کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4645994 | 1342074 | 2008 | 13 صفحه PDF | دانلود رایگان |
The numerical implementation of the parabolised stability equations (PSE) using a spectral/hp-element discretisation is considered, and the numerical stability of the governing equations is presented. Analogous to the primitive variable form of the two-dimensional PSE, the equations are ill-posed; although choosing an Euler implicit scheme in the streamwise z-direction yields a stable scheme for sufficiently large step sizes (Δz>1/|β|, where β is the streamwise wavenumber). The source of the instability is a residual ellipticity that remains in the equations, and presents itself as an upstream propagating acoustic wave. Neglecting this term relaxes the lower limit on the step-size restriction. The θ-scheme is also considered, allowing the step-size restriction of the scheme to be determined. The explicit scheme is always unstable, whereas neglecting the pressure gradient term shows stable eigenspectra for θ⩾0.5.
Journal: Applied Numerical Mathematics - Volume 58, Issue 7, July 2008, Pages 1017-1029