摘要
针对流动线性稳定性分析中切比雪夫谱配置法对求解参数具有较高敏感性的问题,利用该方法求解关于布拉修斯速度分布的二维平行流稳定性方程,研究了配置点数目、截断距离、坐标变换方式及边界条件施加方式对获得的模态特征值影响规律.结果表明,减小配置点数目和截断距离分别降低特征向量拟合精度和半无界远场边界条件模拟准确性,而过大的配置点数目和截断距离则使模态特征值易受舍入误差影响而发生偏差;在所有模态特征值中,SP族及与A族相交处最易受配置点数目和截断距离影响;当截断距离较大时,指数坐标变换方式计算结果优于代数坐标变换结果,当截断距离较小时结论相反;边界条件的施加方式对模态特征值影响不大,采取返还矩阵法施加方式获得的方程算子矩阵最稳定.
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.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
2016年第8期1246-1254,1263,共10页
Journal of Shanghai Jiaotong University
基金
国家自然科学基金项目(11202131)
国家重点基础研究发展规划(973)项目(2014CB744804)
上海市科委科研计划项目(13DZ0511300)资助
