Well-conditioned ultraspherical and spectral integration methods for resolvent analysis of channel flows of Newtonian and viscoelastic fluids

Gokul Hariharan, Satish Kumar, Mihailo R. Jovanović

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Modal and nonmodal analyses of fluid flows provide fundamental insight into the early stages of transition to turbulence. Eigenvalues of the dynamical generator govern temporal growth or decay of individual modes, while singular values of the frequency response operator quantify the amplification of disturbances for linearly stable flows. In this paper, we develop well-conditioned ultraspherical and spectral integration methods for frequency response analysis of channel flows of Newtonian and viscoelastic fluids. Even if a discretization method is well-conditioned, we demonstrate that calculations can be erroneous if singular values are computed as the eigenvalues of a cascade connection of the frequency response operator and its adjoint. To address this issue, we utilize a feedback interconnection of the frequency response operator with its adjoint to avoid computation of inverses and facilitate robust singular value decomposition. Specifically, in contrast to conventional spectral collocation methods, the proposed method (i) produces reliable results in channel flows of viscoelastic fluids at high Weissenberg numbers (∼500); and (ii) does not require a staggered grid for the equations in primitive variables.

Original languageEnglish (US)
Article number110241
JournalJournal of Computational Physics
Volume439
DOIs
StatePublished - Aug 15 2021

Bibliographical note

Funding Information:
This work is supported in part by the National Science Foundation under Award CBET-1510654 and by the Air Force Office of Scientific Research under Award FA9550-18-1-0422 . The Minnesota Supercomputing Institute (MSI) at the University of Minnesota is acknowledged for providing computing resources.

Funding Information:
This work is supported in part by the National Science Foundation under Award CBET-1510654 and by the Air Force Office of Scientific Research under Award FA9550-18-1-0422. The Minnesota Supercomputing Institute (MSI) at the University of Minnesota is acknowledged for providing computing resources.

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Computational tools for PDEs
  • Input-output analysis
  • Newtonian and viscoelastic fluid mechanics
  • Resolvent analysis
  • Spatio-temporal frequency responses
  • Spectral integration method

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