Ensemble Kalman Filtering for Flows With Shocks

Ensemble Kalman filter (EnKF) is adopted to assimilate pressure observations in simulation of the Sod shock tube flow. When the diaphragm position is known, EnKF is effective and the assimilation is successful. When the diaphragm position is uncertain, the analysis step of the EnKF leads to significant oscillations which can be traced back to the steep gradients associated with the shock and the contact surface. Specifically, the variance in the location of the diaphragm among the ensemble members leads to a sufficiently large variance in the shock and contact surface positions, which in turn causes locally large updates during analysis. The updated fields can therefore become unphysical, for example having locally negative pressure. We will examine the key parameters that undermine successful assimilation. We will proceed to discuss mitigating strategies, including nonlinear transformations of the state that ensure positivity of thermodynamic variables.