Stagnation point heat flux characterization under numerical error and boundary conditions uncertainty

Abstract

The numerical simulation of hypersonic atmospheric entry flows is a challenging problem. Prediction of quantities of interest, such as surface heat flux and pressure, is strongly influenced by the mesh quality using conventional second-order spatial accuracy schemes while depending on boundary conditions, which may generally suffer from uncertainty. This paper illustrates one of the first systematic quantification of the numerical error and the uncertainty-induced variability for the simulation of hypersonic flows. Specifically, a mesh-convergence study using grid adaptation tools is coupled with surrogate-based approaches to Uncertainty Quantification. The illustrative example is the simulation of the EXPERT vehicle of the European Space Agency employing the US3D solver. First, we show the benefits in using mesh adaptation to simulate hypersonic flows under uncertainty. On the one hand, this practice reduces the numerical uncertainty associated with each prediction and, on the other hand, allows us to obtain a more reliable surrogate model for Uncertainty Quantification by preventing non-physical heat flux values.Secondly, we perform a sensitivity analysis to compare the numerical uncertainty associated with a given mesh with the UQ-induced variability for a specific quantity of interest. In the case considered, the impact of the numerical uncertainty turned out to be at least one order of magnitude less than the quantity of interest variability. This result indicates the possibility of using coarse and adapted meshes for future UQ studies.