A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows

Christoph J. Mack; Peter J. Schmid

doi:10.1016/j.jcp.2009.09.019

A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows

Christoph J. Mack, Peter J. Schmid

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

The combination of iterative Krylov-based eigenvalue algorithms and direct numerical simulations (DNS) has proven itself an effective and robust tool in solving complex global stability problems of compressible flows. A Cayley transformation is required to add flexibility to our stability solver and to allow access to specific parts of the full global spectrum which would be out of reach without such a transformation. In order to robustify the overall global stability solver an efficient ILU-based preconditioner has been implemented. With this Cayley-transformed DNS-based Krylov method two flow cases were successfully investigated: (i) a compressible mixing layer, a rather simple but well-known problem, which served as a test case and (ii) a supersonic flow about a swept parabolic body, a challenging large-scale flow configuration. © 2009 Elsevier Inc. All rights reserved.

Original language	English (US)
Pages (from-to)	541-560
Number of pages	20
Journal	Journal of Computational Physics
Volume	229
Issue number	3
DOIs	https://doi.org/10.1016/j.jcp.2009.09.019
State	Published - Feb 1 2010
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)
Computer Science Applications

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10.1016/j.jcp.2009.09.019

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abstract = "The combination of iterative Krylov-based eigenvalue algorithms and direct numerical simulations (DNS) has proven itself an effective and robust tool in solving complex global stability problems of compressible flows. A Cayley transformation is required to add flexibility to our stability solver and to allow access to specific parts of the full global spectrum which would be out of reach without such a transformation. In order to robustify the overall global stability solver an efficient ILU-based preconditioner has been implemented. With this Cayley-transformed DNS-based Krylov method two flow cases were successfully investigated: (i) a compressible mixing layer, a rather simple but well-known problem, which served as a test case and (ii) a supersonic flow about a swept parabolic body, a challenging large-scale flow configuration. {\textcopyright} 2009 Elsevier Inc. All rights reserved.",

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AB - The combination of iterative Krylov-based eigenvalue algorithms and direct numerical simulations (DNS) has proven itself an effective and robust tool in solving complex global stability problems of compressible flows. A Cayley transformation is required to add flexibility to our stability solver and to allow access to specific parts of the full global spectrum which would be out of reach without such a transformation. In order to robustify the overall global stability solver an efficient ILU-based preconditioner has been implemented. With this Cayley-transformed DNS-based Krylov method two flow cases were successfully investigated: (i) a compressible mixing layer, a rather simple but well-known problem, which served as a test case and (ii) a supersonic flow about a swept parabolic body, a challenging large-scale flow configuration. © 2009 Elsevier Inc. All rights reserved.

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A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows

Abstract

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