An SPH--mesh Coupling for Vesicle Dynamics in Shear Flow

Abstract: We present a novel computational framework that couples smoothed particle hydrodynamics~(SPH) with a triangulated membrane mesh to simulate the dynamics of vesicles suspended in fluids. A novel interface-tracking approach enforces membrane impermeability naturally, without resorting to non-physical constraints such as particle reflection or bounce-back boundary conditions. The membrane model incorporates four distinct bending energy formulations, namely the minimal model, the spontaneous curvature (SC) model, the bilayer couple (BC) model, and the area difference elasticity (ADE) model, providing a versatile tool for diverse biophysical scenarios. The framework is rigorously validated against equilibrium shapes and tank-treading motion of a vesicle, demonstrating excellent agreement with previous theoretical and numerical studies. A systematic investigation into the effects of each bending model on the vesicle's inclination angle, revolution frequency, and morphology in shear flow reveals key physical insights. Notably, spontaneous curvature has a negligible effect on steady-state orientation but profoundly alters rotational dynamics at low reduced volumes through the emergence of dumbbell-like shapes with deep constrictions. In contrast, the BC and ADE models induce characteristic asymmetric and stomatocyte morphologies. Our results establish the proposed SPH--mesh coupling as an accurate and robust tool for exploring the complex, shape-dependent dynamics of vesicles in fluid flows.