Screech tones are the high intensity shock-associated noise with discrete frequency in imperfectly supersonic jet. Accuracte numerical simulation of shock-associated noise requires numerical scheme with high order accuracy, low dissipation and low dispersion as well as robust shock-capturing ability. The applicability of eight kinds of upwind/symmetric WENO schemes for the direct numerical simulation of screech tone is evaluated through comparison study on the spectral characteristics and direct numerical simulations of underexpanded supersonic cold jet issuing from circular sonic nozzle. The spectral characteristics based on the approximate dispersion relation shows that the adaptive central-upwind (WENO-SYMCU-6) scheme has the best resolution and the minimum value of point-per-wavelength. However, the comparison of nonlinear response indicates that the improved upwind WENO-ZM-5 (\(p=1\)) scheme has almost the weakest nonlinear response for the single Fourier mode. And the performances in the direct numerical simulations also show that the WENO-ZM-5 (\(p=1\)) scheme is the best. With this method, not only the screech tones of the high amplitude axisymmetric mode are obtained, but also a variety of high-frequency coupling modes with the highest amplitudes can be distinguished in a wider spectrum range. And there is no nonphysical high-frequency wave induced by the nonlinear implementation of WENO schemes at the near region of the nozzle exit lip.

尖声是不完全超音速喷射中具有离散频率的高强度震动相关噪声。冲击相关噪声的精确数值模拟需要具有高阶精度，低耗散和低色散以及强大的冲击捕捉能力的数值方案。通过对圆音速喷嘴超扩音速冷射流的频谱特性和直接数值模拟的比较研究，评价了八种上风/对称WENO方案在尖叫声直接数值模拟中的适用性。基于近似色散关系的光谱特征表明，自适应中心逆风（WENO-SYMCU-6）方案具有最佳分辨率和每波长点的最小值。然而，\（p = 1 \））方案对于单傅立叶模式几乎具有最弱的非线性响应。直接数值模拟的性能也表明，WENO-ZM-5（\（p = 1 \））方案是最好的。通过这种方法，不仅可以获得高幅度轴对称模式的刺耳音调，而且还可以在更宽的频谱范围内分辨出具有最高幅度的各种高频耦合模式。WENO方案的非线性实施不会在喷嘴出口唇缘附近产生非物理高频波。