We introduce a new approach for adaptive mesh refinement in which adaptivity is driven by low rank decomposition and optimal sensing of the dynamically evolving flow field. This method seeks an ordered set of locations for mesh adaptation from the instantaneous data-driven basis of an online proper orthogonal decomposition of the velocity, which organizes features into sparse optimal orthogonal modes based on an energy norm. The sensing is achieved via a computationally expedient discrete empirical interpolation method using rank-revealing QR factorization (Drmac and Gugercin SIAM J Sci Comput 38(2):A631–A648, 2016). The methodology is applicable to a wide range of numerical discretizations, and is tested on a spatiotemporally evolving incompressible turbulent jet, a complex wind turbine wake, and supersonic flow over a forward-facing step. The proposed approach is demonstrated to predict accurate velocity statistics and yield significantly smaller grids in comparison to gradient-based methods. The algorithm is seen to focus refinement in the vicinity of dynamically significant regions such as those characterized by high turbulence kinetic energy, coherent structures and shock interactions. Moreover, the approach does not require parameters or thresholds, which may be difficult to obtain for complex flows, to be known a priori to facilitate mesh adaptation.

中文翻译：

---

基于最优稀疏感知的自适应网格细化方法

我们引入了一种自适应网格细化的新方法，其中自适应性由低秩分解和动态演化流场的最佳感知驱动。该方法从速度的在线适当正交分解的瞬时数据驱动基础中寻找一组有序的网格自适应位置，该方法基于能量范数将特征组织成稀疏的最佳正交模式。传感是通过使用秩显示 QR 分解的计算上方便的离散经验插值方法实现的（Drma​​c 和 Gugercin SIAM J Sci Comput 38(2):A631–A648, 2016）。该方法适用于广泛的数值离散化，并在时空演化的不可压缩湍流射流、复杂的风力涡轮机尾流和超音速流上进行了测试。与基于梯度的方法相比，所提出的方法被证明可以预测准确的速度统计数据并产生明显更小的网格。该算法被认为专注于动态重要区域附近的细化，例如以高湍流动能、相干结构和激波相互作用为特征的区域。此外，该方法不需要先验地知道对于复杂流可能难以获得的参数或阈值以促进网格自适应。相干结构和冲击相互作用。此外，该方法不需要先验地知道对于复杂流可能难以获得的参数或阈值以促进网格自适应。相干结构和冲击相互作用。此外，该方法不需要先验地知道对于复杂流可能难以获得的参数或阈值以促进网格自适应。