The gradient term suppression (GTS) method for removing the hydrodynamic instability appearing in the time-domain solutions of the linearized Euler equations (LEE) along a lined flow duct is assessed. For this, the characterization of a convective instability in the time domain, with the aid of a complementary modal analysis, is first presented. The effect of the mesh size and spatial filtering on the instability is investigated. In particular, a convergence of the instability in the time domain is achieved for a small enough grid size. The consequence of suppressing the mean flow gradient term on the modes is then investigated. It is shown that the unstable modes are indeed removed, but also that acoustic modes are significantly modified, especially for low Helmholtz numbers. The GTS method is finally applied to the NASA grazing impedance tube benchmark. It is found that tuning the weight of the mean flow gradient term within the LEE can be effective for suppressing the instability while conserving a reasonable accuracy of the acoustic component.

评估了梯度项抑制（GTS）方法，该方法用于消除沿衬里流动管道在线性化Euler方程（LEE）的时域解中出现的流体动力不稳定性。为此，首先提出了在时域内对流不稳定性的表征，并借助互补模态分析。研究了网格大小和空间滤波对不稳定性的影响。特别地，对于足够小的网格尺寸，实现了时域中的不稳定性的收敛。然后研究了在模式上抑制平均流量梯度项的结果。结果表明，确实消除了不稳定的模态，而且显着地改变了声模，特别是对于低亥姆霍兹数。最终，将GTS方法应用于NASA放牧阻抗管基准测试。发现在LEE内调整平均流量梯度项的权重可以有效地抑制不稳定性，同时保持合理的声学分量精度。