  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.
