A time-resolved CFD simulation of irregular vortex shedding in the turbulent wake…
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement
Scientific Computing for Physicists, Ch The uncertainty of a simulated number: inputs, sensitivity and correlated output
Problem
A time-resolved CFD simulation of irregular vortex shedding in the turbulent wake behind a cylinder, with cycle-to-cycle fluctuations, records the instantaneous drag coefficient CD once per timestep once the wake is statistically steady, for N=214=16384 steps. The sample mean is CˉD=1.200 and the sample standard deviation of the individual readings is σCD=0.128. Blocking gives the standard error of the mean, σ^b, at block size b: b: 1, 2, 4, 8, 16, 32, 64, 128, 256 σ^b: 0.0010, 0.0014, 0.0019, 0.0026, 0.0032, 0.0037, 0.0039, 0.0040, 0.0040 An ordinary bootstrap that resamples the 16384 raw readings independently with replacement gives a standard error for the coefficient of variation CV=σCD/CˉD of 0.00060. A coarse and a fine mesh give CˉD=1.200 and CˉD=1.198 respectively. The inflow Reynolds number is known to ±2%; propagated linearly through the code's drag response this gives an input uncertainty uinput=0.010 on CˉD.
((a)) Using the chapter's plateau criterion, read off the plateau of the blocking curve and find the statistical inefficiency s and τint (in steps).
((b)) Find the effective sample size Neff.
((c)) Explain why the ordinary-bootstrap value 0.00060 is too small here. Describe how a moving-block bootstrap would give a trustworthy standard error for CV: what is resampled, what block length you would choose from part (a) and why, and what is recomputed. Say why multiplying 0.00060 by s is not a substitute.
((d)) Assemble the uncertainty budget for CˉD (statistical, numerical from the mesh comparison, input as given) and quote the final result.