of compressible isotropic turbulence, and Swanson et al 41 studied decaying, homogeneous isotropic turbulence using various weighted essentially non-oscillatory (WENO) schemes and compared solutions with select theories.…”

Section: Introductionmentioning

confidence: 99%

Noise from Isotropic Turbulence

Miller

2017

AIAA Journal

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Turbulence naturally returns to isotropy and often possesses locally isotropic regions. This paper presents a new method to predict noise from turbulence that has returned or is returning to isotropy. The Navier-Stokes equations are decomposed into anisotropic and isotropic turbulent components and corresponding radiating waves. An analytical solution is proposed for the radiating waves associated with isotropic turbulence that contains arguments involving the vector Green's function of the Navier-Stokes equations and the multi-order two-point cross-correlation of the Navier-Stokes equations involving turbulent fluctuations. Using the theory of isotropic turbulence, the two-point cross-correlation of the Navier-Stokes equations is written as a vector-normalized, two-point cross-correlation multiplied by corresponding wavenumber spectra of the structure functions. Composite structure functions of the field variables are adapted from canonical theory of isotropic turbulence. The vector-normalized two-point cross-correlation involves arguments of separation distance, wavenumber, and corresponding turbulent length and time scales. A solution of the vector Green's function of the linearized Navier-Stokes equation for acoustic pressure is derived. A simple system of differential and algebraic equations is proposed to model the statistics of stationary and decaying isotropic turbulence, which are arguments of the model equation. Predictions of acoustic and turbulent statistics are compared with a wide variety of measurements and direct numerical simulations from various sources over a range of Reynolds numbers and initial scales. Predictions compare favorably with previous theories, direct numerical simulations, and measurements.

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