In order to simulate cellular blood, a coarse-grained spectrin-link (SL) red blood cell (RBC) membrane model is coupled with a lattice-Boltzmann (LB) based suspension solver. The LB method resolves the hydrodynamics governed by the Navier--Stokes equations while the SL method accurately models the deformation of RBCs under numerous configurations. This method has been parallelized using Message Passing Interface (MPI) protocols for the simulation of dense suspensions of RBCs characteristic of whole blood on world-class computing resources. Simulations were performed to study rheological effects in unbounded shear using the Lees-Edwards boundary condition with good agreement with rotational viscometer results from literature. The particle-phase normal-stress tensor was analyzed and demonstrated a change in sign of the particle-phase pressure from low to high shear rates due to RBCs transitioning from a compressive state to a tensile state in the flow direction. Non-Newtonian effects such as viscosity shear thinning were observed for shear rates ranging from 14-440 inverse seconds as well as the strong dependence on hematocrit at low shear rates. An increase in membrane bending energy was shown to be an important factor for determining the average orientation of RBCs, which ultimately affects the suspension viscosity. The shear stress on platelets was observed to be higher than the average shear stress in blood, which emphasizes the importance of modeling platelets as finite particles. Hagen-Poiseuille flow simulations were performed in rigid vessels for investigating the change in cell-depleted layer thickness with shear rate, the Fåhraeus-Linqvist effect, and the process of platelet margination. The process of platelet margination was shown to be sensitive to platelet shape. Specifically, it is shown that lower aspect ratio particles migrate more rapidly than thin disks. Margination rate is shown to increase with hematocrit, due to the larger number of RBC-platelet interactions, and with the increase in suspending fluid viscosity.