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 th...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 Nth-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.展开更多
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, w...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 I 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.展开更多
从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光...从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光场慢变包络、光强度的二维和三维分布的直观图形,以及相应能量(无量纲)。结果表明,孤子的存在不是任意的,而是依赖于一定的能量。当光脉冲能量不足以支持孤子的存在时,其解呈振荡形式,说明不存在孤子解。同时还给出介质的饱和参数、孤子在传播方向上的波矢k对孤子模式的影响等有意义的结论。展开更多
基金supported by the National Natural Science Foundation of China(Nos.1133200711202147+2 种基金and 9216111)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120032120007)the Open Fund from State Key Laboratory of Aerodynamics(Nos.SKLA201201 and SKLA201301)
文摘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 Nth-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.
文摘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 I 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.
文摘从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光场慢变包络、光强度的二维和三维分布的直观图形,以及相应能量(无量纲)。结果表明,孤子的存在不是任意的,而是依赖于一定的能量。当光脉冲能量不足以支持孤子的存在时,其解呈振荡形式,说明不存在孤子解。同时还给出介质的饱和参数、孤子在传播方向上的波矢k对孤子模式的影响等有意义的结论。
