Department of Mechanical Engineering, University of California Berkeley, Berkeley, California.
Department of Mechanical Engineering, Northern Arizona University, Flagstaff, Arizona.
Int J Numer Method Biomed Eng. 2019 Jan;35(1):e3148. doi: 10.1002/cnm.3148. Epub 2018 Oct 7.
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.
许多心血管过程涉及血液和血管壁之间的质量传递。有限元方法常用于数值模拟这些过程。心血管质量传递问题的特征通常是高佩克莱数，需要精细的近壁网格分辨率以及使用稳定化技术来避免数值不稳定性。在这项工作中，我们开发了一组使用有限元方法解决高佩克莱数近壁质量传递问题的指南。我们使用一个稳定的、理想化的测试案例来研究所需的网格分辨率和有限元基阶次，以准确捕捉近壁浓度边界层，以及几种常用的稳定化技术的性能。线性四面体网格被发现优于具有等效自由度的二次四面体网格，并且对于这些类型的问题，常用的捕捉间断稳定化技术被发现过于扩散。从理想化测试案例中得出的最佳实践随后应用于典型的患者特定血管血流建模应用，结果发现，通过人为增加质量扩散率来避免数值困难的常用技术提供了定性相似但定量错误的结果。
