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Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics

Research output: Contribution to journalArticle

Sabrina R. Lynch, Nitesh Nama, Zelu Xu, Christopher J. Arthurs, Onkar Sahni, C. Alberto Figueroa

Original languageEnglish
Article numbere3378
JournalInternational Journal For Numerical Methods In Biomedical Engineering
Volume36
Issue number9
DOIs
Accepted/In press1 Jan 2020
Published1 Sep 2020

King's Authors

Abstract

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Péclet 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 discussed in this paper successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.

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