Abstract The research on hypersonic boundary layer transition is a recent focal point in fluid dynamics. One of the effective numerical methods for transition study is the high-order shock-fitting method, which is especially suitable for dealing with shock-related interactions and removing post-shock oscillations as compared with shock-capturing methods. Currently, explicit time-stepping schemes are mainly used for shock-fitting methods. In comparison, implicit schemes have received less attention due to the extra complexity arising from dynamic shock and moving mesh, even though they can accelerate the convergence speeds for steady flows by up to an order of magnitude. In this paper, two implicit time-stepping methods, GMRES (generalized minimum residual) and LR (line-relaxation), are realized for the efficient calculation of steady flow fields using the 5th-order shock-fitting method. The gas models include both calorically perfect gas and 5-species thermal-chemical non-equilibrium gas required for high-speed and high-enthalpy flows. The results of test cases showed that the convergence rates of GMRES+LR and LR are 4 to 20 times faster than the explicit/semi-implicit Runge-Kutta schemes. Therefore, the usage of implicit GMRES and LR as time-stepping schemes raises the computational efficiency for obtaining steady boundary layer flows, which helps the important high-order shock-fitting methods play a greater role in the study of hypersonic boundary layer stability and transition.

中文翻译：

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具有高效隐式时间步长方案的高超声速流动应用中高阶激波拟合方法的收敛加速

摘要 高超声速边界层跃迁的研究是流体动力学的近期研究热点。过渡研究的有效数值方法之一是高阶激波拟合方法，与激波捕获方法相比，它特别适合处理与激波相关的相互作用和消除激波后的振荡。目前，显式时间步长方案主要用于冲击拟合方法。相比之下，由于动态冲击和移动网格带来的额外复杂性，隐式方案受到的关注较少，尽管它们可以将稳定流的收敛速度加快一个数量级。在本文中，两种隐式时间步长方法，GMRES（广义最小残差）和LR（线松弛），实现了使用 5 阶冲击拟合方法对稳定流场的有效计算。气体模型包括热量完美气体和高速和高焓流所需的 5 种热化学非平衡气体。测试用例的结果表明，GMRES+LR 和 LR 的收敛速度比显式/半隐式 Runge-Kutta 方案快 4 到 20 倍。因此，隐式GMRES和LR作为时间步长方案的使用提高了获得稳定边界层流的计算效率，这有助于重要的高阶激波拟合方法在高超声速边界层稳定性和过渡研究中发挥更大的作用。 . 气体模型包括热量完美气体和高速和高焓流所需的 5 种热化学非平衡气体。测试用例的结果表明，GMRES+LR 和 LR 的收敛速度比显式/半隐式 Runge-Kutta 方案快 4 到 20 倍。因此，隐式GMRES和LR作为时间步长方案的使用提高了获得稳定边界层流的计算效率，这有助于重要的高阶激波拟合方法在高超声速边界层稳定性和过渡研究中发挥更大的作用. 气体模型包括热量完美气体和高速和高焓流所需的 5 种热化学非平衡气体。测试用例的结果表明，GMRES+LR 和 LR 的收敛速度比显式/半隐式 Runge-Kutta 方案快 4 到 20 倍。因此，隐式GMRES和LR作为时间步长方案的使用提高了获得稳定边界层流的计算效率，这有助于重要的高阶激波拟合方法在高超声速边界层稳定性和过渡研究中发挥更大的作用。 .