Stabilized explicit material point method for fluid flow and fluid-structure interaction simulations using dual high-order B-spline volume averaging

Traditional explicit Material Point Methods (MPM) for weakly compressible fluids often suffer from volumetric locking, cell-crossing instability, and excessive energy dissipation, particularly in fluid-structure interaction (FSI) scenarios. This study presents a stabilized explicit MPM framework that integrates dual high-order B-spline volume averaging to address these challenges. The proposed dual averaging technique simultaneously smooths deformation gradients and pressure fields using cubic B-spline basis functions to eliminate cell-crossing errors and reduce volumetric locking. A blended APIC/FLIP mapping scheme is developed to enhance energy conservation and stability at coarse grid resolutions. The framework is further enhanced by seamlessly integrating various complementary techniques such as $\delta$-correction, pressure smoothing, and specialized boundary handling for more robust and effective modeling of free-surface and FSI problems. The framework is rigorously validated through benchmark cases, including 1D elastic wave propagation, Poiseuille flow, lid-driven cavity flow, water sloshing, dam break, and water impact on elastic obstacles. The simulation results demonstrate a remarkable reduction in pressure oscillations and improved particle distribution uniformity compared to prior MPM approaches. The proposed method establishes a robust and efficient tool for large-deformation FSI problems and bridges gaps in accuracy and stability for industrial-scale applications.