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Chin. Phys. B, 2016, Vol. 25(8): 084701    DOI: 10.1088/1674-1056/25/8/084701

Improved algorithm for solving nonlinear parabolized stability equations

Lei Zhao(赵磊), Cun-bo Zhang(张存波), Jian-xin Liu(刘建新), Ji-sheng Luo(罗纪生)
Department of Mechanics, Tianjin University, Tianjin 300072, China
Abstract  Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers.
Keywords:  improved NPSE approach      stationary crossflow vortices      fundamental resonance      hypersonic boundary layers  
Received:  29 January 2016      Revised:  28 March 2016      Published:  05 August 2016
PACS:  47.20.Ib (Instability of boundary layers; separation)  
  47.40.Ki (Supersonic and hypersonic flows)  
  47.20.Lz (Secondary instabilities)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).
Corresponding Authors:  Jian-xin Liu     E-mail:

Cite this article: 

Lei Zhao(赵磊), Cun-bo Zhang(张存波), Jian-xin Liu(刘建新), Ji-sheng Luo(罗纪生) Improved algorithm for solving nonlinear parabolized stability equations 2016 Chin. Phys. B 25 084701

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