Mode decomposition of nonlinear eigenvalue problems and application in flow stability
Mode decomposition of nonlinear eigenvalue problems and application in flow stability
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非线性特征值问题的模态分解及其在流动稳定性中的应用
DOI：
10.1007/s10483-014-1820-6
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Luo Ji-sheng
中科院分区：
文献类型：
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作者：
Gao Jun;Luo Ji-sheng
在马赫数为4.5的平板边界层入口引入不同扰动形式进行直接数值模拟。根据线性化Navier-Stokes方程及其伴随方程的双正交本征函数系，很容易实现直接数值模拟结果分解为离散简正模态。分解系数可以通过数值结果与伴随方程的特征函数之间的内积来求解。对于二次多项式特征值问题，以简单的形式给出内积算子，并将其推广到N次多项式特征值问题。算例说明简化模态分解可用于分析直接数值模拟结果。
Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to anNth-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.