Uncertainty quantification for chaotic fluid dynamics

Abstract

We study mesh convergence issues for a representative chaotic flow problem. Convergence in the sense of pointwise convergence fails as new structures emerge with each new level of mesh refinement. We formulate convergence in terms of statistical averages. Care is made to divide the problem into homogeneous regions, and statistical convergence is found for each such region. Automated feature extraction is the tool used for this decomposition.We study of averaged equations, and the closure problem which arises in their derivation. The accuracy of the closure terms is discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)