Stagnation Point Heat Flux Characterization Under Numerical Error and Boundary Conditions Uncertainty

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 the boundary conditions, which generally suffer from uncertainty. This paper explores these two aspects, illustrating a CFD study on the forebody of the EXPERT vehicle of the European Space Agency employing the US3D solver. First, the numerical error on quantities of interest is characterized on four nested meshes on the nominal conditions; it is shown that grid adaptation tools guarantees a better trend of the numerical error and improves the order of convergence. This behavior translates into having less numerical uncertainty associated with the estimate of the quantity of interest. Secondly, boundary condition uncertainties are propagated, and a surrogate model is built for the four nested meshes for each quantity of interest. The impact of the average numerical uncertainty turned out to be at least one order of magnitude less than the model variability for the chosen uncertainty space, guarantying the robustness of the built model. It is also shown that the importance of numerical uncertainty is reduced more by adapting the grid than by refining it. The study also pointed out how the systematic use of grid adaptation should avoid carbuncle effects that may compromise a correct heat flux estimation, with consequent impact on the surrogate model building and numerical uncertainties