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Finite difference methods for viscous incompressible global stability analysis. (English) Zbl 1242.76208

Summary: In the present article some high-order finite-difference schemes and in particularly dispersion-relation-preserving (DRP) family schemes, initially developed for computational aeroacoustic problems, are used for global stability issue. (The term global is not used in weakly-non-parallel framework but rather for fully non-parallel flows. Some authors refer to this approach as “BiGlobal”.) These DRP schemes are compared with different classical schemes as second and fourth-order finite-difference schemes, seven-order compact schemes and spectral collocation scheme which is usually employed in such stability problems. A detailed comparative study of these schemes for incompressible flows over two academic configurations (square lid-driven cavity and separated boundary layer at different Reynolds numbers) is presented, and we intend to show that these schemes are sufficiently accurate to perform global stability analyses.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76E99 Hydrodynamic stability
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics

Software:

Eigtool; eigs; ARPACK
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Full Text: DOI

References:

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