A parameter sensitivity study of chebyshev collocation method in hydrodynamic linear stability analysis

作者：Zhang, Yuxuan; Li, Weipeng^*; Wang, Fuxin

来源：Journal of Shanghai Jiaotong University, 2016, 50(8): 1246-1254 and 1263.

DOI：10.16183/j.cnki.jsjtu.2016.08.017

• Chebyshev collocation method
• Collocation points
• Different boundary condition
• Exponential mapping
• Operator matrices
• Orr-Sommerfeld equations
• Parameter sensitivities
• Unbounded domain

In order to gain insight into the high sensitivity of Chebyshev collocation method to solving parameters when applied to hydrodynamic linear stability analysis, a study of impacts of collocation point numbers, truncation distances, mapping methods and boundary condition implementation methods in Chebyshev collocation method on eigenvalues of Orr-Sommerfeldequation for Blasius profile were conducted. The results show that reduced collocation point numbers and truncation distances contaminate the fitting accuracy of eigenvectors and simulation precision of unbounded domain flow respectively, while too large ones render eigenvalues more susceptible to round off errors and result in a deviation as well.In addition, of all eigenvalues, those in SP branch and in the intersection of SP branch and A branch are most sensitive to collocation point numbers and truncation distances.For a relatively large truncation distance, the exponential mapping method is superior to the algebraic mapping method while for a relatively small truncation distance, the opposite is true. Different boundary condition implementation methods impose a negligible influence on eigenvalues, but in terms of the operator matrix stability, the 'giveback matrix'method should be given priority to.

• 出版日期2016
• 单位上海交通大学