MPS method is frequently applied to calculate violent slamming problems. However, asymmetric particle distribution and particle thrusting on free surface would rise computational instability and inaccuracy. In this study, the proposed MPS method consists of a modified space potential particle (SPP) scheme in which the position vector SPP is only determined by a symmetry condition. Two dam breaking flows are simulated. Enhancement of stability by the modified SPP scheme is demonstrated. Besides, the numerical results of the proposed MPS method are in good agreement with the experimental results.


Fluid flow slamming on wall is a common and frequent phenomenon in nature. Violent slamming phenomenon could produce huge instantaneous impact force and cause damage to structures. Therefore, it requires special attention in ocean engineering. The slamming phenomenon is often accompanied by severe changes in the free surface. For grid methods, dealing with severe change of free surface is a challenge. In contrast, particle methods based on Lagrangian description can more easily capture interface or free surface (Fujioka, 2013; Shimizu et al., 2020). As one of the particle methods, the Moving particle semi-implicit (abbr. as MPS) method is frequently adopted to calculate violent slamming problems, such as dam breaking (Yang and Zhang, 2018; Khayyer et al., 2021), tank sloshing (Pan et al., 2008; Pan et al., 2012), water slamming (Shibata et al., 2013; Khayyer and Gotoh, 2016; Gotoh et al., 2021), green water flow (Shibata et al., 2012). Although the MPS method has natural advantage in simulating violent fluid flow with free surface, it still has some deficiencies needed to be improved, such as insufficient accuracy and consistency, unphysical oscillation and particle thrusting.

Koshizuka and Oka (1996) derived the original Laplacian operator from a time-dependent diffusion problem. Later, several Laplacian operators were derived by calculating the divergence of the original gradient operator, such as Zhang et al. (2006), Khayyer and Gotoh (2010) and Xu and Jin (2016). The consistency and accuracy of the above mentioned Laplacian operators (including the original one) are insufficient under irregular distribution. For further improving the consistency and accuracy, arbitrary-order consistent operators based on the MLS method (Tamai and Koshizuka, 2014), a second-order Laplacian model with corrective matrix (Duan et al., 2019) and a renormalized Laplacian operator with first-order consistency (Liu et al., 2019) have been developed. These operators have higher accuracy and consistency, but they have the issue of instability and require additional technique (such as OPS (Khayyer et al., 2017) and PS (Duan et al., 2018)) to ensure stability.

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