Spatial instabilities of the incompressible attachment-line flow using sparse matrix Jacobi-Davidson techniques

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    Abstract

    We consider the linear stability of incompressible attachment-line flow within the spatial framework. No similarity or symmetry assumptions for the instability modes are introduced and the full two-dimensional representation of the modes is used. The perturbation equations are discretized on a two-dimensional staggered grid. A high order finite difference scheme has been developed which gives rise to a large, sparse, quadratic, eigenvalue problem for the instability modes. The benefits of the Jacobi–Davidson method for the solution of this eigenvalue system are demonstrated and the approach is validated in some detail. Spatial stability results are presented subsequently. In particular, instability predictions at very high Reynolds numbers are obtained which show almost equally strong instabilities for symmetric and antisymmetric modes in this regime.
    Original languageEnglish
    Pages (from-to)315-329
    JournalApplied scientific research
    Volume59
    Issue number315
    DOIs
    Publication statusPublished - 1998

    Keywords

    • Jacobi–Davidson method
    • sparse quadratic eigenvalue systems
    • METIS-140450
    • Incompressible attachment-line flow
    • IR-85953
    • Hydrodynamic stability

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