Flow between rotating concentric cylinders, or the Taylor Couette flow, has been studied extensively because of its rich physics, ranging from axisymmetric steady laminar flow, to fully developed turbulent flow. In the present study, we advocate the use of this problem as a benchmark case for scale-resolving simulation, such as large eddy simulation (LES) and direct numerical simulation (DNS). The problem is attractive because of its simple geometry, simple boundary conditions, and complex physics involving wall-shear induced and centrifugal instability. Unlike the well-known fully developed channel flow, this problem has a curved wall boundary, and it is unnecessary to add a source term to the governing equations to sustain the fully developed turbulent flow. A p-refinement study for Re = 4000 is performed first to establish DNS data, including the time history of enstrophy, which can be used as an accuracy and resolution indicator to evaluate numerical methods, and is orders of magnitude faster than using the mean flow quantities and Reynolds stresses to evaluate solution quality. Finally, an hp-refinement study is performed to establish the relative accuracy and efficiency of high-order schemes of various accuracy.

中文翻译：

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具有弯曲壁的尺度解析模拟基准：Taylor Couette 流

旋转同心圆柱体之间的流动，或 Taylor Couette 流动，由于其丰富的物理性质，从轴对称稳定层流到完全发展的湍流，已被广泛研究。在本研究中，我们提倡将此问题用作尺度解析模拟的基准案例，例如大涡模拟 (LES) 和直接数值模拟 (DNS)。这个问题很有吸引力，因为它具有简单的几何形状、简单的边界条件以及涉及壁剪诱导和离心不稳定性的复杂物理。与众所周知的完全发展的通道流不同，该问题具有弯曲的壁边界，并且没有必要在控制方程中添加源项来维持完全发展的湍流。首先对 Re = 4000 进行 p 细化研究以建立 DNS 数据，包括熵的时间历程，可用作评估数值方法的准确性和分辨率指标，并且比使用平均流量和雷诺应力评估解质量快几个数量级。最后，进行 hp 细化研究以建立各种精度的高阶方案的相对精度和效率。