We demonstrate a method for direct numerical simulations (DNS) of incompressible, flat-plate, zero pressure gradient, turbulent boundary layers, without the use of auxiliary simulations or fringe regions, in a streamwise periodic domain via the homogenized Navier-Stokes equations. This approach is inspired by Spalart's original (1987) method, but improves upon his drawbacks while simplifying the implementation. Most simulations of flat-plate boundary layers require long streamwise domains owing to the slow boundary layer growth and inflow generation techniques. Instead, we use anticipated self-similarity to solve the equations in a normalized coordinate system to allow for streamwise periodicity, similar to Spalart's original method. The resulting integral values, the skin friction coefficient and shape factor, $H_{12}$ and $C_f$, are within $\pm 1\%$ and $\pm 3\%$ of the empirical fits. The mean profiles show good agreement with spatially developing DNS and experimental results for a wide range of Reynolds numbers from ${\text{Re}}_{{\delta }^{*}}=1460$ to 5650. The method manages to reduce computational costs by an estimated one to two orders of magnitude.

中文翻译：

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通过均质化的Navier-Stokes方程对统计平稳的周期性周期性边界层进行直接数值模拟

我们演示了通过均质化的Navier-Stokes方程在流周期域中对不可压缩的平板，零压力梯度，湍流边界层进行直接数值模拟（DNS）的方法，而无需使用辅助模拟或边缘区域。这种方法的灵感来自Spalart的原始方法（1987），但在简化实现的同时改善了他的缺点。由于缓慢的边界层生长和流入生成技术，大多数平板边界层的模拟都需要长的流向域。取而代之的是，我们使用预期的自相似性在归一化坐标系中求解方程，以允许流向周期性，类似于Spalart的原始方法。所得的积分值，皮肤摩擦系数和形状系数，$H_{12}$ 和 $C_F$，在 $\pm \mathrm{1个}％$ 和 $\pm 3％$经验拟合。平均分布图与空间发展的DNS以及来自以下范围的广泛雷诺数的实验结果显示出良好的一致性${\text{回覆}}_{{\delta }^{*}}=1460$ 至5650。该方法设法将计算成本降低了大约一到两个数量级。