Heart valve fluid–structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method that can address the challenges with an outcome of high-fidelity flow solutions. The SCFSI analysis enables dealing with the fluid and structure parts individually at different steps of the solutions sequence, and also enables using different methods or different mesh resolution levels at different steps. In the isogeometric SCFSI analysis here, the first step is a previously computed (fully) coupled Immersogeometric Analysis FSI of the heart valve with a reasonable flow solution. With the valve leaflet and arterial surface motion coming from that, we perform a new, higher-fidelity fluid mechanics computation with the space–time topology change method and isogeometric discretization. Both the immersogeometric and space–time methods are variational multiscale methods. The computation presented for a bioprosthetic heart valve demonstrates the power of the method introduced.

中文翻译：

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心脏瓣膜等几何顺序耦合 FSI 分析与时空拓扑变化方法

心脏瓣膜流固耦合 (FSI) 分析是心血管流体力学中具有计算挑战性的案例之一。挑战包括通过复杂几何形状的不稳定流动、大运动的固体表面以及瓣叶之间的接触。我们在此介绍了一种等几何顺序耦合 FSI (SCFSI) 方法，该方法可以通过高保真流解决方案的结果来应对挑战。SCFSI 分析可以在求解序列的不同步骤中单独处理流体和结构部分，并且还可以在不同步骤中使用不同的方法或不同的网格分辨率级别。在此处的等几何 SCFSI 分析中，第一步是先前计算的（完全）耦合的具有合理流量解决方案的心脏瓣膜的浸入几何分析 FSI。随着瓣叶和动脉表面运动来自于此，我们使用时空拓扑变化方法和等几何离散化来执行新的、更高保真度的流体力学计算。浸没几何方法和时空方法都是变分多尺度方法。为生物人工心脏瓣膜提供的计算证明了所引入方法的能力。