An Efficient SPH Framework for Modeling Binary Granular Mixtures and Implications for Granular Flows

A two-way coupling numerical framework based on smoothed particle hydrodynamics (SPH) is developed in this study to model binary granular mixtures consisting of coarse and fine grains. The framework employs updated Lagrangian SPH to simulate fine grains, with particle configurations updated at each time step, and total Lagrangian SPH to efficiently model coarse grains without updated particle configurations. A Riemann solver is utilized to introduce numerical dissipation in fine grains and facilitate their coupling with coarse grains. To enhance computational efficiency, a multiple time-stepping scheme is initially applied to manage the time integration coupling between coarse and fine grains. Several numerical experiments, including granular column collapse, low-speed impact craters, and granular flow impacting blocks, are conducted to validate the stability and accuracy of the proposed algorithm. Subsequently, two more complex scenarios involving a soil–rock mixture slope considering irregular coarse particle shapes, and bouldery debris flows on natural terrain, are simulated to showcase the potential engineering applications. Finally, a detailed analysis is performed to evaluate the computational efficiency advantages of the present approach. The findings of this study are consistent with previous experimental and numerical results, and the implementation of a multiple time-stepping scheme can improve computational efficiency by up to 600%, thereby providing significant advantages for large-scale engineering simulations.