In this paper, we propose several improvements to existing fictitious domain/distributed Lagrange multiplier (FD/DLM) type immersed fluid–structure interaction (FSI) methods targeted for FSI analysis of heart valve dynamics. We utilize the variational multiscale (VMS) method to improve accuracy and robustness on under-resolved grids expected with immersed FSI techniques, as well as for the wide range of Reynolds numbers observed over the cardiac cycle. For time discretization, we use a variant of the generalized-α method that achieves second order accuracy for pressure, and present a new predictor–corrector algorithm necessary for the present approach. We focus on immersed nearly-incompressible solids, as most biological soft tissues are modeled this way. We investigate several different forms of dilatational penalty terms and various modeling assumptions that can be made for immersed nearly-incompressible solids to counteract errors that arise from weak satisfaction of the incompressibility constraint and interpolation between the fluid and overlapping solid meshes. Several test problems are considered to evaluate the proposed immersed FSI framework, including an idealized heart valve problem with heterogeneous leaflets as well as an anisotropic model for the valves.

中文翻译：

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一种针对心脏瓣膜应用的浸没式流体-结构相互作用方法


在本文中，我们对现有的虚构域/分布式拉格朗日乘子 （FD/DLM） 型浸没式流体-结构相互作用 （FSI） 方法提出了几项改进，该方法旨在分析心脏瓣膜动力学的 FSI。我们利用变分多尺度 （VMS） 方法来提高浸入式 FSI 技术预期低分辨率网格的准确性和稳健性，以及在心动周期中观察到的广泛雷诺数。对于时间离散化，我们使用了广义α方法的一种变体，该方法实现了压力的二阶精度，并提出了一种当前方法所需的新预测器-校正器算法。我们专注于浸没的几乎不可压缩的固体，因为大多数生物软组织都是以这种方式建模的。我们研究了几种不同形式的膨胀罚项和各种建模假设，这些假设可以用于浸没的几乎不可压缩的固体，以抵消由于不满足不可压缩性约束以及流体和重叠实体网格之间的插值而产生的误差。考虑了几个测试问题来评估所提出的浸没式 FSI 框架，包括具有异质瓣叶的理想化心脏瓣膜问题以及瓣膜的各向异性模型。