Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Padé literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.