Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid dynamics (CFD) often are coupled to reduced circuit and/or solid mechanics models. These allow for realistic simulations of hemodynamics in the heart or the aorta, but come at additional computational cost and complexity. In this contribution, we design a novel block preconditioner for the solution of the stabilized Navier–Stokes equations coupled to reduced-order models of a non-local nature. These models encompass lumped-parameter systems that impose flux-dependent boundary tractions, and Galerkin reduced-order models that can be used to account for outlying mechanical structures. Here we propose a 3 × 3 preconditioner derived from the block factorization and approximation to the Schur complement(s). The solver performance is demonstrated for a series of examples with increasing complexity, culminating in a reduced FSI simulation in a patient-specific contracting left heart model. For all test cases, we show that our proposed approach is superior to other frequently presented 2 × 2 schemes that merge stiffness contributions from reduced models into the fluid Jacobian or consolidate some variables for the purpose of efficiency—with an up to six times shorter overall computing time and/or only half as many linear iterations.

中文翻译：

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与非局部性质的约简模型耦合的流体动力学的有效块预调节器


对心血管血流进行建模是生物医学工程中许多应用的核心。为了适应心血管系统的复杂性，在边界条件和周围血管组织方面，计算流体动力学 （CFD） 通常与简化回路和/或固体力学模型耦合。这些允许对心脏或主动脉中的血流动力学进行真实模拟，但会带来额外的计算成本和复杂性。在这篇文章中，我们设计了一种新的块预条件器，用于求解与非局部性质的降阶模型的稳定 Navier-Stokes 方程。这些模型包括施加磁通量依赖性边界牵引的集总参数系统，以及可用于解释外围机械结构的 Galerkin 降阶模型。在这里，我们提出了一个 3 × 3 预条件器，该预条件器源自区组分解和对 Schur 补码的近似。求解器性能通过一系列复杂性不断增加的示例进行演示，最终在患者特定的收缩左心模型中实现了减少的 FSI 仿真。对于所有测试用例，我们表明我们提出的方法优于其他经常提出的 2 × 2 方案，这些方案将简化模型的刚度贡献合并到流体雅可比矩阵中或合并一些变量以提高效率——总计算时间缩短了六倍和/或线性迭代次数只有一半。