Reconstruction of turbulent flow based on data assimilation methods is of significant importance for improving the estimation of flow characteristics by incorporating limited observations. Existing works mainly focus on using only one observation data source, e.g., velocity, wall pressure, lift or drag force, to reconstruct the flow. In practical applications observations are disparate data sources that often vary in dimension and quality. Simultaneously incorporating these disparate data is worth investigation to improve the flow reconstruction. In this work, we investigate the disparate data assimilation with ensemble methods to enhance the reconstruction of turbulent mean flows. Specifically, a regularized ensemble Kalman method is employed to incorporate the observation of velocity and different sources of wall quantities (e.g., wall shear stress, wall pressure distribution, lift and drag force). Three numerical examples are used to demonstrate the capability of the proposed framework for assimilating disparate observation data. The first two cases, i.e., a one-dimensional planar channel flow and a two-dimensional transitional flow over plate, are used to incorporate both the sparse velocity and wall friction. In the third case of the flow over periodic hills, the wall pressure distribution and the lift and drag force are regarded as observation in addition to velocity, to recover the flow fields. The results demonstrate the merits of incorporating various disparate data sources to improve the accuracy of the flow-field estimation. The ensemble-based method can assimilate disparate data non-intrusively and robustly without requiring significant changes to the model simulation codes. The method demonstrated here opens up possibilities for assimilating realistic experimental data, which are often disparate.

基于数据同化方法的湍流重建对于通过结合有限的观测来改进对流动特性的估计具有重要意义。现有的工作主要集中在仅使用一个观测数据源（例如速度，壁压，升力或拖曳力）来重建流量。在实际应用中，观测值是不同的数据源，通常在尺寸和质量上有所不同。同时纳入这些不同的数据值得研究，以改善流量重建。在这项工作中，我们使用集成方法研究不同的数据同化，以增强湍流平均流的重建。具体而言，采用正规化的集成卡尔曼方法来合并对速度和壁量的不同来源（例如，壁面剪应力，壁面压力分布，升力和阻力）。三个数值示例被用来证明所提出的框架吸收不同观测数据的能力。前两种情况，即一维平面通道流和板上的二维过渡流，被用于兼顾稀疏速度和壁摩擦。在周期性山上流动的第三种情况下，除了速度以外，还应考虑壁面压力分布以及升力和阻力，以恢复流场。结果证明了合并各种不同的数据源以提高流场估计精度的优点。基于集成的方法可以非侵入性和鲁棒性地吸收异构数据，而无需对模型仿真代码进行重大更改。这里展示的方法为同化真实的实验数据开辟了可能性，而实际的实验数据通常是完全不同的。