有限振幅T-S波在非平行边界层中的非线性演化研究

研究对非平行边界层稳定性有重要影响的非线性演化问题,导出与其相应的抛物化稳定性方程组,发展了求解有限振幅T-S波的非线性演化的高效数值方法。这一数值方法包括预估-校正迭代求解各模态非线性方程并避免模态间的耦合,采用高阶紧致差分格式,满足正规化条件,确定不同模态非线性项表和数值稳定地作空间推进。通过给出T-S波不同的初始幅值,研究其非线性演化。算例与全Navier-Stokes方程的直接数值模拟(DNS)的结果作了比较。

Nonlinear Evolution Analysis of T-S Disturbance Wave at Finite Amplitude in Nonparallel Boundary Layers

The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T_S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor_corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T_S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier_Stokes equations.