Error scaling of wall-modeled large-eddy simulation of compressible wall turbulence

Error scaling properties of large-eddy simulation of compressible wall-bounded turbulent flows are characterized. The statistical quantities of interest investigated are the mean velocity profile, wall stress, and wall heat transfer. The errors scale as (Δ/L)^α Re_τ^γ M^β, where Δ is the characteristic grid resolution, Re_τ is the friction Reynolds number, L is the meaningful length-scale to normalize Δ in order to collapse the errors across the wall-normal distance, and M is the Mach number to account for compressibility effects in the channel flow. Different length-scales are used in determining L such that errors along the wall-normal distance are effectively collapsed. The exponents α, γ, and β are estimated using theoretical analysis and validated through numerical simulations.