Title:

Quantification of Uncertainties in high speed fluid flow simulations

Abstract:

Numerical simulation of fluid flows is a key ingredient in the aerodynamic
design of high speed flying vehicles. Uncertainties
  in the atmospheric environment, geometrical imperfections and operating
conditions, can have a strong impact on the overall performance but are
rarely quantified.
The recent development of efficient uncertainty propagation methods has
created the opportunity to  augment the design process with a rigorous
evaluation of the confidence in the numerical predictions.

The talk will introduce the PSAAP Center at Stanford, which is focused on
the simulations of  a hypersonic vehicle. The main difficulty in the
computations of these high speed flows is the presence of sharp
discontinuities (shocks) and sudden state- transitions; this also creates a
challenge for the  uncertainty propagation methods.

Two approaches based on modification of the stochastic collocation
methodology will be introduced.
The first is based on the construction of a global interpolant, while the
second uses a local decomposition of the parameter space. The current status
and the remaining issues will be described.
A recent analysis of stochastic Galerkin methods for hyperbolic systems in
the presence of discontinuities will also be described.