Kolahdouz E M, Bhalla A P S, Scotten L N, Craven B A, Griffith B E
Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, United States Food and Drug Administration, Silver Spring, MD, USA.
Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA.
J Comput Phys. 2021 Oct 15;443. doi: 10.1016/j.jcp.2021.110442. Epub 2021 May 18.
This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but the computational tests indicate that the methodology introduced here remains stable for selected test cases across a range of solid-fluid density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.
本文介绍了一种尖锐界面方法，用于模拟涉及浸没在粘性不可压缩流体中的刚体的流固相互作用（FSI）。该方法的能力通过一系列测试案例进行了基准测试，并通过生物医学FSI的大规模模型进行了演示。本文开发的数值方法，我们称之为浸入式拉格朗日-欧拉（ILE）方法，通过为流体和固体子域求解单独的动量方程，整合了分区和浸入式FSI公式的各个方面，就像在分区公式中一样，同时也使用了动态流体和结构区域的非协调离散化，就像在浸入式公式中一样。使用了一种简单的狄利克雷-诺伊曼耦合方案，其中浸入固体的运动由沿流固界面评估的流体牵引力驱动，流体沿该界面的运动被约束为与固体速度匹配，从而满足无滑移条件。为了开发一种实用的数值方法，我们采用了一种惩罚方法，该方法近似地在流固界面上施加无滑移条件。在耦合策略中，流固界面的单独离散化通过类似刚性弹簧的惩罚力与体积固体网格相连。我们的流固耦合方案依赖于用于离散几何形状的浸入界面方法（IIM），这使得能够精确确定复杂内部界面上的速度和应力。FSI的数值方法可能会受到与附加质量效应相关的不稳定性的影响，但计算测试表明，这里介绍的方法在一系列固液密度比的选定测试案例中保持稳定，包括极小、几乎相等、相等和大密度比。生物医学FSI演示案例包括使用该方法模拟脉冲复制器中双叶机械心脏瓣膜的动力学，以及在患者平均下腔静脉解剖模型中模拟血栓运输所获得的结果。
