We present a high-performance computational framework (Hemocell) with validated cell-material models, which provides the necessary tool to target challenging biophysical questions in relation to blood flows, e.g. the influence of transport characteristics on platelet bonding and aggregation. The dynamics of blood plasma are resolved by using the lattice Boltzmann method (LBM), while the cellular membranes are implemented using a discrete element method (DEM) coupled to the fluid as immersed boundary method (IBM) surfaces. In the current work a selected set of viable technical solutions are introduced and discussed, whose application translates to significant performance benefits. These solutions extend the applicability of our framework to up to two orders of magnitude larger, physiologically relevant settings.