Randomized resolvent analysis

Abstract

Performing global resolvent analysis for high-Reynolds-number turbulent flow calls for the handling of a large discrete operator. Even though such large operator is required in the analysis, most applications of resolvent analysis extracts only a few dominant resolvent response and forcing modes. Here, we consider the use of randomized numerical linear algebra to reduce the dimension of the resolvent operator for achieving computational speed up and memory saving compared to the standard resolvent analysis. To accomplish this goal, we utilize sketching of the linear operator with random test matrices with a Gaussian distribution and with insights from the base flow incorporated to perform singular value decomposition on a low-rank matrix holding dominant characteristics of the full resolvent operator. The strength of the randomized resolvent analysis is demonstrated on a turbulent separated flow over an airfoil. This randomized approach clears the path towards tackling resolvent analysis for higher-Reynolds number bi- and tri-global base flows.

14 pages, 9 figures

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• Resolvent4py: a parallel Python package for analysis, model reduction and control of large-scale linear systems