PDEs with Uncertainty

Looking at the history of numerical methods for PDEs, the first steps were about improving the modelling: 1D → 2D → 3D steady → unsteady laminar flow → turbulence modelling → large eddy simulation → direct Navier-Stokes simple geometries (e.g. a wing) → complex geometries (e.g. an aircraft in landing configuration) adding new features such as combustion, coupling to structural / thermal analyses, etc.... and then engineering switched from analysis to design