The objective of this work is to perform a direct numerical simulation of turbulent channel flow where all essential scales of
motion are resolved due to variable time-stepping algorithm in various time advancement method and different discritized form
of convection term. A pseudo spectral method (Fourier series in stream-wise and span-wise directions and Chebychev polynomial
expansion in normal direction) is employed for the spatial derivatives. The time advancement is carried out by different semiimplicit
and splitting schemes. Also Alternating and Linearized forms are added to four commonly used forms of the convective
term, referred to as divergence, Convection, skew-symmetric, and rotational. Spectral method based on the primitive variable
formulation is used in Cartesian coordinates with two periodic and one non-periodic boundary condition in three dimensional
directions &Omega=[0,4&pi]×[-1,1]×[0,2&pi]. The friction Reynolds number for channel flow is set to be Re&tau=175 and the computational
grids of 128×65×128 are used in the x, y and z directions, respectively. The comparison is made between turbulent quantities
such as the turbulent statistics, wall shear velocity, standard deviation of u and total normalized energy of instantaneous velocities
in different time-discretization methods and different forms of nonlinear term. The present results show that third-order timediscretizations
forward Euler for explicit terms and backward Euler for implicit terms can minimize the computational cost of
integration by maximizing the time step, while keeping the CFL number near a threshold in time-discretization schemes. Also, the
de-aliased results of turbulence statistics do indicate that different expressions of nonlinear terms have minor discrepancy in
pseudo spectral method. The results show that the most desirable approach is a combination of variable time stepping third order
backward difference algorithm and rotational form, which provides reduced cost and further accuracy improvements.
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