In three-dimensional applications of the Moving Particle Semi-Implicit (MPS) method, free-surface identification is commonly based on particle number density, which can lead to misclassification of surface particles and consequently degrade the accuracy of pressure field predictions. To address this issue, an improved formulation for computing the relative position divergence (RPD) is first developed to achieve better consistency with theoretical values. Based on geometrical considerations and test cases involving internal cavities, a set of surface identification criteria suitable for three-dimensional conditions is established. Building upon the improved RPD formulation, a new free-surface particle detection method is proposed by coupling the relative position divergence with an approximate surface normal vector estimation (RPD + NV). Validation using geometrical models demonstrates that the proposed method can accurately identify surface particles on convex and concave boundaries as well as within cavity-containing configurations. Further assessments through a series of MPS simulations—including hydrostatic, dam-break, and damped oscillation cases—show that both the improved RPD method and the combined RPD + NV scheme effectively reduce pressure oscillations. In particular, the RPD + NV method significantly decreases false negatives and false positives in surface particle identification, leading to smoother and more physically consistent pressure fields, without introducing a noticeable increase in computational cost. Therefore, the proposed surface particle detection method provides a robust and efficient solution for three-dimensional MPS simulations.
Ge et al. (Tue,) studied this question.