“…It appeared in the pioneering work of Gingold and Monaghan (1977) and Lucy (1977) for applications in astrophysics. Subsequently, the SPH method has been used in diverse fields of physics and engineering, including the study of convection flows (Aly and Raizah, 2020;Shakibaeinia, 2020a, 2020b;Aly et al, 2021), fluid-structure interactions (Xu et al, 2019;Salehizadeh and Shafiei, 2022;Zhang et al, 2022;Dai et al, 2023;Long and Su, 2023), free surface flow (Fang et al, 2006;Violeau and Issa, 2007;Aly et al, 2013;Heydari et al, 2022;Lan et al, 2023), multiphase flows (Hu and Adams, 2006;Zhang et al, 2019;Almasi et al, 2021) and more.…”