Arterial blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the design. Consequently, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluids, such as blood or polymer melts. In these fluids, subtle differences in the local shear-rate can have a drastic impact on the flow. Existing numerical solution strategies devised for Newtonian fluids are either not applicable or ineffective in such scenarios. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid-structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and a realistic setting of blood flow through an abdominal aortic aneurysm.

中文翻译：

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一种有效的分步方案，用于涉及不可压缩粘性流的流固耦合

动脉血流、大坝或船舶建造以及生物医学和通用工程中的许多其他问题都涉及与弹性结构相互作用的不可压缩流动。这种相互作用会严重影响变形和应力状态，进而影响设计。因此，此类物理过程的任何可靠模型都必须考虑流体和固体的耦合。然而，非牛顿流体的复杂性会增加，例如血液或聚合物熔体。在这些流体中，局部剪切速率的细微差异会对流动产生巨大影响。为牛顿流体设计的现有数值求解策略在这种情况下要么不适用，要么无效。为了解决这些缺点，我们在这里提出了一个高阶的准确，以分步流体求解器为中心的附加质量稳定流固耦合方案。我们比较了算法的几种隐式和半隐式变体，并验证了空间和时间的收敛性。数值示例在基准测试和通过腹主动脉瘤的血流的真实设置中均显示出良好的性能。