We address the computational challenges of and presents results from ventricle-valve-aorta flow analysis. Including the left ventricle (LV) in the model makes the flow into the valve, and consequently the flow into the aorta, anatomically more realistic. The challenges include accurate representation of the boundary layers near moving solid surfaces even when the valve leaflets come into contact, computation with high geometric complexity, anatomically realistic representation of the LV motion, and flow stability at the inflow boundary, which has a traction condition. The challenges are mainly addressed with a Space–Time (ST) method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method. The three special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The ST-discretization feature of the integrated method, ST-SI-TC-IGA, provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow in the LV, valve and aorta. The moving-mesh feature of the ST framework enables high-resolution computation near the leaflets. The ST-TC enables moving-mesh computation even with the TC created by the contact between the leaflets, dealing with the contact while maintaining high-resolution representation near the leaflets. The ST-IGA provides smoother representation of the LV, valve and aorta surfaces and increased accuracy in the flow solution. The ST-SI connects the separately generated LV, valve and aorta NURBS meshes, enabling easier mesh generation, connects the mesh zones containing the leaflets, enabling a more effective mesh moving, helps the ST-TC deal with leaflet–leaflet contact location change and contact sliding, and helps the ST-TC and ST-IGA keep the element density in the narrow spaces near the contact areas at a reasonable level. The ST-SI-TC-IGA is supplemented with two other special methods in this article. A structural mechanics computation method generates the LV motion from the CT scans of the LV and anatomically realistic values for the LV volume ratio. The Constrained-Flow-Profile (CFP) Traction provides flow stability at the inflow boundary. Test computation with the CFP Traction shows its effectiveness as an inflow stabilization method, and computation with the LV-valve-aorta model shows the effectiveness of the ST-SI-TC-IGA and the two supplemental methods.

中文翻译：

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具有时空等几何离散化和拓扑变化的心室-瓣膜-主动脉血流分析

我们解决了心室-瓣膜-主动脉血流分析的计算挑战并提供了结果。在模型中包括左心室 (LV) 使流入瓣膜并因此流入主动脉的血流在解剖学上更加逼真。挑战包括即使在瓣叶接触时也能准确表示移动固体表面附近的边界层、具有高几何复杂性的计算、LV 运动的解剖学真实表示以及流入边界处的流动稳定性（具有牵引条件）。这些挑战主要通过空间-时间 (ST) 方法解决，该方法在核心周围集成了三种特殊的 ST 方法，即 ST 变分多尺度 (ST-VMS) 方法。三种特殊方法是 ST 滑动界面 (ST-SI) 和 ST 拓扑变化 (ST-TC) 方法和 ST 等几何分析 (ST-IGA)。与标准离散化方法相比，集成方法 ST-SI-TC-IGA 的 ST 离散化功能可提供更高阶的精度。VMS 功能解决了与 LV、瓣膜和主动脉中不稳定流动的多尺度性质相关的计算挑战。ST 框架的移动网格功能可以在传单附近进行高分辨率计算。ST-TC 即使使用由小叶之间的接触创建的 TC 也能进行移动网格计算，在处理接触的同时保持小叶附近的高分辨率表示。ST-IGA 可更平滑地显示 LV、瓣膜和主动脉表面，并提高流量解决方案的准确性。ST-SI 连接单独生成的 LV、瓣膜和主动脉 NURBS 网格，使网格生成更容易，连接包含小叶的网格区域，实现更有效的网格移动，帮助 ST-TC 处理小叶 - 小叶接触位置变化和接触滑动，并帮助 ST-TC 和 ST-IGA 将接触区域附近狭窄空间中的元素密度保持在合理水平。ST-SI-TC-IGA 在本文中补充了另外两种特殊方法。一种结构力学计算方法根据 LV 的 CT 扫描和 LV 容积比的解剖学真实值生成 LV 运动。约束流剖面 (CFP) 牵引提供流入边界处的流动稳定性。使用 CFP Traction 的测试计算表明其作为流入稳定方法的有效性，