  Numerical simulations of cardiovascular mass transport pose significant
challenges due to the wide range of P\'eclet numbers and backflow at 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 instabilities when backflow
occurs at Neumann boundaries, we propose an approach based on the prescription
of the total flux. In addition, we introduce a "consistent flux" outflow
boundary condition and demonstrate its superior performance over the
traditional zero diffusive flux boundary condition. Lastly, we discuss
discontinuity capturing (DC) stabilization techniques to address the well-known
oscillatory behavior of the solution near the concentration front in
advection-dominated flows.We present numerical examples in both idealized and
patient-specific geometries to demonstrate the efficacy of the proposed
procedures. The three contributions dis-cussed in this paper enable to
successfully address commonly found challenges when simulating mass transport
processes in cardiovascular flows.
