2026/05/31 by Amirreza Rouhi, Vishal Kumar, Wen Wu +2
#physics.flu-dyn
Towards computational cost saving for direct numerical simulations (DNSs) of wall turbulence, we formulate an unstructured grid-generation framework, termed η-grid, where the wall-normal (y) and spanwise (z) grid sizes are proportional to the local Kolmogorov scale η. The framework consists of an inner layer, with a thickness ∼ 50 viscous units, with viscous-scaled grid sizes similar to a conventional DNS grid: 0.3 \lesssim Δy+ \lesssim 4, Δz+ ≃ 5 over a smooth wall, and ℓ+/30 \lesssim Δy+, Δz+ \lesssim 4 over uneven surfaces, where ℓ+ is the smallest surface wavelength. Above the inner layer, Δy+ ≃ Δz+ ≃ 2η+. We test η-grid with finite volume and spectral element solvers, and conduct DNSs of turbulent channel flows and boundary layers over smooth wall and various streamwise-aligned riblets, up to friction Reynolds number δ+0 = 1000. We assess the accuracy of η-grid against the conventional Cartesian grids, through comparison with the reference DNS and experimental data. Results from η-grid and the Cartesian grids differ by less than 1%, in terms of turbulence statistics up to second-order, and the energy spectra. For turbulent channel flows with 103 \lesssim δ+0 \lesssim 104, the number of grid points with η-grid (Nη) scales ∝ δ+02.47 over a smooth wall, and ∝ δ+02.0-2.47 over riblets, whereas the number of grid points with a Cartesian grid and hyperbolic-tangent y-grid (NTanh) scales ∝ δ+03.0. By δ+0 = 6000, Nη/NTanh ≃ 0.1 over a smooth wall, and Nη/NTanh ≃ 0.04 over typical drag-reducing riblets, with viscous-scaled spacing 15.