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 computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass 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.

本文介绍了一种锐界面方法来模拟涉及浸入粘性不可压缩流体中的刚体的流固耦合 (FSI)。该方法的功能使用一系列测试用例进行基准测试，并使用大型生物医学 FSI 模型进行演示。本文开发的数值方法，我们称为浸入式拉格朗日-欧拉 (ILE) 方法，通过求解流体和固体子域的单独动量方程（如在分区公式中一样），集成了分区和浸入式 FSI 公式的各个方面，同时还使用动态流体和结构区域的不一致离散化，如浸入式配方中。使用简单的狄利克雷-诺伊曼耦合方案，其中浸入固体的运动由沿流体-结构界面评估的流体牵引力驱动，并且流体沿该界面的运动被约束以匹配固体速度，从而满足无滑移条件。为了开发实用的数值方法，我们采用了一种惩罚方法，该方法沿着流体-结构界面近似施加无滑移条件。在耦合策略中，流体-结构界面的单独离散通过刚性弹簧状罚力连接到体积实体网格。我们的流固耦合方案依赖于离散几何形状的浸入界面法 (IIM)，该方法能够准确确定沿复杂内部界面的速度和应力。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，此处介绍的方法对于选定的测试用例在广泛的固体-流体质量密度比范围内保持稳定，包括极小、几乎相等、相等，和大的密度比。生物医学 FSI 演示案例包括使用该方法获得的结果，以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凝块的输送。