A Modified Time Advancement Algorithm for Optimizing Channel Flow Analysis in Direct Numerical Simulation Method

In this research a direct numerical simulation (DNS) of turbulent flow is performed in a geometrically standard case like plane channel flow. Pseudo spectral (PS) method is used due to geometry specifications and very high accuracy achieved despite relatively few grid points. A variable time-stepping algorithm is proposed which may reduce requirement of computational cost in simulation of such wall-bounded flow. Channel flow analysis is performed with both constant and varied time-step for ۱۲۸ × ۶۵×۱۲۸ grid points. The time advancement is carried out by implicit third-order backward differentiation scheme for linear terms and explicit forward Euler for nonlinear convection term. PS method is used in Cartesian coordinates with Chebychev polynomial expansion in normal direction for one non-periodic boundary condition. Also Fourier series is employed in stream-wise and span-wise directions for two periodic boundary conditions. The friction Reynolds number is about Reτ=۱۷۵ based on a friction velocity and channel half width. Standard common rotational form was chosen for discritization of nonlinear convective term of Navier-Stocks equation. The comparison is made between turbulent quantities such as the turbulent statistics, Reynolds stress, wall shear velocity, standard deviation of (u) and total normalized energy of instantaneous velocities in both time-discretization methods. The results show that if final decision rests on economics, the proposed variable time-stepping algorithm will be proper choice which satisfies the accuracy and reduces the computational cost.

Keywords:

Channel flow , Pseudo spectral method , Variable time , Direct numerical simulation , stepping algorithm