A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems

The effectiveness of this method is illustrated for a modified version of Kraichnan-Orszag three-mode problem where a discontinuous pdf is associated to the stochastic variable, and for a nozzle flow with shocks. The results have been analyzed in terms of accuracy and probability measure flexibility. Finally, the importance of the probabilistic reconstruction in the stochastic space is shown up on an example where the exact solution is computable, the viscous Burgers equation.