Reducing the computational demand of direct numerical simulation via assimilation of experimental data*

Direct numerical simulations (DNS) rapidly establish small scales of turbulence, however large scales require large domains and long simulation times. In contrast, experimental measurements capture large scales yet struggle to resolve smaller scales due to measurement noise. This work seeks to reduce the required computational domain of DNS by replacing the simulation of large scales with data from experimental measurements. To account for measurement uncertainty and disparity in measured and resolved scales, data assimilation is performed by an ensemble Kalman filter, via which the limited domain DNSs are nudged towards the experimental measurements. To explore the extent to which this approach can reduce the computational domain without sacrificing the accuracy of the resolved scales, an incompressible homogeneous isotropic code was modified to simultaneously simulate a fully resolved DNS and an ensemble of smaller simulations from which the Kalman gain is calculated and applied. The fully resolved DNS is subsampled and filtered to represent experimental data of varying resolution and accuracy.