Quantifying Uncertainty in CFD

Abstract

There has been recently an intense interest in verification and validation of large-scale simulations and in quantifying uncertainty, and several workshops have been organized to address this subject. Characterization of uncertainty is a complex subject in general, but it can be roughly classified as numerical uncertainty and physical uncertainty. The former includes spatiotemporal discretization errors, errors in numerical boundary conditions (e.g., outflow), errors in solvers or geometry description, etc. On the other hand, physical uncertainty includes errors due to unknown boundary and initial conditions, imprecise transport coefficients or interaction terms, insufficient knowledge of the flow geometry, approximate constitutive laws, etc. Coupled problems involving source and interaction terms tend to be particularly difficult to simulate even deterministically, so providing error bars for such solutions is an even more difficult task. Uncertainty can also be characterized as epistemic, i.e., reducible, or as irreducible. For example, if much finer simulations are performed or better experiments with higher resolution instruments are conducted, that will provide more accurate boundary conditions. This will reduce the uncertainty level. But even in such cases, and certainly in many simulations of realistic configurations, uncertainty is irreducible beyond some level due to insufficient detail of input, e.g., background turbulence and random roughness. There are no absolutely quiet wind tunnels and the ocean or the atmosphere are not quiet environments either.