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.
翻译:血液流动、大坝或船舶建造以及生物医学和一般工程中的其他许多问题涉及与弹性结构相互作用的不压缩流动,这种相互作用严重影响到畸形和压力状态,进而影响工程设计过程。因此,任何可靠的物理过程模型都必须考虑流体和固体的混合。然而,非纽顿流体模型的复杂性增加,如用于血液或聚合物流动等,在这些流体中,当地剪裁率的细微差异可能会对流体产生巨大影响,从而对同时存在的问题产生巨大影响。在那里,基于牛顿流体分步或投影计划的现有(半隐含)隐含的解决方案战略并不适用,而非纽顿流体液体的扩展可导致大量数字的间接费用,取决于所选的流体溶液溶剂。为了解决这些缺陷,我们在此提出了一个更高级的准确、添加质表质的流体结构互动计划,以分步的液体溶液溶剂溶液溶液溶液溶液溶液溶液溶液溶液解剂为中心。我们比较了几种隐含和半隐含的变体,并核查空间和时时时时时空流的趋趋一致。从一个理想的模型基准显示一个良好的生理基准。