Data Assimilation for Turbulent Channel Flow and Pressure Computation using Omnidirectional Integration

Numerical data assimilation incorporates the theoretical model-based prediction with experimental observations and seeks their optimal reconciliation to achieve the optimal forecast of a dynamical process. In this study, we present an application of data assimilation to improve the spatial data availability of time-resolved tomographic Particle Image Velocimetry (PIV) measurements. The PIV spatial resolution is limited by the particle spatial concentration, which often leaves void spots in the fluid domain. Simple interpolations can fill the gap at the price of ignoring the physics of the problem, governed by the Navier-Stokes equations. In contrast, by using data assimilation, the discrepancy between the computed velocity field and the measured velocity values, as quantified by a cost function, is minimized through the adjoint method. We use the Johns Hopkins turbulence database as test cases. To compute the pressure field, instead of solving the Poisson equation, the parallel ray omnidirectional integration technique (Liu et al. 2016) is adopted at each time step. The ultimate objective of this project is to establish a noise-tolerant data assimilation framework that can be used as an augmentation tool for PIV measurements.