A New Extrapolation-Based Uncertainty Estimator for Computational Fluid Dynamics

A new Richardson extrapolation-based uncertainty estimator is developed which utilizes a global order of accuracy. Various metrics are used to quantitatively evaluate the uncertainty estimators the most important of which is conservativeness which the percentage of uncertainty estimates which bracket the true solution. Another metric is the effectivity index which is a relative measure of accuracy (of either the error or the uncertainty estimate) compared to the true solution. Conservativeness and effectivity of the discretization uncertainty estimators are used to assess the proposed uncertainty estimator compared to other uncertainty estimators such as the GCI and the Factor of Safety method. Four two-dimensional, inviscid flow fields with exact solutions are used to calibrate the uncertainty estimator. Numerous additional solutions computed using different computational fluid dynamics codes with exact solutions and a zero pressure gradient, turbulent flat plate numerical benchmark are used to test the new uncertainty estimator. The proposed uncertainty estimator is developed with a focus on local variables and shows significant improvement in effectivity and conservativeness compared to existing extrapolation-based uncertainty estimates.

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