Abstract Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in urban areas. Unfortunately, simulating high Reynolds number flows over complex terrain is still a big challenge. Therefore, we present a simplified version of the wall modeled immersed boundary method by Chester et al. (J. Comput. Phys. 2007; 225: 427–448). By preventing the extrapolation and iteration steps in the original method, the proposed approach is much easier to implement and more computationally efficient. Furthermore, the proposed method only requires information that is available to each processor and thus is much more efficient for simulations performed on a large number of cores. These are crucial considerations for algorithms that are deployed on modern supercomputers and will allow much higher grid resolutions to be considered. We validate our method against wind tunnel measurements for turbulent flows over wall-mounted cubes, a two-dimensional ridge, and a three-dimensional hill. We find very good agreement between the simulation results and the measurement data, which shows this method is suitable to model high Reynolds number flows over complex terrain.

中文翻译：

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复杂地形上高雷诺数流动的壁面模型浸入边界法

摘要 模拟复杂地形对高雷诺数流动的影响对于提高我们对风电场流动动力学、丘陵或山区花粉和污染物的扩散以及城市地区流动的理解非常重要。不幸的是，在复杂地形上模拟高雷诺数流仍然是一个很大的挑战。因此，我们提出了 Chester 等人的墙建模浸入边界方法的简化版本。(J. Comput. Phys. 2007; 225: 427–448)。通过防止原始方法中的外推和迭代步骤，所提出的方法更容易实现且计算效率更高。此外，所提出的方法只需要每个处理器可用的信息，因此对于在大量内核上执行的模拟效率更高。这些是部署在现代超级计算机上的算法的关键考虑因素，并将允许考虑更高的网格分辨率。我们针对壁挂式立方体、二维山脊和三维山丘上的湍流的风洞测量验证了我们的方法。我们发现模拟结果和测量数据之间非常吻合，这表明该方法适用于模拟复杂地形上的高雷诺数流动。