In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an inadequate resolution might introduce numerical noise that triggers premature transition. With AMR, we enable the design of three different and independent meshes for the non-linear base flow, the linear direct and adjoint solutions. Each of those is designed to reduce the truncation and quadrature errors for its respective solution, which are measured via the spectral error indicator. We provide details about the workflow and the refining procedure. The numerical framework is validated for the two-dimensional flow past a circular cylinder, computing a portion of the spectrum for the linearised direct and adjoint Navier-Stokes operators.

翻译：本文提出了自适应网格细化(AMR)技术在不可压缩流全局稳定性分析中的创新应用。精确的网格设计对于过渡流至关重要，因为不当的分辨率可能引入数值噪声，导致过早的转捩。通过AMR技术，我们能够为非线性的基态流、线性直接解和伴随解分别设计三种独立且不同的网格。每种网格均基于谱误差指示器测量，旨在减少对应解的截断误差和求积误差。我们详细阐述了工作流程与细化过程。该数值框架通过二维圆柱绕流进行了验证，计算了线性化直接和伴随Navier-Stokes算子谱的部分特征值。