Medical devices which serve as a flow conduit during blood draws may contain regions of shear stress which cause red blood cell rupture, termed hemolysis. The degree of hemolysis can be quantified with the hemolysis index (HI), which is a function of the shear stress, and the time red blood cells are exposed to the shear. In the current paper, various computational fluid dynamics (CFD) studies were conducted to evaluate the effect of mesh settings and solver settings on derived quantities such as HI. Mesh settings explored were the number of boundary layers, growth rate, transition ratio, and core mesh refinement; the solver setting explored was the user-defined scalar (UDS) diffusivity coefficient. For fluid flow through a simple pipe, mass-averaged HI at the pipe outlet and the HI profile along the pipe radius at the outlet were the output quantities used for code verification by comparing them to analytical solutions. The results indicated that the mass-averaged HI and radial profile were highly sensitive to the number of boundary mesh layers, the boundary layer growth rate, the transition ratio between core mesh and boundary layer, and core mesh refinement. HI quantities were less sensitive to variations in the UDS diffusivity coefficient. The current study seeks to determine appropriate mesh settings that will provide a reasonable match between CFD and analytical solution quantity magnitudes and their gradients.