This paper presents some of the first results of global linear stability analyses performed using a bespoke eigensolver that has recently been implemented in the next generation flow solver framework CODA. The eigensolver benefits from the automatic differentiation capability of CODA that allows computation of the exact product of the Jacobian matrix with an arbitrary complex vector. It implements the Krylov–Schur algorithm for solving the eigenvalue problem. The bespoke tool has been validated for the case of laminar flow past a circular cylinder with numerical results computed using the TAU code and those reported in the literature. It has been applied with both second-order finite volume and high-order discontinuous Galerkin schemes for the case of laminar flow past a square cylinder. It has been demonstrated that using high-order schemes on coarser grids leads to well-converged eigenmodes with a shorter computation time compared to using second-order schemes on finer grids.

中文翻译：

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下一代计算流体动力学求解器中的定制稳定性分析工具

本文介绍了使用定制特征求解器进行全局线性稳定性分析的一些初步结果，该特征求解器最近已在下一代流求解器框架 CODA 中实现。特征求解器受益于 CODA 的自动微分功能，它允许计算雅可比矩阵与任意复向量的精确乘积。它实现了 Krylov-Schur 算法来解决特征值问题。该定制工具已针对流过圆柱体的层流情况进行了验证，并使用 TAU 代码和文献中报告的数值计算结果。对于流过方形圆柱体的层流情况，它已应用于二阶有限体积和高阶不连续伽辽金格式。已经证明，与在更精细的网格上使用二阶方案相比，在较粗的网格上使用高阶方案可以得到收敛良好的本征模，并且计算时间更短。