A multiscale SPH particle model of the near-wall dynamics of leukocytes in flow

A novel multiscale Lagrangian particle solver based on SPH is developed with the intended application of leukocyte transport in large arteries. In such arteries, the transport of leukocytes and red blood cells can be divided into two distinct regions: the bulk flow and the near-wall region. In the bulk flow, the transport can be modeled on a continuum basis as the transport of passive scalar concentrations. Whereas in the near-wall region, specific particle tracking of the leukocytes is required and lubrication forces need to be separately taken into account. Because of large separation of spatio-temporal scales involved in the problem, simulations of red blood cells and leukocytes are handled separately. In order to take the exchange of leukocytes between the bulk fluid and the near-wall region into account, solutions are communicated through coupling of conserved quantities at the interface between these regions. Because the particle tracking is limited to those leukocytes lying in the near-wall region only, our approach brings considerable speedup to the simulation of leukocyte circulation in a test geometry of a backward-facing step, which encompasses many flow features observed in vivo.