A new free surface identification method for 3D MPS method

In the Moving Particle Semi-Implicit (MPS) method, free surface identification in three dimensions has traditionally relied on particle number density. However, this approach often leads to misidentification of surface particles, which in turn compromises the accuracy of pressure field calculations. In this study, an improved formulation for calculating the relative position divergence (RPD) is first proposed to better align with theoretical expectations, and a surface identification criterion for three-dimensional cases is established using a model with internal cavities. Based on this, an improved surface particle identification method is introduced by combining RPD with an estimation of the surface normal vector (RPD + NV). Validation through geometry-based models demonstrates that the proposed approach can accurately capture surface features, including sharp corners, concave and convex regions, and internal cavities. Further verification using a series of MPS simulations, including static water, dam break, and damped oscillation scenarios, confirms that both the improved RPD method and the combined RPD + NV scheme can effectively suppress pressure fluctuations. Moreover, the proposed method significantly reduces false negatives and false positives in surface particle identification, resulting in a smoother and more accurate pressure field. Consequently, the proposed surface identification method is well-suited for three-dimensional MPS simulations.