Governing Equations

Before starting a CFD simulation, it is always good to take a look at the governing equations underlying the physics. In this case, although we have additional complexities such as pulsatile flow and non-Newtonian fluids, the governing equations are the same as any other fluids problem. The most fundamental governing equations are the continuity equation and the Navier-Stokes equations. Here, let's have a quick review of the equations.
Continuity Equation:

However, as blood can be regarded as an incompressible fluid, the rate of density change is zero, thus the continuity equation above can be further simplified in the form below:

The Navier-Stokes Equation:

One thing to notice in the Navier-Stokes equation is that the viscosity coefficient of μ is not a constant but rather a function of shear rate. Blood gets less viscous as the shear rate increases (shear thinning). Here, we model the blood viscosity using the Carreau fluids model. The mathematical formulation of the Carreau model is as follows:

In the equations above, μ_eff is the effective viscosity. μ₀ , μ_inf , λ, and n are material coefficients.

For the case of blood [2],