不可压缩广义牛顿流场的流固耦合问题的高效分裂步长格式
Efficient split-step schemes for fluid-structure interaction involving incompressible generalised Newtonian flows
摘要：
血液流动、水坝或船舶建造以及生物医学和一般工程中的许多其他问题涉及与弹性结构相互作用的不可压缩流。这种相互作用严重影响变形和应力状态，进而影响工程设计过程。因此，这种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，对于所使用的非牛顿流体模型，例如，用于血液或聚合物流动。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，从而对耦合问题产生巨大影响。在那里，现有的（半）隐式求解策略的基础上分裂步骤或投影计划牛顿流体是不适用的，而扩展到非牛顿流体可能会导致大量的数值开销取决于所选择的流体求解器。为了解决这些缺点，我们在这里提出了一个高阶精度，附加质量稳定的流体-结构相互作用的计划围绕分裂步骤流体求解器。我们比较了几个隐式和半隐式的算法的变种，并验证收敛的空间和时间。数值例子显示良好的性能，在基准和理想化的设置通过腹主动脉瘤的血流考虑生理参数。
英文摘要：
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 engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-)implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. 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 an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters.
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