Immersed boundary (IB) method with a wall function for high Reynolds number flows is attractive when the boundary is complex and evolving. However, when combined with IB method, existing wall functions cannot produce smooth wall shear stress, which is important for many processes such as erosion. The root cause is the discontinuity between the log‐law and laminar layers in most wall functions. A wall function in IB methods is typically enforced through IB cells. However, for complex and evolving boundaries, IB cells can be located in either the log‐law layer or the laminar layer, which follow different laws. To remedy this, a new method is introduced with a y⁺‐adaptive strategy. The idea is that when an IB cell is too close to an IB, it is replaced by a neighboring fluid cell further away from the boundary. Consequently, all IB cells are in the log‐law layer. The resulting wall shear stress is much smoother. This adaptive strategy is a compromise between how accurate the location of an IB wall is represented and the smoothness of simulated wall shear. Example cases in 1D, 2D, and 3D show the y⁺‐adaptive wall function produces results compared well with theory and experiments.

中文翻译：

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具有y +自适应墙函数的沉浸边界方法用于平滑墙剪

当边界复杂且不断变化时，具有高雷诺数流的壁函数的浸入边界（IB）方法很有吸引力。但是，当与IB方法结合使用时，现有的墙函数无法产生平滑的墙剪应力，这对于许多过程（例如腐蚀）很重要。根本原因是大多数墙函数中对数律层和层流层之间的不连续性。IB方法中的墙函数通常通过IB单元强制执行。但是，对于复杂且不断变化的边界，IB单元可以位于遵循不同定律的对数律层或层流层中。为了解决这个问题，我们引入了y ⁺的新方法适应性策略。这个想法是，当IB单元格离IB太近时，将其替换为距离边界更远的相邻流体单元格。因此，所有IB单元都在对数律层中。所得的壁切应力要平滑得多。这种自适应策略是在IB墙的位置表示准确度与模拟墙剪的平滑度之间的折衷。在1D，2D和3D中的示例案例显示，与理论和实验相比较，y ⁺自适应墙函数产生的结果更好。