An efficient multi-resolution SPH framework for multi-phase fluid-structure interactions

Applying different spatial and temporal resolutions for different sub-systems is an effective approach to increase computational efficiency for particle-based methods. However, it still has many challenges in terms of achieving an optimized computational efficiency and maintaining good numerical robustness and accuracy for the simulation of multi-phase flows involving large density ratio and interacting with rigid or flexible structures. In the present work, based on the multi-resolution smoothed particle hydrodynamics (SPH) method [Zhang et al., JCP 429, 110028 (2021)], an efficient multi-resolution SPH framework for multi-phase fluid-structure interactions (FSI) is proposed. First, an efficient multi-phase model, exploiting different density reinitialization strategies instead of applying different formulations to implement mass conservation to the light and heavy phases, respectively, is developed and the same artificial speed of sound for both phases can be used. Then, the transport velocity formulation is rewritten by applying temporal local flow state dependent background pressure to eliminate the unnatural voids, unrealistic phase separation and decrease the numerical dissipation. Finally, the one-sided Riemann-based solid boundary condition is modified to handle the FSI coupling in both single- and multi-resolution scenarios in the triple point. A set of examples involving multi-phase flows with high density ratio, complex interface and multi-phase FSI are studied to demonstrate the efficiency, accuracy and robustness of the present method.