Optimum algorithm for channel flow analysis in direct numerical simulation method

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 semi- implicit 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 ω=[0,4π]*[-1,1]*[0,2π]. the friction reynolds number for channel flow is set to be reτ=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 time- discretizations 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