The Effect of Nonlinear Form in Direct Numerical Simulation of Channel Flow Analysis

Analysis of turbulent plane channel flow is performed by direct numerical simulation. In this paper
common forms of the nonlinear term are applied to solve Navier-Stokes equations by using pseudo
spectral method. The Navier-Stokes equations are expanded with Chebychev and Fourier series in PS
method and commonly used forms of the nonlinear terms
 
 are explained and applied,
referred to as divergence, convection, skew-symmetric, rotational, alternating and linearized form. The
results of channel flow analysis are presented due to those six forms of the nonlinear terms .The
computational grids of 128×65×128 in computational domain of 1=[0,46]×[-1,1]×[0,26] are used in
the x, y and z directions, respectively. The friction Reynolds number for channel flow is set to be
Re=175.
The comparison is made between turbulent quantities such as the turbulent statistics 

  

 The
results show that that the rotational and linearized forms are more appropriate than other schemes,
especially than skew-symmetric form. But it must be noted that linearized form is not energyconserving
so it is not stable and applicable in all situations. Hence the choice of nonlinear term
reduces to the rotational form in analysis of pseudo spectral method which satisfies robustness and
accuracy and reduces the computational cost at about 62% (compared to other schemes). From
practical point of view, different types of nonlinear term do affect in reduction of total running time at
higher Reynolds number and greater domain in fluid flow, which provides decreased cost and time in
direct numerical simulation of channel flow if final decision rests on economics.