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Although the problems studied in this work are limited to 2D cases, the single-phase model lends itself naturally to large-scale 3D scenarios. Compared with the multiphase solver, this single-phase model is much simpler in the algorithm, more efficient in computation, and meanwhile retains good accuracy and robustness. We verify the single-phase model through several droplet dynamics simulations including initially squared droplets, the oscillating droplet, binary head-on coalescence of droplets, and the wetting problems. The central angle method is incorporated into the single-phase model. We develop two free-surface detection algorithms: (1) a two-step detection combining the number of neighboring particles method and the arc-method, and (2) a central angle-based method, which is proved to be much more efficient than the reference counterparts. In this work, we propose a single-phase model of surface tension based on fast free-surface detections. Current smoothed particle hydrodynamics models for surface tension are mostly multiphase-based and computationally expensive. Surface tension plays a crucial role in many practical issues ranging from the bubble and droplet dynamics to the super-hydrophilic and hydrophobic bio-inspired designs.