A cost-effective pseudo-spectral scheme for high-Reynolds-number channel-flow DNS: Accuracy, effective resolution, and computational cost under memory constraints

Direct numerical simulation (DNS) of turbulent channel flow at 𝑅 ⁢ 𝑒 𝜏 = 𝑂 ⁡ ( 1 ⁢ 0 4 – 1 ⁢ 0 5 ) requires maintaining the necessary level of numerical accuracy while minimizing the computational, memory, and communication costs associated with pseudo-spectral discretization. In this study, we quantify the computational efficiency of several nonlinear-term formulations and aliasing-control strategies for channel-flow DNS employing Fourier spectral discretization in the wall-parallel directions and second-order central differences in the wall-normal direction. The accuracy, effective resolution, memory usage, and computational cost of each combination are systematically evaluated. The results demonstrate that the skew-symmetric formulation combined with a 62/64 selective filter not only provides the best overall balance between accuracy and computational efficiency, but also achieves the highest numerical accuracy among all methods when compared under equal computational or memory cost. This combination therefore offers a practical and scalable approach for high-Reynolds-number DNS on modern supercomputers.