To improve the research methods in petroleum industry, we develop a fast algorithm to simulate droplet motions in oil and water two phase flow, using phase field model to describe the phase distribution in the flow process. An efficient partial difference equation solver—Shift-Matrix method is applied here, to speed up the calculation coding in high-level language, i.e. Matlab and R. An analytical solution of order parameter is derived, to define the initial condition of phase distribution. The upwind scheme is applied in our algorithm, to make it energy decay stable, which results in the fast speed of calculation. To make it more clear and understandable, we provide the specific code for forming the coefficient matrix used in Shift-Matrix Method. Our algorithm is compared with other methods in different scales, including Front Tracking and VOSET method in macroscopic and LBM method using RK model in mesoscopic scale. In addition, we compare the result of droplet motion under gravity using our algorithm with the empirical formula common used in industry. The result proves the high efficiency and robustness of our algorithm and it’s then used to simulate the motions of multiple droplets under gravity and cross-direction forces, which is more practical in industry and can be extended to wider application.
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