Numerical modeling of non-Newtonian biomagnetic fluid flow

Blood flow dynamics have an integral role in the formation and evolution of cardiovascular diseases. Simulation of blood flow has been widely used in recent decades for better understanding the symptomatic spectrum of various diseases, in order to improve already existing or develop new therapeutic techniques. The mathematical model describing blood rheology is an important component of computational hemodynamics. Blood as a multiphase system can yield significant non-Newtonian effects thus the Newtonian assumption, usually adopted in the literature, is not always valid. To this end, we extend and validate the pressure correction scheme with discontinuous velocity and continuous pressure, recently introduced by Botti and Di Pietro for Newtonian fluids, to non-Newtonian incompressible flows. This numerical scheme has been shown to be both accurate and efficient and is thus well suited for blood flow simulations in various computational domains. In order to account for varying viscosity, the symmetric weighted interior penalty (SWIP) formulation is employed for the discretization of the viscous stress tensor. We disregard the dependency of the viscosity on spatial derivatives of the velocity in the Jacobian computation. Even though this strategy yields an approximated Jacobian, the convergence rate of the Newton iteration is not significantly affected, thus computational efficiency is preserved. Numerical accuracy is assessed through analytical test cases, and the method is applied to demonstrate the effects of magnetic fields on biomagnetic fluid flow. Magnetoviscous effects are taken into account through the generated additive viscosity of the fluid and are found to be important. The steady and transient flow behavior of blood modeled as a Herschel-Bulkley fluid in the presence of an external magnetic field, is compared to its Newtonian counterpart in a straight rigid tube with a 60% axisymmetric stenosis. A break in flow symmetry and marked alterations in WSS distribution are noted.