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Randomized resolvent analysis

Jean Hélder Marques Ribeiro*, Chi-An Yeh†, and Kunihiko Taira‡

  • Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, California 90095, USA

  • *jeanmarques@ucla.edu
  • †cayeh@seas.ucla.edu
  • ‡ktaira@seas.ucla.edu
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Phys. Rev. Fluids 5, 033902 – Published 18 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.033902

Abstract

Performing global resolvent analysis for high-Reynolds-number turbulent flow calls for the handling of a large discrete operator. Even though such a 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 triglobal base flows.

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Phys. Rev. Fluids 5, 033902– Published 18 March, 2020
  • Received 18 May 2019
  • Accepted 25 February 2020
Article part of CHORUS
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