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Linear stability of flow in a differentially heated cavity via large‐scale eigenvalue calculations

Elizabeth A. Burroughs (Department of Mathematics, Humboldt State University, Arcata, California, USA)
Louis A. Romero (Department of Computational Mathematics and Algorithms, Sandia National Laboratories, Albuquerque, New Mexico, USA)
Richard B. Lehoucq (Department of Computational Mathematics and Algorithms, Sandia National Laboratories, Albuquerque, New Mexico, USA)
Andrew G. Salinger (Department of Parallel Computational Sciences, Sandia National Laboratories, Albuquerque, New Mexico, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 September 2004

Abstract

Locates the onset of oscillatory instability in the fluid flow inside a differentially heated cavity with aspect ratio 2 by computing a steady‐state and analyzing the stability of the system via eigenvalue approximation. Discusses the choice of parameters for the Cayley transformation so that the calculation of selected eigenvalues of the transformed system will reliably answer the question of stability. Also presents an argument that due to the symmetry of the problem, the first two unstable modes will have eigenvalues that are nearly identical, and the numerical experiments confirm this. Finally, locates a co‐dimension 2 bifurcation signifying where there is a switch in the mode of initial instability. The results were obtained using a parallel finite element CFD code (MPSalsa) along with an Arnoldi‐based eigensolver (ARPACK), a preconditioned Krylov method code for the necessary linear solves (Aztec), and a stability analysis library (LOCA).

Keywords

Citation

Burroughs, E.A., Romero, L.A., Lehoucq, R.B. and Salinger, A.G. (2004), "Linear stability of flow in a differentially heated cavity via large‐scale eigenvalue calculations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 14 No. 6, pp. 803-822. https://doi.org/10.1108/09615530410544328

Publisher

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Emerald Group Publishing Limited

Copyright © 2004, Emerald Group Publishing Limited