Self-consistent parabolized stability equation (PSE) method for compressible boundary layer

The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determin...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2015-07, Vol.36 (7), p.835-846
Main Authors: Zhang, Yongming, Su, Caihong
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical Mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-015-1951-9