"If a man will begin with certainties, he shall end in doubts;
but if he will be content to begin with doubts, he shall end in certainties." - F. Bacon - 1605.

The availability of powerful computational resources and general purpose numerical algorithms creates increasing opportunities to attempt flow simulations in complex systems. How accurate are the resulting predictions? Are the mathematical and physical models correct? Do we have sufficient information to define relevant operating conditions? In general, how can we establish error bars on the results?

Uncertainty Quantification (UQ) aims at developing rigorous methods to characterize the impact of limited knowledge on quantities of interest. At the interface between physics, mathematics, probability and optimization, and although quite mature in the experimental community, UQ efforts are in their infancy in computational science.

Our group is focused on the quantification of uncertainties in computational fluid dynamics.

Simulations of turbulent flow around a cylinder subject to "uncertain" heating. The colors correspond to temperature. The plot on the right, shows the expected temperature, E(T), and the corresponding uncertainty (99% confidence range) in the wake region. >> Read more Simulations of transonic flow around an airfoil subject to uncertain free stream conditions. The pressure distributions corresponding to the extrema of the free stream Mach number range do not envelope the overall uncertainty because of the strong non-linearity of the shock-induced separation. >> Read more