Abstract A recently developed fourth-order accurate implicit residual smoothing scheme (IRS4) is investigated for the large eddy simulation of turbomachinery flows, characterized by moderate to high Reynolds numbers and subject to severe constraints on the maximum allowable time step if an explicit scheme is used. For structured multi-block meshes, the proposed approach leads to the inversion of a scalar pentadiagonal system by mesh direction, which can be done very efficiently. On the other hand, applying IRS4 at each stage of an explicit Runge–Kutta time scheme allows to increase the time step by a factor 5 to 10, leading to substantial savings in terms of overall computational time. With respect to standard second-order fully implicit approaches, the IRS4 does not require approximate linearization and factorization procedures nor inner Newton-Raphson subiterations. As a consequence, it represents a better cost-accuracy compromise for the numerical simulations of turbulent flows where the maximum time step is controlled by the lifetime of the smallest resolved turbulent structures. Numerical results for the well-documented high-pressure VKI LS-89 planar turbine cascade illustrate the potential of IRS4 for significantly reducing the overall cost of turbomachinery large eddy simulations, while preserving an accuracy similar to the explicit solver even for sensitive quantities like the heat transfer coefficient and the turbulent kinetic energy field.

中文翻译：

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使用高阶隐式残差平滑方案的涡轮机械流的大涡模拟

摘要 研究了最近开发的四阶精确隐式残差平滑方案 (IRS4) 用于涡轮机械流的大涡模拟，其特点是雷诺数中等至高，如果使用显式方案，则对最大允许时间步长有严格限制。 . 对于结构化的多块网格，所提出的方法导致通过网格方向对标量五对角系统进行反演，这可以非常有效地完成。另一方面，在显式 Runge-Kutta 时间方案的每个阶段应用 IRS4 可以将时间步长增加 5 到 10 倍，从而大大节省总体计算时间。关于标准的二阶完全隐式方法，IRS4 不需要近似线性化和分解过程，也不需要内部 Newton-Raphson 子迭代。因此，它代表了湍流数值模拟的更好的成本精度折衷，其中最大时间步长由最小解析湍流结构的寿命控制。有据可查的高压 VKI LS-89 平面涡轮叶栅的数值结果说明了 IRS4 在显着降低涡轮机械大涡模拟的总体成本方面的潜力，同时即使对于热等敏感量也能保持与显式求解器相似的精度传递系数和湍动能场。它代表了湍流数值模拟的更好的成本精度折衷，其中最大时间步长由最小解析湍流结构的寿命控制。有据可查的高压 VKI LS-89 平面涡轮叶栅的数值结果说明了 IRS4 在显着降低涡轮机械大涡模拟的总体成本方面的潜力，同时即使对于热等敏感量也能保持与显式求解器相似的精度传递系数和湍动能场。它代表了湍流数值模拟的更好的成本精度折衷，其中最大时间步长由最小解析湍流结构的寿命控制。有据可查的高压 VKI LS-89 平面涡轮叶栅的数值结果说明了 IRS4 在显着降低涡轮机械大涡模拟的总体成本方面的潜力，同时即使对于热等敏感量也能保持与显式求解器相似的精度传递系数和湍动能场。