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Despite the large increase in computer power and the advances in solver technology, unsteady flow problems still may require a vast amount of computing time. In this work two approaches are investigated that should lead to a reduction in computing times for unsteady subsonic flows. In the first part of this work a new refinement strategy for grid adaptation is proposed that enables the user to a priori define the maximum usable computer resources. In the second part of this work a Jacobian-free Newton-Krylov algorithm is tailored for unsteady subsonic flow problems. With this algorithm...

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.

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.