标题： 一种数据驱动的收敛加速器，用于加速和稳定伪时间步进 显示英文标题

标题： A data-driven convergence booster for accelerating and stabilizing pseudo time-stepping

摘要： 本文介绍了一种新颖的数据驱动收敛加速器，该方法不仅加快了收敛速度，还在获得稳态解较为困难的情况下稳定了解。该方法利用中间解构建解残差的降阶模型（ROM），并在低维ROM子空间中定期求解最小二乘问题。残差的二阶近似和法方程的使用从方法论的角度使本工作区别于文献中的类似方法。从应用角度来看，与之前专注于线性系统或理想化问题的研究不同，我们严格评估了该方法在实际计算流体力学（CFD）应用中的性能。除了降低点迭代求解器的线性系统的时间复杂度外，我们还展示了在求解非线性纳维-斯托克斯方程的隐式格式中，所需伪时间步数的显著减少。在包括亚音速无粘和跨音速湍流情况在内的多种二维和三维流动中，该方法在实际运行时间上 consistently 实现了3到4倍的速度提升。最后，所提出的方法作为一种稳健的稳定器，能够在不依赖对称边界条件的情况下，使原本表现出持续非定常性的流动（如涡旋脱落或跨音速抖动）收敛到稳态解。 显示英文摘要

摘要： This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a reduced-order model (ROM) of the solution residual using intermediate solutions and periodically solves a least-square problem in the low-dimensional ROM subspace. The second-order approximation of the residual and the use of normal equation distinguish this work from similar approaches in the literature from the methodology perspective. From the application perspective, in contrast to prior studies that focus on linear systems or idealized problems, we rigorously assess the method's performance on realistic computational fluid dynamics (CFD) applications. In addition to reducing the time complexity of point-iterative solvers for linear systems, we demonstrate substantial reductions in the number of pseudo-time steps required for implicit schemes solving the nonlinear Navier-Stokes equations. Across a range of two- and three-dimensional flows-including subsonic inviscid and transonic turbulent cases-the method consistently achieves a 3 to 4 times speedup in wall-clock time. Lastly, the proposed method acts as a robust stabilizer, capable of converging to steady solutions in flows that would otherwise exhibit persistent unsteadiness-such as vortex shedding or transonic buffet-without relying on symmetry boundary conditions.