Particle methods, known for their Lagrangian mesh-free framework and inherent ability to track moving interfaces, have been extensively used to simulate molten core behaviors. However, traditional particle methods often suffer from accuracy loss when particle distributions become irregular. Although existing high-order discretization schemes can improve accuracy, traditional methods have limited ability to handle near-free surfaces and are prone to numerical instability due to incomplete or biased particle configurations, making it challenging to accurately identify complex free-surface locations.
 In this study, we developed a novel particle method that enhances the accuracy and stability of free-surface flow simulations. Unlike existing consistent particle methods, our approach uniquely decouples the discretization of first- and second-order derivatives, reducing the number of coefficients that must be solved simultaneously and improving both numerical stability and accuracy. Additionally, to address the complex interface shape changes, we applied a curved surface fitting method, which allows for a more precise determination of the free-surface position. Figure 1 shows the results obtained using the proposed method for the dam break benchmark problem involving large deformations and complex topological changes. The results demonstrate notable improvements in the pressure fields and free-surface profiles compared with the existing methods. .
 In the future, we plan to apply the proposed method to practical and realistic simulations of molten-core behaviors during severe accidents, such as melt spreading and molten core-concrete interaction.