Role of Time Integration in Computing Transitional Flows Caused by Wall Excitation

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• 作者：Tapan K. Sengupta ; V. K. Sathyanarayanan…
• 关键词：Spatio ; temporal wave ; front ; Direct numerical simulation ; Dispersion relation preservation schemes ; Turbulent spot formation ; Receptivity analysis
• 刊名：Journal of Scientific Computing
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：65
• 期：1
• 页码：224-248
• 全文大小：1,673 KB
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• 作者单位：Tapan K. Sengupta (1)
  V. K. Sathyanarayanan (1)
  M. Sriramkrishnan (1)
  Akhil Mulloth (1)
  
  1. High Performance Computing Laboratory, Department of Aerospace Engineering, I. I. T. Kanpur, Kanpur, 208 016, India
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

Numerical investigation of receptivity and flow transition in spatio-temporal framework have shown the central role of spatio-temporal wave-front (STWF) created by wall excitation for transition of a two-dimensional (2D) zero pressure gradient boundary layer (ZPGBL) in Sengupta and Bhaumik (Phys Rev Lett 107:154501, 2011). Although the STWF is created by linear mechanism, it is the later nonlinear stage of evolution revealed by the solution of Navier–Stokes equation (NSE), which causes formation of turbulent spots merging together to create fully developed turbulent flow. Thus, computing STWF for ZPGBL from NSE is of prime importance, which has been reported by the present authors following earlier theoretical investigation. Similar computational efforts using NSE by other researchers do not report finding the STWF. In the present investigation we identify the main reason for other researchers to miss STWF, as due to taking a very short computational domain. Secondly, we show that even one takes a long enough domain and detect STWF, use of traditional low accuracy method will not produce the correct dynamics as reported by Sengupta and Bhaumik (2011). The role of time integration plays a very strong role in the dynamics of transitional flows. We have shown here that implicit methods are more error prone, as compared to explicit time integration methods during flow transition. For the present problem, it is noted that the classical Crank–Nicolson method is unstable for 2D NSE. Same error-prone nature will also be noted for hybrid implicit–explicit time integration methods (known as the IMEX methods). One of the main feature of present analysis is to highlight the accuracy of computations by compact schemes used by the present investigators over a significantly longer domain and over unlimited time, as opposed to those reported earlier in the literature for the wall excitation problem. A consequence of taking long streamwise domain enables one to detect special properties of STWF and its nonlinear growth. The main focus of the present research is to highlight the importance of STWF, which is a new class of spatio-temporal solution obtained from the linear receptivity by solving Orr–Sommerfeld equation and nonlinear analysis of NSE. Keywords Spatio-temporal wave-front Direct numerical simulation Dispersion relation preservation schemes Turbulent spot formation Receptivity analysis