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The Effect of Aliased and De-aliased Formulation for DNS Analysis in Plane Poiseuille Flow

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Abstract

In this research, the performance of various aliased and de-aliased schemes was studied in pseudo-spectral (PS) simulation. The PS method was used to perform aliased and de-aliased direct numerical simulation of a turbulent plane Poiseuille channel flow. The effects of aliasing errors in Navier–Stokes equations were examined for both common skew-symmetric and rotational forms. Due to boundary conditions, Fourier series in periodic directions and Chebyshev expansion in normal direction were considered. A third-order backward difference scheme was used for temporal approximation method, and different types of “2/3 rule” de-aliasing procedures in various directions were examined. The results for aliased and de-aliased formulation showed that generally, the skew-symmetric form gives the most accurate results. But de-aliased rotational form was more robust and presented fewer errors. The amount of aliasing errors for the ordinary rotation form is about two times larger than for De-aliased XYZ rotational scheme and common skew-symmetric form. From a practical point of view, the choice between the skew-symmetric form and de-aliased rotational method with the same accuracy reduces to the last one if final decision rests on the amount of computational time.

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Abbreviations

C(u):

The constant term of NSE

dt :

Varied time step

e x :

Unit vector in x direction

k :

Wave number

k A :

Aliased wave number

L(u):

Linear term of NSE

L x :

Period in stream-wise direction

L y :

Period in normal direction

L z :

Period in span-wise direction

N(u):

Nonlinear term of NSE

p tot(x;t):

Total pressure field

p(x;t):

Periodic fluctuating pressure

q :

Modified pressure

Re L :

Initial Reynolds number

Re τ :

Friction Reynolds number

T m :

mth Chebyshev polynomial

u(x):

Vector of velocity flow

u tot(x;t):

Total fluid velocity field

\(\hat{\tilde{u}}_{kx,ny,kz}\) :

Spectral coefficients of u

U(y):

Velocity of base flow

u(x;t):

Fluctuating velocity

α :

Coefficient of the discretization formula in SBDF3

β :

Coefficient of the discretization formula in SBDF3

ζ :

Coefficient of the discretization formula in SBDF3

∆x + :

Grid spacing in the stream-wise direction in wall unit

∆y +min :

Minimum grid spacing in normal directions in wall unit

∆y +max :

Maximum grid spacing in normal directions in wall unit

∆z + :

Grid spacing in the span-wise directions in wall unit

Π x (t):

Spatially constant base pressure gradient

Ω :

Computational domain

ν :

Viscosity

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Authors and Affiliations

  1. Department of Civil Engineering, Payame Noor University, Tehran, Islamic Republic of Iran

    Elham Rajabi

  2. Department of Civil Engineering, Khaje Nasir University of Technology, Tehran, Islamic Republic of Iran

    Mohammad Reza Kavianpour

Authors
  1. Elham Rajabi
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  2. Mohammad Reza Kavianpour
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Correspondence to Elham Rajabi.

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Rajabi, E., Kavianpour, M.R. The Effect of Aliased and De-aliased Formulation for DNS Analysis in Plane Poiseuille Flow. Iran J Sci Technol Trans Civ Eng 41, 77–85 (2017). https://doi.org/10.1007/s40996-016-0032-1

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  • DOI: https://doi.org/10.1007/s40996-016-0032-1

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