DC-APIC: A decomposed compatible affine particle in cell transfer scheme for non-sticky solid–fluid interactions in MPM

Despite the material point method (MPM) provides a unified particle simulation framework for coupling of different materials, MPM suffers from sticky numerical artifacts, which is inherently restricted to sticky and no-slip interactions. In this paper, we propose a novel transfer scheme called Decomposed Compatible Affine Particle in Cell (DC-APIC) within the MPM framework for simulating the two-way coupled interaction between elastic solids and incompressible fluids under free-slip boundary conditions on a unified background grid. Firstly, we adopt particle-grid compatibility to describe the relationship between grid nodes and particles at the fluid–solid interface, which serves as the guideline for subsequent particle–grid–particle transfers. Then we develop a phase-field gradient method to track the compatibility and normal directions at the interface. Secondly, to facilitate automatic MPM collision resolution during solid–fluid coupling, in the proposed DC-APIC integrator, the tangential component will not be transferred between incompatible grid nodes to prevent velocity smoothing in another phase, while the normal component is transferred without limitations. Finally, our comprehensive results confirm that our approach effectively reduces diffusion and unphysical viscosity compared to traditional MPM.