Evaluating Statistical Error in Unsteady Automotive Computational Fluid Dynamics Simulations

Among the many sources of uncertainty in an unsteady computational fluid dynamics (CFD) simulation, the statistical uncertainty in the mean value of a fluctuating quantity (for example, the drag coefficient) is of practical importance for vehicle design and development. This uncertainty can be reduced by extending the simulation run length, however, this increases the computational cost and leads to longer turnaround times. Moreover, it is desirable to be able to run an unsteady CFD simulation for the minimum amount of time necessary to reach an acceptable amount of uncertainty in the quantity of interest. This work assesses several methods for calculating the uncertainty in the mean of an unsteady signal. Simulated noise is used to validate the methods, and evaluation is carried out using signals from CFD simulations of realistic vehicle geometries. Calculating the uncertainty in the difference between two signals is also discussed. Finally, several methods are compared for estimating the stabilization (or “burn in”) time, which is present in the initialization of any unsteady CFD simulation.