Fluid flows are characterized by uncertain inputs such as random initial data, material and flux coefficients, and boundary conditions. The current volume addresses the pertinent issue of efficiently computing the flow uncertainty, given this initial randomness. It collects seven original review articles that cover improved versions of the Monte Carlo method (the so-called multi-level Monte Carlo method (MLMC)), moment-based stochastic Galerkin methods and modified versions of the stochastic collocation methods that use adaptive stencil selection of the ENO-WENO type in both physical and stochastic space. The methods are also complemented by concrete applications such as flows around aerofoils and rockets, problems of aeroelasticity (fluid-structure interactions), and shallow water flows for propagating water waves. The wealth of numerical examples provide evidence on the suitability of each proposed method as well as comparisons of different approaches.

Timothy Barth: Non-Intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities.- Philip Beran and Bret Stanford: Uncertainty Quantification in Aeroelasticity.- Bruno Després, Gaël Poëtte and Didier Lucor: Robust uncertainty propagation in systems of conservation laws with the entropy closure method.- Richard P. Dwight, Jeroen A.S. Witteveen and Hester Bijl: Adaptive Uncertainty Quantification for Computational Fluid Dynamics.- Chris Lacor, Cristian Dinescu, Charles Hirsch and Sergey Smirnov: Implementation of intrusive Polynomial Chaos in CFD codes and application to 3D Navier-Stokes.- Siddhartha Mishra, Christoph Schwab and Jonas ¦ukys: Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in nonlinear systems of balance laws.- Jeroen A.S. Witteveen and Gianluca Iaccarino: Essentially Non-Oscillatory Stencil Selection and Subcell Resolution inUncertainty Quantification.