Finite element modeling of near-wall mass transport in cardiovascular flows.

Abstract

Many cardiovascular processes involve mass transport between blood and the vessel wall. Finite element methods are commonly used to numerically simulate these processes. Cardiovascular mass transport problems are typically characterized by high Péclet numbers, requiring fine near-wall mesh resolution as well as the use of stabilization techniques to avoid numerical instabilities. In this work, we develop a set of guidelines for solving high-Péclet-number near-wall mass transport problems using the finite element method. We use a steady, idealized test case to investigate the required mesh resolution and finite element basis order to accurately capture near-wall concentration boundary layers, as well as the performance of several commonly used stabilization techniques. Linear tetrahedral meshes were found to outperform quadratic tetrahedral meshes of equivalent degrees of freedom, and the commonly used discontinuity-capturing stabilization technique was found to be overly diffusive for these types of problems. Best practices derived from the idealized test case were then applied to a typical patient-specific vascular blood flow modeling application, where it was found that the commonly applied technique of avoiding numerical difficulties by artificially increasing mass diffusivity provides qualitatively similar but quantitatively erroneous results.