Adaptive Ensemble Square Root Filter with consistent ensemble reconstruction method for two-phase flows

This work develops an adaptive Ensemble Square Root Filter framework combined with an ensemble reconstruction method for inverse parameter estimation of two-phase flows. We consider the deterministic Ensemble Square-Root Kalman Filter in the Ensemble Transform Kalman Filter formulation. An adaptive strategy is employed to construct low-dimensional local observations, while the ensemble size is dynamically adjusted according to the corresponding observation subset. An ensemble reconstruction procedure is introduced to enable ensemble-size variation while preserving the ensemble mean and covariance information in a statistical sense. The proposed framework avoids the additional sampling noise introduced by perturbed observations in the standard EnKF and improves parameter-estimation performance in small-ensemble settings. Twin experiments of the flow around a circular cylinder and quasi-incompressible two-phase flow in microchannel-based heat exchangers are performed. Comparative results demonstrate that the proposed method achieves reliable parameter estimation with significantly reduced ensemble sizes, thereby lowering computational cost while maintaining estimation accuracy.