A New Extrapolation-Based Uncertainty Estimator for Computational Fluid Dynamics

Abstract

A new Richardson extrapolation-based uncertainty estimator is developed which utilizes a global order of accuracy. The most significant difference between the proposed uncertainty estimator (referred to as the global deviation uncertainty estimator) and others in the literature is that we compute uncertainty estimates at all cells/nodes in the domain regardless of the local convergence behavior (i.e., even if the local solution is oscillatory with grid refinement). Various metrics are used to quantitatively calibrate and evaluate the uncertainty estimator compared to the true solution. The metrics are used to assess the global deviation uncertainty estimator compared to other commonly used uncertainty estimators of the same type such as the original grid convergence index (GCI) and the factor of safety method. Four two-dimensional, steady, inviscid flow fields with exact solutions are used to calibrate the parameters in the proposed uncertainty estimator and make up about 30% of the total solution data set. The evaluation data set is composed of several additional steady, two-dimensional and three-dimensional solutions computed using different computational fluid dynamics codes with exact solutions including a zero pressure gradient turbulent flat plate with a well-defined numerical benchmark. All solutions are formally first- or second-order accurate. The global deviation uncertainty estimator is developed using an empirical approach with a focus on local variables and shows significant improvement compared to existing extrapolation-based uncertainty estimates, even when applied to regions where the local convergence behavior is divergent or oscillatory.