Boundary-extended Stokesian dynamics for many-body hydrodynamics of active particles in arbitrarily shaped domains

Active particles such as swimming cells and microrobots are often suspended in geometrically confined environments. Understanding their collective motion in such domains is essential for a wide range of biological and engineering systems. However, existing methods face challenges in accurately resolving many-body far-field hydrodynamic interactions while retaining lubrication accuracy in near-contact configurations. In this study, we propose a novel methodology termed Boundary-extended Stokesian Dynamics (BxSD). The BxSD utilizes the multipole expansion and the boundary element method (BEM) for far-field interactions, together with the lubrication theory for near-field interactions. This framework enables accurate computation of many-body dynamics of active particles in an arbitrarily shaped boundary, accounting for hydrodynamic interactions. The validity of the BxSD is first examined by analyzing the shearing and squeezing motions of a solitary squirmer under various wall configurations. In addition, the accumulation of numerical errors in many-body simulation is assessed. The results show that the BxSD achieves accuracy comparable to the BEM for typical wall geometries. Moreover, under the present direct-solver implementation, the BxSD allows simulations with 10-100 times more squirmers at a fixed computational cost, or equivalently reduces the computational time by approximately an order of magnitude for a fixed system size. The BxSD provides an efficient computational framework for studying active suspensions in complex geometries.