应用数学和力学（英文版）
應用數學和力學（英文版）
응용수학화역학（영문판）
APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION)
2014年
6期
667-674
,共8页
nonlinear eigenvalue problem%mode decomposition%spatial mode%adjoint equation%orthogonal relationship
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 an N th-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.
