This paper introduces a sharp-interface approach to simulating fluid-structure interaction involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. We use a penalty method involving two representations of the fluid-structure interface. These two representations are connected by approximate Lagrange multiplier forces that impose kinematic interface conditions. This approach also enables the use of multi-rate time stepping, which allows us to take different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method for discrete surfaces to impose stress jump conditions along complex interfaces. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures for cases in which part of the solid boundary does not contact the incompressible fluid. Comparisons are made with computational and experimental benchmarks. We also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a cylindrical blood clot in an inferior vena cava filter.

翻译：本文提出了一种尖锐界面方法，用于模拟涉及柔性体的流固耦合问题，这些柔性体由一般非线性材料模型描述，并涵盖广泛的密度比范围。这种新型柔性体浸没拉格朗日-欧拉（ILE）方法结合了浸没边界（IB）方法在几何与区域求解上的灵活性，同时具备与贴体方法相当的精度，能够清晰地解析流体-固体界面的流动与应力分布。与许多IB方法不同，ILE公式对流体和固体子区域采用独立的动量方程，并通过狄利克雷-诺伊曼耦合策略，利用简单的界面条件连接流体与固体子问题。我们采用一种包含流固界面两种表示的惩罚方法，通过近似拉格朗日乘子力施加运动学界面条件，从而连接这两种表示。该方法还支持多时间步长推进，允许对流体和固体子问题采用不同的时间步长。我们的流体求解器依赖于一种针对离散曲面的浸没界面方法，用以沿复杂界面施加应力跳跃条件。体积结构化网格的动力学行为通过标准有限元方法求解大变形非线性弹性问题，基于近似不可压缩固体力学公式。该公式还兼容可压缩结构，适用于固体边界部分不与不可压缩流体接触的情况。研究结果与计算及实验基准进行了对比验证。我们通过模拟下腔静脉滤器中圆柱形血凝块的传输与捕获过程，进一步展示了该方法的应用能力。