Abstract Global linear stability analysis of open flows leads to difficulties associated to boundary conditions, leading to either spurious wave reflections (in compressible cases) or to non-local feedback due to the elliptic nature of the pressure equation (in incompressible cases). A novel approach is introduced to address both these problems. The approach consists of solving the problem using a complex mapping of the spatial coordinates, in a way that can be directly applicable in an existing code without any additional auxiliary variable. The efficiency of the method is first demonstrated for a simple 1D equation modeling incompressible Navier–Stokes, and for a linear acoustics problem. The application to full linearized Navier–Stokes equation is then discussed. A criterion on how to select the parameters of the mapping function is derived by analyzing the effect of the mapping on plane wave solutions. Finally, the method is demonstrated for three application cases, including an incompressible jet, a compressible hole-tone configuration and the flow past an airfoil. The examples allow to show that the method allows to suppress the artificial modes which otherwise dominate the spectrum and can possibly hide the physical modes. Finally, it is shown that the method is still efficient for small truncated domains, even in cases where the computational domain is comparable to the dominant wavelength.

中文翻译：

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使用复杂的绘图技术对流体流动进行有效的稳定性分析

摘要 开放流的全局线性稳定性分析导致与边界条件相关的困难，导致虚假波反射（在可压缩情况下）或由于压力方程的椭圆性质（在不可压缩情况下）导致非局部反馈。引入了一种新颖的方法来解决这两个问题。该方法包括使用空间坐标的复杂映射解决问题，其方式可以直接应用于现有代码，无需任何额外的辅助变量。该方法的效率首先在一个简单的一维方程建模不可压缩 Navier-Stokes 和线性声学问题中得到证明。然后讨论了完全线性化 Navier-Stokes 方程的应用。通过分析映射对平面波解的影响，推导出映射函数参数的选取准则。最后，该方法针对三个应用案例进行了演示，包括不可压缩的射流、可压缩的孔色调配置和经过翼型的流动。这些示例允许表明该方法允许抑制人工模式，否则这些人工模式在频谱中占主导地位并且可能隐藏物理模式。最后，表明该方法对于小的截断域仍然有效，即使在计算域与主波长相当的情况下也是如此。可压缩的孔色调配置和流过翼型。这些示例允许表明该方法允许抑制人工模式，否则这些人工模式在频谱中占主导地位并且可能隐藏物理模式。最后，表明该方法对于小的截断域仍然有效，即使在计算域与主波长相当的情况下也是如此。可压缩的孔色调配置和流过翼型。这些示例允许表明该方法允许抑制人工模式，否则这些人工模式在频谱中占主导地位并且可能隐藏物理模式。最后，表明该方法对于小的截断域仍然有效，即使在计算域与主波长相当的情况下也是如此。