Large-Scale Eigenvalue Calculations for Stability Analysis of Steady Flows on Massively Parallel Computers

Technical Report · Sun Aug 01 04:00:00 EDT 1999

DOI:https://doi.org/10.2172/10357· OSTI ID:10357

Lehoucq, Richard B ^[1]; Salinger, Andrew G

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1. Sandia National Laboratories

We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady state leads to a generalized eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration, which must be done iteratively for the algorithm to scale with problem size. A representative model problem of 3D incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation.

• Research Organization: Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 10357
• Report Number(s): SAND99-1593
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
BIFURCATION
EIGENVALUES
GRASHOF NUMBER
HEAT TRANSFER
INCOMPRESSIBLE FLOW
PARALLEL PROCESSING
STEADY FLOW