The multiphase field (MPF) method has been widely used for microstructural evolution and immiscible multiphase flow simulations. In this study, we have developed an ordered active parameter tracking (OAPT) method for efficient simulations of the multiple phases using the MPF method. The algorithm and performance of the OAPT method are presented and compared to those of the conventional active parameter tracking (CAPT) method. The grain growth problems were simulated for demonstration, and the results show good agreement with the conventional one and about four to seven-fold performance improvement. Moreover, we demonstrate the application of the proposed method for the multiphase flow problem, namely the turbulent bubbly downflow. The OAPT method can speed up the calculation by four folds while maintaining the original accuracy.
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