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SPH method is one of the most used numerical mesh-free methods in CFD simulations which can easily model problems with free surfaces. Considering the importance of surface tension in most engineering applications and the capability of SPH method in simulating free surfaces, a single-phase method for implementing surface tension is introduced in this study. Unlike time-consuming multi-phase simulations, this methoddoes not need to model the second lighter  fluid, which reduces the CPU-time and memory requirements substantially. Mirror imaginary particles are used near the free surface to obtain surface properties such as surface normal vector and curvature, which are required in surface tension calculation. The advantages of using these imaginary particles are explained qualitatively through the use of some examples of droplet dynamics. This method is applied to several benchmark problems in surface tension simulations, and acceptable results are obtained.

Surface tension simulation of free surface flows using smoothed particle hydrodynamics