Intrusive generalized polynomial chaos with asynchronous time integration for the solution of the unsteady Navier–Stokes equations

Abstract

Generalized polynomial chaos provides a reliable framework for many problems of uncertainty quantification in computational fluid dynamics. However, it fails for long-time integration of unsteady problems with stochastic frequency. In this work, the asynchronous time integration technique, introduced in previous works to remedy this issue for systems of ODEs, is applied to the Kármán vortex street problem. For this purpose, we make use of a stochastic clock speed that provides the phase shift between the realizations and enables the simulation of an in-phase behavior. Results of the proposed method are validated against Monte Carlo simulations and show good results for statistic fields and point-wise values such as phase portraits, as well as PDFs of the limit cycle. We demonstrate that low-order expansions are sufficient to meet the demands for some statistic measures. Therefore, computational costs are still competitive with those of the standard form of intrusive generalized polynomial chaos (igPC) and its non-intrusive counterpart (NigPC).