Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan, USA.
Department of Surgery, University of Michigan, Ann Arbor, Michigan, USA.
Int J Numer Method Biomed Eng. 2020 Sep;36(9):e3378. doi: 10.1002/cnm.3378. Epub 2020 Aug 3.
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.
心血管质量传输的数值模拟由于 Peclet 数范围广泛和 Neumann 边界处的回流而面临重大挑战。在本文中，我们提出并讨论了几种数值工具，以在稳定有限元计算框架的背景下解决这些挑战。为了克服 Neumann 边界处回流时出现的数值不稳定性，我们提出了一种基于总通量规定的方法。此外，我们引入了一种“一致通量”出流边界条件，并证明了它比传统的零扩散通量边界条件具有更好的性能。最后，我们讨论了间断捕捉 (DC) 稳定化技术，以解决在对流主导流中靠近浓度前沿的解的著名振荡行为。我们在理想化和患者特定的几何形状中提供了数值示例，以证明所提出的方法的有效性。本文讨论的三个贡献成功地解决了在心血管流动中模拟质量传输过程时常见的挑战。
