Numerical Considerations for Advection-Diffusion Problems in Cardiovascular Hemodynamics

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Peclet numbers present in cardiovascular flows and backflow at outlet (Neumann) boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical stability issues when backflow occurs in Neumann boundaries we propose an approach based on the prescription of the total flux. In addition, we propose a consistent flux boundary condition at the outlet boundaries and demonstrate its superiority over the traditional zero diffusive flux boundary condition in preserving the physical accuracy of the solution. Lastly, we discuss Discontinuity-Capturing (DC) stabilization techniques to address the well-known oscillatory behavior in the solution near the advancing wavefront in advection-dominated flows. We present numerical examples in both idealized and patient-specific geometries to demonstrate the efficacy of the proposed formulation. The proposed numerical framework represents a powerful computational tool to investigate mass transport in cardiovascular processes.