A multiscale data assimilation with the ensemble Kalman filter

In this paper, a multiscale data assimilation approach is constructed to evaluate boundary conditions for particle fluxes in numerical simulations of particle transport problems. An adaptation of the ensemble Kalman filtering (EnKF) method is used as the engine for estimation and filtering across scales. To implement this multiscale approach, a multiscale bridging model, which can predict the particle fluxes across arbitrary spatial intervals in any scale, is developed by considering particles undergoing transverse random walk emitted along a continuous boundary corresponding to the finest scale. In the model, particle fluxes across one scale are taken as the parameter set which is used to determine fluxes across another scale. The significance of this multiscale model is demonstrated through an example. Ensembles of Gaussian random processes of particle fluxes along the boundary are generated as the microscale model state according to a specified a priori information on the error covariance or spectral density functions. Measurements of particle quantities are taken at macroscale locations above the boundary and assimilated with model predictions to update the micro- and macroscale particle fluxes using the inverse analysis scheme of the multiscale EnKF approach. The updated random macroscale fluxes can be used as consistent boundary conditions for numerical simulations, such as large eddy simulation.